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Order Number 8717718
On-line, adaptive, optimal control of a high-density, fed-batch fermentation of streptomyces C5
Schlasner, Steven Mark, Ph.D.
The Ohio State University, 1987
UMI 300N.ZeebRd. Ann Arbor, MI 48106
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ON-LINE, ADAPTIVE, OPTIMAL œNTROL OF A HIGH-DENSITY, FED-BATCH
FERMENTATION OF STREPTOMYCES C5
DISSERTATION
Presented In Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Steven Mark Schlasner, B.A., B.S., M.B.A., M.S.
*****
The Ohio State University
1987
Dissertation Committee: Approved by
W-K Lee — Q o_ D.R. Skidmore Adviser W.R. Strohl Department of Chemical Engineering Copyright by Steven Mark Schlasner 1987 To My Wife,
Betsy
11 ACKNOWLEDGEMENTS
I express heartfelt appreciation to Drs. Won-Kyoo Lee and William R.
Strohl for their guidance and insight throughout the research. Thanks, too, to Dr. Duane R. Skidmore, the remaining member of my dissertation committee, for his suggestions and comments. Gratitude is expressed to Donald E. Ordaz for his invaluable assistance during the experimental portion of the research. Appreciation is also expressed to Michael L. Dekleva and Michael
B. Kukla for their technical assistance. To my wife, Betsy, daughter,
Jacqueline, and other members of my family, I offer thanks for their patience, support and encouragement.
iii VITA
May 23, 1952 ...... B o m - Glendive, Montana
1974 ...... B.A., St. Olaf College, Northfield, Minnesota
1974 - 1978...... United States Air Force Officer Ellsworth Air Force Base, South Dakota
1977 ...... M.B.A., University of South Dakota, Vermillion, South Dakota
1980 ...... B.S., South Dakota School of , Mines and Technology, Rapid City, South Dakota
1980 - Present ...... United States Air Force Reserve Officer, United States Air Force Wright Aeronautical Laboratories, Wright-Patterson Air Force Base, Ohio
1983 ...... M.S., The Ohio State University Columbus, Ohio
FIELDS OF STUDY
Major Field: Chemical Engineering Studies in chemical process control with Dr. WonHCyoo Lee.
Minor Field: Microbiology Studies in industrial microbiology with Dr. William R. Strohl.
iv TABLE OF CONTENTS
DEDICATION ...... 11
ACKNOWLEDGEMENTS ...... Ill
VITA ...... Iv
LIST OF TABLES ......
LIST OF F I G U R E S ...... ^
LIST OF S Y M B O L S ......
CHAPTER PAGE
I . INTRODUCTION ......
Introduction ...... The Importance and Evolution of Fermentation Processes ...... Potential Improvements In Fermentation Processes ...... Goal and System Definition ...... Obstacles to Achievement of Desired Goals ...... 9 Objectives ...... 11
II. LITERATURE REVIEW ...... 15
Introduction ...... 15 High (Cell) Density Fermentation ...... 15 Bloreactor Configuration ...... 19 B a t c h ...... 19 Continuous ...... 20 Semi-batch ...... 22 Plug-flow ...... 25 Microorganisms ...... 25 Y e a s t ...... 26 Escherichia coll ...... 27 Penicllium spp...... 27 Bacillus subtilis ...... 28 Bacillus thuringiensis ...... 28 Streptomyces spp...... 28 Optimal Control Methods ...... 29 Static optimization ...... 29 Dynamic optimization ...... 30 State and Parameter Estimation...... 43 Indirect measurement ...... 44 Filtering...... 44 Estimation ...... 45 Measurement error detection ...... 69
III. EXPERIMENTAL APPARATUS ...... 70
Fermentor ...... 70 Vessel ...... 70 Agitation...... 71 Gas flow ...... 71 Temperature control ...... 72 Microcomputer ...... 72 Microcomputer hardware ...... 73 Microcomputer software ...... 74 Peripherals ...... 77 Sensors and Actuators ...... 82 Oxygen off-gas analysis ...... 83 Carbon dioxide off-gas analysis ...... 84 Fermentor pressure measurement ...... 84 Gas flow rate measurement...... 85 pH measurement ...... 86 Dissolved oxygen measurement ...... 87 Dissolved carbon dioxide measurement ...... 87 Foam control ...... 89 Glucose analyzer ...... 90 Turbidity measurement ...... 93 Glucose feed rate measurement...... 94 Temperature measurement ...... 94 Agitation r a t e ...... 95 Stepping motor actuators ...... 96 Gas flow controllers ...... 97 Relay box ...... 99 Auxiliary devices ...... 101 Air conditioning subsystem ...... 102 Miscellaneous components ...... 103 Continuous culture apparatus ...... 104
vi IV. ORGANISM, MATERIALS, AND METHODS ...... 107
Microorganism ...... 108 Cuture Maintenance ...... 109 Media ...... 110 Fermentation Preparation and Performance ...... Ill Shake-flask culture ...... 112 Continuous culture ...... 112 Batch and fed-batch fermentations ...... 114 Off-Line Analyses and Assays ...... 117 Dry weight ...... 117 Optical density ...... 117 Protein assay ...... 118 Elemental biomass analyses ...... 118 Glucose analysis ...... 119 Nitrate analysis ...... 119 Phosphate analysis ...... 120 Organic acid a n a l y s i s ...... 121 Anthracycline analysis ...... 121 Ammmonia analysis ...... 121
V. ESTIMATOR AND CONTROL SCHEME DEVELOPMENT ...... 123
Estimator Development ...... 124 Optimal controller Development ...... 133
VI. SOFTWARE DEVELOPMENT ...... 142
Simulation Software ...... 142 Software utilized ...... 142 Program descriptions ...... 143 Software design ...... 145 Obstacles ...... 1^7 On-Line experimentation ...... 150 Software utilized ...... 150 Program flow ...... 151 Software design ...... 153 O b s t a c l e s ...... 157 Data Analysis and Display ...... 158 Software utilized ...... 159 Software design ...... 159 O b s t a c l e s ...... 159
VII. PRELIMINARY EXPERIMENTATION ...... 162
Phase One ...... 163 Phase Two ...... 166 Phase Three ...... 172 Related Research ...... 174 Ammonia nitrogen source ...... 174
vii other carbon sources ...... 175 Growth under oxygen limitation ...... 176 Summary of Preliminary Experimentation ...... 177
VIII. SIMULATION RESULTS AND DISCUSSION ...... 179
Simulation Study Strategy ...... 180 Process simulator ...... 181 Specific factors studied ...... 182 Bench-mark Simulation ...... 183 Performance Improvement through Additional State Variables ...... 187 Effects of Changes In the R Matrix and of Measurement Noise Level ...... 189 Effects of Changes In the P Matrix and of Eror In Initial Estimates ...... 191 Effect of Cube Root Growth L a w ...... 192 Effect of e-RhodomycInone Production ...... 193 Effect of Double Substrate Limitation, Glucose and O x y g e n ...... 193 Effects of Changes In the Q Matrix and of Measurement Noise Level ...... 194 Estimator Performance with a Constraint on Specific Growth R a t e ...... 195 Combined Estimator and Optimal Controller Performance ...... 196 Summary of R e s u l t s ...... 196
IX. EXPERIMENTAL RESULTS AND DISCUSSION...... 200
Fermentation O n e ...... 200 Fermentation T w o ...... 202 Fermentation Three ...... 208 Summary of On-Line Experimentation ...... 217
X. CONCLUSIONS...... 219
APPENDICES
A. HARDWARE SCHEMATICS...... 224
B. COMPUTER PROGRAM LISTINGS ...... 228
C. SIMULATION RESULTS ...... 304
D. ON-LINE EXPERIMENTATION RESULTS ...... 344
LIST OF REFERENCES ...... 368
vlll LIST OF TABLES
TABLE PAGE
1. Instrument Characteristics ...... 106
2. Expressions for the Series of Each Element of the State Transition Matirx (STM) ...... 160
ix LIST OF FIGURES
FIGURES PAGE
1. Experimental Apparatus ...... 225
2. Interrupt Generator ...... 226
3. Temperature Sensor ...... 226
4. Agitation Tachometer ...... 227
5. Standard Simulation Actual and Estimates Biomass Concentration ...... 303
6. Standard Simulation Actual and Estimated Substrate Concentration ...... 305
7. Standard Simulation Actual and Estimated Dissolved Oxygen Concentration ...... 306
8. Standard Simulation Actual and Estimated Specific Growth Rate ...... 306
9. Standard Simulation Actual and Estimated Overall Substrate Y i e l d ...... 307
10. Standard Simulation Actual and Estimated Oxygen Mass Transfer Coefficient ...... 307
11. Standard Simulation Actual and Estimated Overall Oxygen Y i e l d ...... 308
12. Standard Simulation Actual and Estimated Saturated Dissolved Oxygen Concentration ...... 308
13. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator Without Additional Dynamics ...... 309 14. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator Without Additional Dynamics ...... 309
15. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics While Applying the Estimator Without Additional Dynamics ...... 310
16. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics While Applying the Estimator Without Additional Dynamics ...... 310
17. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics While Applying the Standard E s t i m a t o r ...... 311
18. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics While Applying the Standard Estimator...... 311
19. Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating a Rapid Decrease in k^a While Applying the Estimator Without Additional Dynamics ...... 312
20. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating a Rapid Decrease in k^a While Applying the Estimator Without AdditionalDynamics ...... 312
21. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating a Rapid Decrease in kj^a While Applying the Estimator Without Additional Dynamics ...... 313
22. Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating a Rapid Decrease in kj^a While Applying the Standard Estimator ...... 313
23. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating a Rapid Decrease in k^a While Applying the Standard Estimator ...... 314
24. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating a Rapid Decrease in kj^a While Applying the Standard Estimator ...... 314
xi 25. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix...... 315
26. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix ...... 315
27. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix...... 316
28. Actual and Estimated Substrate Yield for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix ...... 316
29. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix ...... 317
30. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Oxygen Yield-Related Term of the R Matrix...... 317
31. Actual and Estimated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Oxygen Yield-Related Term of the R Matrix...... 318
32. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Oxygen Yield-Related Term of the R Matrix...... 318
33. Actual and Estimated Oxygen Yield for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Oxygen Yield-Related Termof the R Matrix...... 319
34. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a 0.1 Decrease in the Oxygen Yield-Related Term of the R Matrix...... 319
xii 35. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Substrate Concentration-Related Term of the R Matrix...... 320
36. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 320
37. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 321
38. Actual and Estimated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 321
39. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 322
40. Actual and Estimated Substrate Yield for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 322
41. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 323
42. Actual and Estimated Oxygen Yield for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 323
43. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix...... 324
44. Actual and Estimated Biomass Concentration for a Process Simulating a 3x Increase in Measurement Noise While Applying the Standard Estimator...... 324
45. Actual and Estimated Substrate Concentration for a Process Simulating a 3x Increase in Measurement Noise While Applying the Standard Estimator...... 325
xiii 46. Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator ...... 325
47. Actual and Estimated Specific Growth Rate for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator ...... 326
48. Actual and Estimated Substrate Yield for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator ...... 326
49. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator ...... 327
50. Actual and Estimated Oxygen Yield for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator ...... 327
51. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator . . 328
52. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Standard Estimator with a lOx Greater Error In the Initial Biomass Concentration Estimate...... 328
53. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Standard Estimator with a No Error In the Initial State Estimate ...... 329
54. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Standard Estimator with a lOx Increased Error In the Initial State Estimate ...... 329
55. Actual and Estimated Biomass Concentration for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator ...... 330
56. Actual and Estimated Specific Growth Rate for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator ...... 330
57. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator ...... 331
xlv 58. Actual and Estimated Oxygen Yield for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator...... 331
59. Actual and Estimated Substrate Yield for a Process Simulating Error in Biomass Composition While Applying the Standard Estimator ...... 332
60. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating Error in Biomass Composition While Applying the Standard Estimator ...... 332
61. Actual and Estimated Oxygen Yield for a Process Simulating Error in Biomass Composition While Applying the Standard Estimator...... 333
62. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics ...... 333
63. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics ...... 334
64. Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics ...... 334
65. Actual and Estimated Specific Growth Rate for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics ...... 335
66. Actual and Estimated Substrate Yield for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics ...... 335
XV 67. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics ...... 336
68. Actual and Estimated Oxygen Yield for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics...... 336
69. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator ...... 337
70. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator ...... 337
71. Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator ...... 338
72. Actual and Estimated Specific Growth Rate for a Process Simulating Contois Kinetics, a Rapid Decrease in kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator ...... 338
73. Actual and Estimated Substrate Yield for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator ...... 339
74. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator ...... 339
75. Actual and Estimated Oxygen Yield for a Process Simulating Contois Kinetics, a Rapid Decrease in kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator ...... 340
xvi 76. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator . . 340
77. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator having a Constraint of 0.1 h~^ as the Maximum Estimated Specific Growth R a t e ...... 341
78. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator having a Constraint of 0.1 h as the Maximum Estimated Specific Growth R a t e ...... 341
79. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Estimator Without Additional Dynamics ...... 342
80. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics and a Rapid Decrease in kj^a While Applying the Estimator Without Additional Dynamics...... 342
81. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Standard Estimator ...... 343
82. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics and a Rapid Decrease in kj^a While Applying the Standard Estimator ...... 343
83. Fermentation Two Actual and Estimated Biomass Concentration...... 345
84. Fermentation Two Actual and Estimated Substrate Concentration...... 345
85. Fermentation Two Actual and Estimated Dissolved Oxygen Concentration ...... 346
86. Fermentation Two Actual and Estimated Specific Growth R a t e ...... 346
87. Fermentation Two Estimated Overall Substrate Yield ...... 347
xvii 88. Fermentation Two Estimated Oxygen Mass Transfer Coefficient...... 347
89. Fermentation Estimated Overall Oxygen Yield ...... 348
90. Fermentation Two Estimated Saturated DissolvedOxygen Concentration ...... 348
91. Fermentation Two Feed Flow Rate ...... 349
92. Fermentation Two Estimated Substrate Maintenance Energy Requirements ...... 349
93. Fermentation Two Estimated Oxygen Maintenance Energy Requirements ...... 350
94. Fermentation Two Carbon Dioxide Evolution Rate...... 350
95. Actual and Estimated Biomass Concentration of Substrate-Corrected Simulation of Fermentation Two ...... 351
96. Actual and Estimated Substrate Concentration of Substrate-Corrected Simulation of Fermentation Two ...... 351
97. Actual and Estimated Dissolved Oxygen Concentration of Substrate-Corrected Simulation of Fermentation Two ...... 352
98. Actual and Estimated Specific Growth Rate of Substrate-Corrected Simulation of Fermentation Two ...... 352
99. Estimated Substrate Yield of Substrate-Corrected Simulation of Fermentation Two...... 353
100. Estimated Oxygen Mass Transfer Coefficient of Substrate-Corrected Simulation of Fermentation Two ...... 353
101. Estimated Oxygen Yield Substrate-Corrected Simulation of Fermentation Two...... 354
102. Estimated Saturated Dissolved Oxygen Concentration of Substrate-Corrected Simulation of Fermentation Two . . . 354
103. Estimated Substrate Maintenance Energy Requirements of Substrate-Corrected Simulation of Fermentation Two ...... 355
104. Estimated Oxygen Maintenance Energy Requirements of Substrate-Corrected Simulation of Fermentation Two ...... 355
xviii 105. Fermentation Three Actual and Estimated Biomass Concentration ...... 356
106. Fermentation Three Actual and Estimated Substrate Concentration ...... 356
107. Fermentation Three Actual and Estimated Dissolved Oxygen Concentration ...... 357
108. Fermentation Three Actual and Estimated Specific Growth R a t e ...... 357
109. Fermentation Three Estimated Overall Substrate Yield .... 358
110. Fermentation Three Estimated Oxygen Mass Transfer Coefficient...... 358
111. Fermentation Three Estimated Overall Oxygen Yield ...... 359
112. Fermentation Three Estimated Saturated Dissolved Oxygen Concentration ...... 359
113. Fermentation Three Feed Flow Ra t e ...... 360
114. Fermentation Three Estimated Substrate Maintenance Energy Requirements ...... 360
115. Fermentation Three Estimated Oxygen Maintenance Energy Requirements ...... 361
116. Fermentation Three Carbon Dioxide Evolution Rate ...... 361
117. Actual and Estimated Biomass Concentration of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three ...... 362
118. Actual and Estimated Substrate Concentration of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three ...... 362
119. Actual and Estimated Dissolved Oxygen Concentration of Substrate and Initial Biomass Corrected Simulation of Fermentation Three ...... 363
120. Actual and Estimated Specific Growth Rate of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three ...... 363
xix 121. Estimated Substrate Yield of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three .... 364
122. Estimated Oxygen Mass Transfer Coefficient of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three ...... 364
123. Estimated Oxygen Yield Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three .... 365
124. Estimated Saturated Dissolved Oxygen Concentration of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three ...... 365
125. Estimated Substrate Maintenance Energy Requirements of Substrate Initial Biomass Estimate Corrected Simulation of Fermentation Three ...... 366
126. Estimated Oxygen Maintenance Energy Requirements of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three ...... 366
127. Actual and Estimated Specific Growth Rate of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three in Which the Estimator was Without Additional Dynamics ...... 367
XX LIST OF SYMBOLS
a gluocose stoichiometric coefficient or Henry's law constant b oxygen stoichiometric coefficient c nitrate stoichiometric coefficient D dilution rate (F/V) d water stoichiometric coefficient e carbon dioixde stoichiometric coefficient F feed flow rate or linearized state function f hydroxide stoichiometric coefficient or non-linear state function g a function that is a component of the objective function or stoichiometric coefficient for a product H Hamiltonian h nonlinear measurement function or integrated function of objective function i index J objective function j index Kg Contois kinetic constant (g, Kq substrate and oxygen saturation constants k discrete time index kra mass transfer coefficient Kp specific product formation rate kg specific substrate consumption rate k^ specific growth rate 1 eigenvalue M linearized measurement function m maintenance energy requirements N order of system of equations n index o dissolved oxgen concentration o* dissolved oxygen concentration of air-saturated water P error covariance matrix or product concentration p costate vector Q process noise covariance matrix q economic factor or relative cost between substrate and biomass R measurement noise covariance matrix r ratio of two elements of matrix
xxi S total substrate s substrate concentration ®feed» H substrate .concentraion in feed t time u control variable V volume V measurement noise vecto w process noise vector X total biomas X biomass concentration or state vector Y, Y' true and overall yields y measurement vector z transformed state vector
S variation $ state transition matrix
[Û. unit Heaviside step function subscripts f final or feed o oxygen s substrate z in transformed space 0 initial (time = 0) superscripts max maximum feasible value s derivative with respect to substrate concentration T transpose * nominal value or value along optimal trajectory - projected value ^ estimated value
xxii CHAPTER I
INTRODUCTION
Introduction
This chapter describes the significance of and problems associated with the application of an optimal controller to a high cell density
fermentation of Streptomyces 05. Discussion will proceed from a discourse
on the general importance of and problems related to fermentation to those
aspects peculiar to this research. This will be accomplished by focusing
upon: (i) the history and importance of fermentation processes; (ii) the
improvements that may be made to such processes; (iii) the difficulties
encountered in realizing those improvements, and; (iv) the specific
objectives of this research.
The Importance and Evolution of Fermentation Processes
Man has employed fermentation processes since prehistoric times.
Commercial exploitation of such processes extends back more than 8000 years
to beer production by the Sumerians and Babylonians (Demain and Solomon,
1981). Despite its antiquity, significant improvements in the range and
quality of fermentation products have appeared only within the last hundred
years as a result of increased study and improved understanding of these
processes (Hoogerheide, 1977). These advances may be characterized as
having occurred in four stages.
1 2
The first stage began before recorded history and concluded In the mid-nineteenth century with the appearance of work by Louis Pasteur. During that period, development of fermentation processes was solely empirical and the products of commercial fermentations were limited almost exclusively to food and beverages which Included: alcohol and bread by yeast; vinegar and preserved milk by bacteria; and cheese by bacteria and molds (Demain and
Solomon, 1981).
The second stage, which extended from Pasteur's studies to those of
Florey with penicillin In the 1940's, was characterized by a substantial
Improvement In the approaches applied to the study of fermentation and, consequently. In the understanding of such processes: the practice of fermentation was transformed from an art to a science. Although the second phase significantly changed the approach to fermentation, the types of products changed little. The few, commercially significant new products
Included only such materials as glycerol, acetone, a few, simple alcohols and acids, a handful of enzymes and baker's yeast. Of these, the acetone-butanol fermentation was of special significance because It was the first Industrial, pure culture fermentation; meaning It was the first large-scale fermentation that had to address the problem of contamination by other microorganisms and bacteriophages (Demain and Solomon, 1981).
The third stage began with Florey and concluded In the 1970's with the development of molecular biology. Unlike the previous phase that was characterized by Improvements In techniques and understanding, the third stage applied that understanding to the Introduction of a variety of new, commercially Important products: complex acids; antibiotics ; vitamins; 3 numerous enzymes ; transformed steroids; polysaccharides; microbial insecticides; and single cell protein (Perlman, 1977).
In contrast to the preceding phases which were distinguished by remarkable increases in either understanding or new commercial products, the fourth phase is characterized by both. The factor that differentiates the fourth phase from the third is the increased facility to manipulate genetic material made possible through advances in molecular biology. This development has resulted in a period of impressive expansion both in terms of process knowledge and the range of products that can be produced by fermentation.
Today, the products of fermentation processes are many and varied; appearing in numerous markets. For this reason it is difficult to estimate the value of the world's or even this nation's annual fermentation production. As a vehicle to providing some perspective of the size of this market, however, it is noted that the 1984 United States' production of five major fermentation products, ethanol, organic acids, industrial enzymes, amino acids and bulk antibiotics were $672M, $256M, $96M, $160M and $2.02B, respectively (Predicasts Forecasts, 1985). These compare to $2.OB for chlorine, the nineth largest volume chemical in 1984, $4.18B for polyester, the highest volume fiber in 1984, and $3.4B for low-density polyethylene, the highest volume plastic in 1984 (Chemical & Engineering News, 1985).
Even larger than the "non-food," fermentation-product sales, however, have been the annual market values of fermented foods and alcoholic beverages which were $3.5B in 1981 and $27B in 1982, respectively (Knorr and Sinskey,
1985). While these data demonstrate that fermentation processes are 4 commercially important today; it appears that they will become even more important in the future.
Microorganisms possess many characteristics that make them desirable as process components : their specificity, low energy requirements, ability to perform complex transformations, environmental acceptability, and flexibility make them candidates for specialty chemical, therapeutic agent and protein production, pollution control, and a variety of other uses, including some bulk chemical production (Perlman, 1977; Burte et al.,
1986). Projected growth for the five previously mentioned fermentation products, ethanol, organic acids, industrial enzymes, amino acids and bulk antibiotics, are expected to be about 14.5 percent per year over the period
1984 to 1987 (Predicasts Forecasts, 1985). This compares quite favorably to chemical production which grew at an 11.4 percent rate during 1984, the largest annual rate over the past 6 years, 1979-1985 (Chemical & Engineering
News, 1986a). The recent activity of biotechnology stocks and the performance of biotechnological firms further attests to the potential of these processes when linked to genetically engineered organisms, as biotechnology stocks significantly out performed the Standard & Poor's 400 index during the fourth quarter of 1985 by posting a 64 percent rise (versus
15 percent for the S&P 400) (Webber, 1986a), and as biotechnology companies recorded a 28.2 percent increase in total revenues in 1985 (Webber, 1986b).
Such evidence leaves little doubt tbat, in the future, fermentation processes will attain even greater prominence among commercial, chemical processes. 5
Potential Improvements in Fermentation Processes
In considering potential Improvements that may be Incorporated Into fermentation processes, It Is convenient to resolve fermentation systems
Into their two major subsystems: the biological subsystem; and the support subsystem. Although Improvements made to either subsystem depend upon the available knowledge about that subsystem, Improvement of the support subsystem Is also dependent upon knowledge of the biological subsystem.
Unfortunately, much less Is presently known about the mechanisms driving the biological subsystem than Is known about those driving the support subsystem due to the greater complexity of the biological subsystem and the fact that only recently have techniques been developed that permit detailed
Investigation of the genetic and physiological mechanisms underlying the behavior of the biological subsystem. Therefore, a greater potential
Improvement In process performance Is expected for an Increased understanding of the biological subsystem than for developing the support subsystem. This has been confirmed by a report by Bristol Laboratories
(Alba et al., 1973) In which Inoculum, medium and aeration Improvements accounted for approximately 62 percent of a nearly tenfold Increase In productivity of an antibiotic, while 38 percent was attributed to
"engineering" Improvements. Unfortunately, the existence of the greater potential of biological subsystem Improvement has resulted In disproportionate attention being given to biological subsystem development.
Clark et al. (1982) described a situation of this sort In comparing the amount of consideration that has been Imparted to microorganisms versus that extended to process control when they wrote: Whilst increasing use is being made of microorganmisms in a wide variety of industrial processes, operation of these has hitherto required surprisingly little understanding of the process dynamics. Instead, success has been based on careful attention to the empirical needs of the organism. The complexities of microbial processes are subject to a high degree of intrinsic control, which is often sufficient for acceptable productivity in the exploitation of a near-natural process. However, progressive interest in the exploitation of minority or unnatural processes, as well as commercial considerations, have demanded more manipulative skills of the industry. Understandably, the extensive accumulation of knowledge concerning the nature of the metabolic pathways involved has given rise to the ability to select, and more recently to engineer, the genotype for productivity in existing and new processes. On the other hand, lack of understanding of the dynamics of a microbial process largely precludes its effective control by physiological or genetic means and, once proven, the process is for the most part, left to its own devices.
Considering, then, the lesser recognized, yet, significant opportunity for process improvement through support subsystem development, there are many aspects of the support subsystem that may be considered to improve fermentation process performance. From a perspective of transport phenomena (energy, mass and momentum transport), improvements in mixing, heat exchange, and interfacial mass transport, among others, could be effected by improvements in bioreactor design. Likewise, study of microbial kinetics in conjunction with transport properties would recommend improved feeding policies resulting in growth patterns that maximize production rates and yields. Improved measurement devices, on-line, off-line or indirect, or improved state and parameter estimation schemes would provide more information about the condition of the organism and the state of the bioreactor which would promote insights into the behavior of the system and contribute to improved process control. Application of advanced, on-line control techniques executed in real-time on more powerful computers would provide more efficient resource utilization. For fermentation processes 7 that require product post-processing, improved unit operations, modified growth patterns, or cell immobilization may assist in providing more efficient post-processing. Even a factor as seemingly insignificant as foam control can be of considerable consequence in many circumstances, and, thus, benefit from study and improvements in technique. Ultimately, for commercial processes, such improvements must generate savings in capital costs and operating expenses that exceed the expense of their development and implementation. For bulk chemical processes savings of only a few hundredths of one cent of expense per pound of product may justify technical development ; for the smaller volume of fermentation processes such savings must be more substantial. This implies that not all efforts to improve the support subsystem may be economically justified, and that the choice of where to invest such effort must be made judiciously.
One area of research that appears to be economically justified is in improved process control. The major expense in commercial fermentation is raw material expense, specifically, carbon substrate (Dale and Linden,
1984). Implementation of advanced control techniques by computers has the potential to significantly reduce this expense by promoting more efficient utilization of present substrates, and, theoretically, by permitting use of cheaper, less refined feed materials. It is these important advantages that justify application of advanced control techniques to fermentation processes. This research addresses that topic in detail.
Goal and System Definition
Traditional techniques of growing microorganisms in submerged culture have relied upon application of pre-established, empirically-determined 8 paths to reproduce previously successful fermentations. Inadequate instrumentation and such open-loop control schemes have provided little ability for such systems to adapt to process changes. The first goal of this research is to address the limitations of traditional techniques by development of an optimal control scheme that can adapt on-line to fermentation process changes.
Traditional fermentation techniques also are not concerned with maximizing biomass through application of optimal, fed-batch feeding policies. While, admittedly, maximization of biomass is not universally desired, there are many situations in which it is sought. Commercial fermentations, for example, frequently seek to obtain the benefits of improved efficiencies conferred by such feeding policies. The second goal of this research, then, is to obtain high cell density through development of an optimal fed-batch operation.
Given these goals and the resources available to this research, the experimental system can now be defined. The two aspects of the system that require characterization are the the biological and support subsystems, that is, the microorganism and experimental apparatus.
Essentially three criteria were applied to the selection of the microorganism to be used in this research. These included: possession of characteristics prevalent in cultures grown commercially; lack of publications of similar or related control research with the microbe; and existence of available information and expertise about the organism. Of the microorganisms considered, Streptomyces C5 appeared to best satisfy these criteria. 9
Fermenter selection was based upon five criteria: operating cost; maintainability; availability; flexibility; and ability to support the necessary instrumentation. Of the five sizes of fermentors available for this research, the 14-liter Microferm fermentors (New Brunswick Company,
Edison, NJ) seemed to be the most suitable.
From these considerations, then, the goal of this research was the optimal control of a high cell density, fed-batch fermentation of
Streptomyces C5.
Obstacles to Achievement of Desired Goals
To achieve the stated goals, this research had to confront three principal obstacles. These included the complexity of the process, inadequate understanding of the process, and equipment limitations.
As is true for most fermentations, growth of Streptomyces C5 in submerged culture is a complex, non-linear, time-varying process. High density fermentations exhibit increased complexity as transport limitations become important. These limitations include mass transport of oxygen or solid substrates possessing limited solubility, momentum transport as the viscosity of the fermentation medium increases, and heat transport as convective transfer dimishes due to poorer mixing as a result of increased viscosity.
Fermentation process control of C5 submerged culture also suffers from a limited understanding of the process, particularly the microorganism.
Although Wang and Stephanopoulos (1984) report that the present understanding of fermentation in general is poor, Hirsch and
McCann-McCormick (1985) describe the present state of knowledge about 10 streptomycetes as being unusually limited, "Despite the body of knowledge that has accumulated over the past 30 or so years on the secondary metabolism of Streptomyces, comparatively little is known about other aspects of their biology. . . . Such a dearth of information may cause some to despair over the state of our understanding of Streptomyces biology."
Knowledge of growth kinetics, lag phase kinetics, morphology, metabolite production and substrate utilization by Streptomyces in general and C5 in particular is imprecise and incomplete. Beyond the microorganism, there are also deficiencies in the present understanding of the behavior of the support subsystem, such as the quantitative effect of medium composition, especially antifoam, upon mass transfer.
Finally, the lack of adequate, on-line sensors and actuators presents additional obstacles to control system development. Although it is the internal state of the organism that determines its growth, there are essentially no sensors capable of measuring these variables on-line.
Instead, the internal state is inferred from measurements of environmental variables, but sensor technology has difficulty in measuring even these variables. In some instances no sensors exist, such as for high-density biomass measurement. In other instances existent sensors are inadequate, being susceptible to interference by medium components, possessing slow response, exhibiting limited ability to withstand sterilization, having a limited automation capability, displaying poor reliability, and exhibiting relatively high noise levels. Likewise, actuators create problems due to drift and the inability to recalibrate automatically on-line. 11
This research will not address all of these problems. However, utilizing the information and resources that are available, a control strategy will be developed to improve system performance over that observed for the traditional, open-loop approach.
Objectives
Five subordinate objectives have to be satisfied prior to attainment of the stated goals of this research. The objectives include: synthesis of an optimal controller; development of a parameters estimation technique; creation of a state estimator; acquisition of fundamental data characteristic of the fermentation; and construction and programming of the experimental apparatus. Prior to discussing these, however, it is necessary to elaborate upon what is meant by the terms "high density" and "optimal" in the statement of the desired goals.
High cell density may be defined from several aspects. In terms of biomass concentration, a fermentation that achieves a greater than ten fold increase in biomass concentration over a culture grown in a shake flask may be considered high-density. The definition may relate to viability, such as a fermentation that produces a ten fold increase in the number of colony-forming units per volume medium over a culture grown in a shake flask. Or, the definition may relate to a mass transfer limitation, such as a fermentation that results in a dissolved oxygen tension of less than 10 percent of air-saturated water when the system has achieved its maximum oxygen mass transfer. Unlike other engineering endeavors that can predict a maximum theoretical yield or output (such as photocell development that can, through the application of thermodynamics, predict a maximum energy 12 conversion efficiency), biological processes are not understood to the extent that accurate, maximal predictions can be made. For example,
Escherichia coli cultures are commonly grown to densities in excess of 100 grams dry biomass per liter. Yet, it would not be erroneous to report a high-density JE. coli culture reaching only 16 grams dry biomass per liter when grown under different conditions (Reiling, et al., 1985). Similarly,
Streptomyces C5 have been grown in the W. R. Strohl lab (The Ohio State
University, Department of Microbiology) in complex media to densities of more than 40 grams per liter (Blackwell, et al., 1987). Yet, in defined media, densities of only one-tenth of that may be acceptable. Therefore, lacking a theoretical basis upon which to define high density, a definition of more than ten times shake flask density will be assumed.
Implied in the statement of the goal is the information that nutrient feed flow rate will be manipulated in some optimal manner to obtain high cell density. There are three perspectives commonly applied in defining the optimum for growth (Parulekar and Lim, 1986). These include: maximum biomass productivity; maximum production rate; and time optimal. The first perspective fixes the duration of the fermentation and performs in such a manner so as to maximize the final biomass. The second leaves the final conditions free so as to maximize the production rate. And, the third fixes the final biomass concentration, minimizing the the time required to achieve the specified state. While it would be realistic to choose the appropriate perspective based upon industrial practice, there appears to be no standard practice. As a result, the time optimal definition has been chosen. 13
Achievement of the established goals require satisfaction of several
supporting objectives. First, since one goal relates to time-optimal growth
in a semibatch bioreactor, development of an optimal controller is required.
Typically, such controllers must incorporate elements that account for biomass production, substrate utilization, product formation, and volume changes (Parulekar and Lim, 1985). High-density fermentations complicate
the development of the controller due to their tendency to reach oxygen
limitation conditions during later stages of fermentation. This condition
requires the addition of a second "substrate" (oxygen) utilization factor to
that of the limiting carbon source utilization factor. Thus, the first objective is to develop a control law that adequately accounts for these
factors.
Second, fermentations characteristically exhibit non-linear, time
varying behavior. Such behavior requires incorporation of a parameter estimation technique that provides the controller with its adaptive
capability.
Third, the optimal controller requires access to measurements of
several state variables, such as biomass concentration. However, reliable devices for measurement of these variables at high density do not exist. To provide an alternative means for acquiring such measurements, state variable
estimation techniques are adopted.
The fourth objective of this research is to obtain kinetic and
thermodynamic data required by the controller. It is not the purpose of
this research to perform experiments to determine fundamental physical
constants (such as Henry's Law constants for various gases in various 14 media), nor to establish the relationship between parameters (such as yields and specific growth rate) and state variables (such as biomass, substrate and product concentrations), nor even to peform medium optimization, since these are not central to the goal of this research and their study would require a considerable effort. Instead, It Is hoped, that careful extrapolation of published Information and access to the experience of other researchers will provide sufficient Information, so that a minimal amount of fundamental experimental work will be required.
The fifth and final objective Is to construct an experimental apparatus capable of acquiring, on-line, required measurements, executing In real-time the requisite control calculations, and performing the necessary actuator functions. Although the Department of Microbiology has, relative to other, similar academic departments. Impressive Instrumentation and equipment, the requirements of performing on-line, adaptive, optimal control will strain the capailltles of the system to the point where new, automated, and more accurate Instruments and computer devices will have to be developed. CHAPTER II
REVIEW OF THE LITERATURE
Introduction
This chapter presents a survey of the literature relevant to the research described in this dissertation. As alluded to in the previous chapter, this research is multifarious; therefore, this chapter will accomplish this survey by resolving the research topic into its essential components, then will briefly discuss the literature relevant to each component. The five principal facets inherent in this research specifically include: high cell density fermentation; the fed-batch bioreactor configuration; the microorganism; optimal control methods; and state and parameter estimation.
High (Cell) Density Fermentation
The goal of the research described herein is to determine a method of growing Streptomyces C5 to produce a high (cell) density culture.
Definition as to what constitutes a high density culture can vary considerably according to the purpose and conditions of the culture. In terms of purpose, if obtaining single cell protein is the objective of the
15 16 fermentation, then final biomass concentration is a reasonable definition.
If, however, the purpose is to produce viable cell mass, then the number of colony forming units on a volume basis of fermentation broth may be more appropriate. Or, from an engineering perspective, high cell density may occur when a mass transfer constraint has been attained. In terms of condition, it should be observed that the maximum feasible cell density is very dependent upon the conditions of the fermentation. That is, for example, cells grown on one substrate may not be capable of reaching the same densities as the same cells grown on another substrate. This is demonstrated by the ability of Mori et al. (1979) to achieve a density of
125 grams/liter of Escherichia coli in a high density fedbatch fermentation using a complex medium, while Reiling et al. (1985) attained only ca. one-eighth that density in growing a high-density, batch culture of E. coli on a minimal medium.
The motivation for this dissertation research is economic; high density cultures more efficiently utilize capital resources, have the potential for producing metabolic products at higher rates and in greater quantities than traditional cultures (assuming product formation and product formation rates are proportional to biomass, the validity of which depends upon the organism and product), and may reduce the effort required during post-processing operations. As desirable and compelling as these advantages may be, the open literature has reported surprisingly few such studies, and even those few have been accomplished principally by only two research teams, one in Israel working in the mid-1970's and, more recently, one in
Japan. 17
The work In Israel at the Hebrew University of Jerusalem was reported
In a series of four papers: Bauer and Shlloach (1974); Slloach and Bauer
(1975); Bauer and Zlv (1976); and Bauer and White (1976). In the first paper, fed-batch runs of Escherichia coll were reported In which pulsed glucose additions were based upon Increases In dissolved oxygen concentration. Maximum reported (dry weight) biomass concentrations In these experiments were 38 gram/liter. In the second paper, growing the same organism at different temperatures with a slmlar glucose feed regiment but with oxygen sparging (Instead of air), a maximum biomass of 55 gram/liter
(dry weight) was reported. The third paper described a study of hlgh-denslty growth of six aerobic bacteria, each of which were grown under an oxygen sparge at two different temperatures In fed-batch. The maximum dry cell concentrations achieved by this research were stated to be: for E. coll W, 68.0 and 34.0 g/1 (at 20°C and 30°C, respectively); for E. coll strain B, 44.8 and 31.2 g/1 (at 25°C and 30°C, respectively); for strain
MRE600, 54.6 and 40.6 (at 25°C and 30°C); for strain K12-3300, 33.2 and 38.2 g/1 (at 30®C and 35°C); for Pseudomonas fluorescens, 31.2 and 20.8 g/1 (at
25°C and 30°C); and for Aerobacter aerogenes, 32.7 and 23.4 g/1 (at 25°C and
30°C, respectively). The final paper, then, reported pilot plant results (a
50 liter vessel) of 47 g/1 (dry weight) of E. coll In a fed-batch, oxygen-sparged fermentation. The work accomplished at The Hebrew University was significant because It demonstrated that hlgh-denslty fermentation was possible. It demonstrated hotf It could be accomplished, it showed, to some extent, that different organisms have significantly different maximum cell conentratlons, and It created benchmarks against which to compare other. 18 similar fermentations.
The Japanese work has been accomplished at Nagoya University by the
Department of Food Science and Technology, and described in a series of four papers (Yano et al., 1979; Mori et al., 1979; Mori et al., 1983; Suzuki et al., 1985). The first three papers report results of oxygen-sparged, fed-batch cultivations employing DO-stats to cultures of Protaminobacter ruber (methanol-assimilating bacterium), Escherichia coli and Candida brassicae, a yeast. These papers reported maximum dry weight cell concentrations for these organisms to be approximately 50 g/1, 125 g/1 and
138 g/1, respectively. The final paper also applied a DO-stat (a device to maintain a constant dissolved oxygen concentration) to a ^ . brassicae high-density culture. However, in this instance, mineral ions were automatically introduced into the medium, which, consequently, produced dry cell mass concentrations of 150 g/1.
Other, more isolated reports of high-density fermentation have been reported in the literature, such as Srinivasan et al. (1977) achieving 29.4 g/1 dry weight in a gradient-feed fermentation of Cellulomonas, Fukuda e^ al. (1978) obtaining 145 g/1 with baker's yeast, Luli et al. (1985) reaching ca. 78 g/1 with coli, and Reiling et al. (1985) achieving 16.5 gram dry biomass/liter with coli B/r grown in a minimal medium. Such reports, however, exhibit little indication of the corporate interest in such fermentations. Interest that filled the conference room to overflowing for a seminar on "High Cell Density Processes for Microbial Cell Production” presented to during the March, 1986 American Society for Microbiology annual meeting, and commercial interest that maintains a veil of secrecy around 19
Phillips Petroleum's 120 gram dry biomass/llter single cell protein process
(Bluestone and Savage, 1986), and Ell Lilly's, among others', hlgh-denslty research.
Bloreactor Configuration
Ignoring multiple reactor configurations and configurations Involving recycle, four fundamental bloreactor configurations are currently recognized: batch; semi-batch; continuous; and plug flow. (Note that, as
Is the custom In fermentation terminology, continuous Is used synonomously with constant stirred tank reactor, even though plug flow Is another class of continuous configuration.) The four configurations differ significantly from the each other In their operation, history, commercial Importance, and characteristic advantages and disadvantages.
Batch. The conventional batch configuration Is the simplest, and, traditionally, has been the most popular bloreactor configuration applied commercially. Operation of this class of bloreactor Involves loading the liquid nutrients Into the fermentor, establishing the desired Initial conditions (temperature, pH, dissolved oxygen and so on). Inoculating the vessel, maintaining desired conditions throughout the run, then harvesting at the end of the fermentation. It Is distinct from the other configurations In that, once Inoculation has occurred no significant, supplementary nutrient addition Is made (although air, antifoam, acid and/or base are commonly Introduced throughout the run).
While conventional batch processing exhibits several desirable advantages. Including simplicity, and the ability to closely regulate reaction conditions. It also suffers from disadvantages that may be 20 exhibited under a variety of circumstances. For example, high nutrient concentrations existent at the beginning of the fermentation can depress growth by substrate Inhibition or glucose effect. In addition, high concentrations may reduce enzyme biosynthesis by catabollte repression.
Conversely, very low concentrations at the end of runs act to terminate secondary metabolite production by starving cells at times when small nutrient additions would extend synthesis by creating nearly-starved conditions (Ratafia, 1985; Yamane and Shimizu, 1984).
Continuous. To avoid the effects of undesirably low or high nutrient concentrations, other reactor configurations have been studied.
Historically, the next configuration given serious consideration was the continuous bloreactor (Elsworth, 1960). The continuous fermentor Is characterized by essentially a continuous flow of nutrients through the bloreactor with nutrient feed entering the reactor while cells, metabolic products, and exhausted medium exit the fermentor.
There are several classes of continuous fermentors, the oldest and most common of which are the turbldostat (also termed the demostat) and the chemostat. The turbldostat functions to control the optical density of the culture by manipulating the nutrient feed rate. It Is capable of growing cells near their maximum specific growth rate. In excess nutrient conditions, but Is Incapable of achieving optimal nutrient utilization efficiency. On the other hand, the chemostat, a continuous reactor In which the nutrient feed rate Is held constant. Is capable of running near maximum nutrient utilization efficiency, but. In practice. Is unstable for growth rates near the maximum (Elsworth, 1960). Other types of continuous 21 bioreactors include the nutristat (in which the substrate concentration in the fermentor is controlled by manipulating the nutrient feed flow rate), the pH-auxostat (in which growth is controlled by manipulation of the nutrient feed rate based upon changes in pH, the ability of which to do so is predicated upon the existence of a relation between pH changes in the medium and growth), and various rate controlled continuous cultures, such as base-addition rate, oxygen-addition/uptake rate and carbon dioxide-evolution rate controlled cultures in which the rates of production/consumption of different chemical species are monitored and used to determine the nutreint feed rate (Agrawal and Lim, 1984).
Although continuous fermentors inherently display the advantages of contiuous processes without exhibiting the limitations described for the batch bioreactors, there are several serious limitations of these systems that have impeded their commercial acceptance. First, for several reasons, such as sensor and pump inadequacies, nutristats, pH-auxostats, and other such "non-traditional" continuous bioreactors have not been demonstrated successfully, even in the laboratory (Agrawal and Lim, 1984). Second, such systems characteristically have wall-growth problems. Third, constant volume control is not unusual for such systems. Fourth, and very importantly, such systems are subject to contamination problems from better competing organisms that are introduced either by mutation or from external sources. Fifth and finally, as has been stated, turbidostats suffer from efficiency problems while chemostats exhibit instability when operating at or near the maximum growth rate. 22
Semi-batch. Another approach to reducing the deleterious effects of extreme nutrient concentrations is to adopt a semi-batch bioreactor configuration with a nutrient feed. Operation of this configuration resembles the batch configuration in that the fermentor is loaded with an initial charge, inoculated, then proceeds without medium withdrawal until the conclusion of the run. It differs from the batch, however, in that fresh nutrients are periodically Introduced into the fermentor during the course of the run. This situation is similar to that during the start-up of a continuous bioreactor.
Records of the commercial application of semi-batch (commonly termed, fed-batch) fermentation begin in the early twentieth century when it was discovered that, in the production of yeast from malt wort, excess wort would result in anaerobic conditions and ethanol production at the expense of yeast cell production. German, Hungarian and Danish patents registered during the years 1915 to 1919 marked the first productlon-scale applications of this configuration. As the years passed, this technique was extended to other processes: glycerol (1919); acetone and butanol (1921); riboflavin
(1946); penicillin (1953); and protease (1954), to name a few. (Whitaker,
1980) Despite the commercial adoption of this nutrient feed technique, however, it was not until the 1970' b that serious, systematic study of the semi-batch configuration was reported (Edwards et_al., 1970). It is valuable to note that similar consideration had been extended to continuous culture techniques almost two decades before the semi-batch configuration
(Elsworth, 1960). 23
Although serious investigation of the semi-batch configuration did not commence until the late 1960's, its history since then has been
unusually active, as exemplified by the number of feed patterns that have
been described in the literature and the confusing nomenclature that has
attended them. Although in 1970 Edwards et al. reported extending the
growth of a culture through the addition of nutrients during the
fermentation, credit for the first use of the term "fed-batch culture" in
1973 has been attributed to Yoshida et al. by Whitaker (1980), and by Pirt
(1975) to Yamane (Yamane and Shimizu, 1984), who subsequently refer to
Burrows (1970). Despite this uncer;.ainty, it appears that the introduction
of the fundamental concept, in fact, may have been due to Martin and
Felsenfeld (1964) through the application of "exponential gradient
generator." Semi-batch nutrient additions has been accomplished without
feedback control using a constant rate, a constantly increasing rate
(gradient-feed), an exponentially increasing rate (exponential fed-batch),
or intermediate increasing rate (quasi-steady-state fed-batch, Pirt, 1975),
and with feedback to maintain a constant nutrient concentration (extended
fed-batch), an optimal trajectory, or other direct or indirect feedback
control techniques (Yamane and Shimizu, 1984). A variant of the fed-batch
mode in which a portion of the batch is withheld at the end of the run to
serve as an innoculum for the next fed-batch cycle has been termed "repeated
fed-batch" by Pirt (1975).
Such interest in the semi-batch bioreactor configuration is
attributable to the advantages this configuration xhibits that batch and
continuous lack. For example, although fed-batch fermentation lacks many of 24 the processing advantages inherent to continuous processes, such as the absence of a requirement to periodically dump and recharge the fermentor, semi-batch operation utilizes capital equipment more flexibly than continuous, in that the same apparatus can rotate between different organisms and different products with greater ease than in continuous processing. Likewise, from a capital expenditure perspective, it is easier to modify a fermentor configured for batch operation to a fed-batch configuration than to a continuous configuration (which is very important, considering most existing plants were originally designed for batch operation). In comparison to batch operation, fed-batch fermentation shares many advantages that have been associated with continuous processing, due to
its ability to mimic the continuous mode by creation of a quasi-steady state, where time rates of change for many variables are zero, except, of course, for volume.
A summary comparison of semi-batch versus continuous processing provides mixed results. In studies of cell productivities, Weigand (1979) and Mori et al. (1983) concluded that repeated fed-batch operation was superior to continuous, but that continuous processing was superior to fed-batch cultivation under most conditions (Repeated fed-batch retains a portion of the batch during harvest to serve as an inoculum for the succeeding batch). In metabolite production studies, Mori et al. (1983) concluded that for "long" operating times continuous operation is superior to fed-batch, but for "large" capacity fermentations the reverse is true.
In commercial production, however, the productivity advantages of continuous culture become subordinate to the practical disadvantages of continuous 25
processing that have been mentioned earlier.
Plug flow. It has been mentioned previously that when a continuous
fermentation process is discussed, it is assumed that the process is a
continuous stired tank reactor. This is not because of ignorance of the
configuration on the part of those involved in fermentation technology, but,
rather, a recognition of the inappropriate characteristics of the
configuration. Other than exhibiting the processing advantages inherent to
any continuous process, the plug flow configuration shares few of the
advantages of the other configurations (such as the simplicity of batch),
but shares many of their disadvantages (such as high nutrient concentration,
in similitude with batch, and susceptibility to wall growth, in resemblance
to continuous). In addition, the plug flow configuration exhibits some of
its own, unique disadvantages, such as the difficulty of obtaining
measurements of important variables along the length of the bioreactor. For
these reasons, plug flow is processus non grata in fermentation technology.
Microorganisms
Selection of an appropriate microorganism to serve as the biological
agent for this research from the more than 100,000 species that exist in nature may appear to have been an insurmountable task. As may be obvious, however, not all species are of commercial value; in fact, only a few
hundred species have been incorporated into industrial processes (Phaff,
1981). Thus, when a selection criterion that the organism must be of
commercial importance is imposed, it is all but these few hundred that are
eliminated from consideration. 26
To further reduce the number of microorganisms being considered, another criterion was established that there must be a substantial, readily accessible experience base from which to acquire information describing the organism (especially, data related to its growth). The purpose of including this selection factor was to increase the efficiency of the research, by reducing the amount of preliminary experimentation that had to be accomplished. Ultimately, the number of groups of candidate microorganisms were reduced to six; yeast (principally, Saccharomyces spp. or Candida spp.); Escherichia coli; Pénicillium spp.; Bacillus subtilis; Bacillus thuringiensis; or Streptomyces spp.. The first four microorganisms were retained for consideration because of the large volume of information that has been published describing them, while the last two were kept due to the local experience by the Department of Microbiology (The Ohio State
University).
Yeast. In studying bioreactor behavior from a control perspective, of those reported in the open literature, systems incorporating yeast appear to be the most popular. An example of this popularity was evident in the
Proceedings of the First IFAC Workshop on Modelling and Control of
Biotechnical Processes (Halme, 1982), where, out of the thirteen papers that described pure culture experimentation, eight involved yeast. Of the remaining reports, two concerned Pénicillium spp. and the rest involved less popular microorganisms. This broad adoption of yeast can be attributed to various positive characteristics of yeast. Yeast are readily available, fast growing (and, therefore, competitive) microorganisms that can be grown to very high densities. They have plasmids, yet are stable with respect to 27 mutation. Additionally, they produce no toxins (which resulted in approval of their use by the Food and Drug Administration), and secrete a variety of products including glycoproteins, an ability not shared by coli (Abelson,
1983).
Escherichia coli. Another microorganism under consideration that has received considerable attention is the bacterium, Escherichia coli.
Like yeast, coli are readily available, fast growing, competitive microorganisms that can be grown to high densities. They have plasmids, but mutant forms tend to revert to wild types. Unlike yeast, coli produce endotoxins and tend, generally, not to secrete proteins (Phaff, 1981).
Despite these last two deficiencies, JE. coli has become a favored organism for recombinant-DNA fermentations.
Pénicillium spp. In the April 6, 1976 (American Chemical Society
Centennial) issue of Chemical & Engineering News, an article by R. L.
Pigford (1976) was published detailing the past century of chemical technology. In that paper, Pigford selected from all the previous achievements of the chemical engineering profession three that especially epitomized the discipline. Those chosen included synthetic ammonia production, catalytic cracking of petroleum, and penicillin production during the war. Having this special significance to chemical engineering and being one of the older biochemical processes has resulted in a substantial accumulation of information (especially, engineering information) about Pénicillium spp. fermentations. The genus. Pénicillium, is a filamentous fungi that is applied industrially to produce antibiotics and some cheeses. Although, like the previous organisms, many organisms of 28 this genus can be easily obtained, they do not grow as fast as the previous organisms.
Bacillus subtilis. Unlike Pénicillium spp., Bacillus subtilis exhibits many of the same positive attributes of the first two organisms: they are fast growing, and ready available; they have plasmids, and have a potential for growth to reasonably high densities. Transcending coli, however, subtilis excretes elaborated secondary metabolites and does not produce the endotoxins manufactured by coli.
Bacillus thuringiensis. Not as popular as the previous microorganisms. Bacillus thuringiensis is an organism with which members of
The Ohio State University Microbiology Department have had some experience.
A reaonably fast growing organism, B^. thuringiensis derives its popularity from its entomopathogenetic trait: it produces a parasporal glycoprotein crystal that is toxic to insects (Miller et al., 1983).
Streptomyces spp. Again, not as popular as previously mentioned microorganisms, Streptomyces is a genus with which members of the
University's Microbiology Department have had some experience (especially,
coelicolor, peucetius, lividans, and Streptomyces C5 by the W. R.
Strohl lab). Streptomycetes are filamentous bacteria that carry plasmids
(with relatively unknown stability under fermentation conditions), and are industrially important in the manufacture of antibiotics (producing, in 1977
(Aharonowitz and Cohen, 1981), 69 of the approximately 100 antibotics that were marketed). To their credit, they secrete proteinacious products, but tend to exhibit slow growth ; consequently, are rather poor competitors. 29
Optimal Control Methods
In their review of computer applications In fermentation technology,
Wang and Stephanopoulos (1984) stated that, "Optimal process control Is perhaps the ultimate objective In applying computers to fermentation processes." Although there are those who would disagree with this sentiment. It Is this concept that binds together the multifarious aspects of this dissertation research.
Fermentor optimization techniques have been classified into two broad categories: static (or point) optimizations, which generally are applied to steady state, continuous fermentations; or dynamic (path or function) optimizations, which normally are associated with unsteady state batch and semibatch fermentations (Wang and Stephanopoulos, 1984)
Static optimization. Static optimization studies can be further subdivided Into off-line and on-line studies.
In off-line situations where adequate models are available, differential calculus can be applied to minimize the nonlinear objective function of the optimizations; subject, of course, to equality constraints obtained from mathematical process models. Wang and Stephanopoulos (1984) reported, however, that too frequently such approaches Ignore physical
Inequality constraints on the state and control variables, resulting In unrealistic controller settings. They go on to recommend that simplex and constrained simplex search techniques may be applied to such problems if analytical solutions cannot be obtained. In off-line situations where the model Is Inaccurate and contains unknown parameters that are functions of the fermentor state, experiments must be accomplished to empirically 30 generate the relations necessary for determination of the optimum state.
Finally, in off-line situations where no model is existent, gradient search methods are applied in determining the optimal point (Weigand, 1978).
Wang and Stephanopoulos (1984) report that on-line fermentation optimization generally involves treatment of the fermentor as a black box which is directed to transverse between selected states to permit observation of the effect of the changes on the objective function. Through these small excursions and application of systematic search methods, improved fermentor performance is sought, but slow system response and poor reproducibility limit the effectiveness of such an approach. Porter (1982) reported that some improvement can be obtained when such methods include statistical variance analyses. Another approach, decribed by Muzychenko et al. (1974), applied a technique for using parameter values for a simple,
Monod model obtained during the transition of the start-up portion of the continuous culture to assist in the estimation the optimal operating point.
The parameters are updated and new optimal points calculated during periods in which the biomass concentration (for chemostat cultures) or dilution rate
(for turbidostat cultures) change; changes supposedly the result of drift in the parameters being estimated.
Dynamic optimization. The majority of fermentation process optimization reported in the literature appears to have involved dynamic optimization methods. Weigand (1978) explains this situation in two ways: first, most fermentations are performed in batch or fed-batch modes which are more amenable to path optimization; and, second, the majority of the literature was prepared by academics who have relatively little concern 31 about the broader plant operations optimization that normally would be approached through the use of static optimization methods.
Two principal techniques that have been applied in optimizing unsteady state fermentations have been dynamic programming (Bellman, 1957) and variational methods (Pontryagin, 1962). Both methods require, as input, the measure (index or criterion) of peformance that is to be optimized, and a mathematical representation of the system including physical constraints, and produce, as output, an optimal control policy. The performance measure,
J, to be minimized or maximized is frequently expressed,
J = h(x(tf),tf) + ^ g(x(t),u(t),t) dt (2.1)
where x and u represent the state and control vectors, respectively, and tg and t£ are the initial and final times.. This form assumes that the initial state has been previously established. Weigand (1978) emphasized, by example, the importance of careful formulation of an objective function to avoid inefficient calculation efforts. Parulekar and Lim (1985), in a review of the fed-batch fermentation literature, described three commonly adopted performance criteria applied in fermentation; these included production or utilization rate; productivity or consumption; and optimal time. The variables typically associated with the indices in fermentations include biomass, metabolities, substrate, profit and cost. The other input into the optimal control scheme, the mathematical represention of the process, consists of the set of dynamic equations that describe the accumulation, comsumption and production of any chemical species introduced 32 or withdrawn from the process, or manufactured or utilized to any significant extent. In addition to these equations, additional relationships may be required to describe how the parameters vary with state and time, and to specify physical constraints that may exist for the state or control variables. From these Inputs, then, the optimization scheme produces a description of the optimal path (profile or trajectory) over time that the control variables must follow to drive the process along the optimum state trajectory.
Although related (Kirk, 1970), dynamic programming and variational methods of optimization are markedly different In how they are Implemented: dynamic programming producing optimal control laws that are not analytical
In form and which require large data storage arrays, while variational methods require solution of a nonlinear, two-point value problem.
Manipulation of the arrays characteristic of dynamic programming methods requires computational power considerably In excess of that presently available for on-line experiments, so that dynamic programming approaches necessarily calculate the optimal control policy off-line, prior to the run.
Such an open-loop approach, then, depends heavily upon the accuracy of the process model upon which Is based. Recognizing that such process knowledge
Is very limited for most fermentation processes. It Is of no surprise that dynamic programming techniques are seldom applied to fermentation processes.
The techniques of choice to perform dynamic optimizations, then, have become variational schemes.
To briefly summarize the development of the variational technique
frequently employed In the derivation of optimal control policies for 33 fermentation processes (adopted from Kirk, 1970), given the Index of performance stated above, equation (2.1), subject to the constraints of the dynamic model.
^ = f(x(t),u(t),t) (2.2) dt and the Initial conditions, x(tg), the necessary (but not, generally, sufficient) conditions for the optimal trajectory over the course of the fermentation are:
dx*(t) =3H(x*(t),u*(t),p*(t),t) (2.3) dt 3p
dp*(t) = -3H(x*(t),u*(t),p*(t),t) (2.4) dt ÔX
0 =^(x*(t),u*(t),p*(t),t) (2.5) Ou
[^(x*(t£),t£)-p*(tf)]^ H(x(t),u(t),p(t),t) = g(x(t),u(t),t) + ^ (2.7) P (t)[f(x(t),u(t),t)] For n constraints, the problem of deriving the optimal policy becomes one of solving the above system of 2n equations by evaluating the 2n constants of Integration (and t^. If tf was not specified) through application of the n Initial condition equations and n (or n+1. If t^ was not specified) 34 algebraic relationships (2.7): a two-point boundary-value problem. Incorporation of control variable constraints, then, is accomplished through the application of Pontryagin's principle (1962). The result is replacement of the vector of differential equations, equation (2.5), with, H(x*(t),u*(t),p*(t),t) 2 H(x*(t),u(t),p*(t),t) (2.8) which is true for all admissible u(t). (For problems formulated as minimization problems, the inequality is reversed.) Kirk (1970) also mentioned, without proof, that if the Hamiltonian does not depend upon time explicitly, the Hamiltonian is constant on the optimal trajectory (being identically zero when the final time, t^, is not fixed). Calculation of the optimal trajectory can be accomplished numerically with difficulty through the use of various final-value iteration or control-vector iteration methods (Wang and Stephanopoulos, 1984). In fermentation process applications, analytic solutions generally are pursued, so as to permit on-line implementation. In surveying the literature for this review only 25 papers were obtained that described optimal control applications to fermentation processes. However, ten review papers were acquired that attempted to survey the literature in this area (Parulekar and Lim, 1985b; Aiba, 1979; Dobry and Jost, 1977; Arminger and Humphrey, 1979; Bull, 1983; Rolf and Lim 1982; Constantinides, 1979; Hampel, 1979; Weigand, 1978; Zabriskie, 1979); indicating, perhaps, that there is more interest in such research than there is research occurring. Or, altenatively, indicating that, since this literature review did not have access to papers from some international 35 fermentation symposia such as the First IFAC Symposium on Modeling and Control of Biotechnological Processes in December of 1985, it may be subject to sampling error. An inconveniencing factor arose in Identifying relevant fermentation process optimal control papers due to the somewhat similar terminology between optimal control (or process optimization) as defined herein, optimal control as related to optimal controllers that act to maintain an optimal state that has been determined to be optimal by some other means (for example, Fawzy and Hinton, 1980; Gallegos and Gallegos, 1982, 1984; Montague et al., 1986; Oguztoreli et al., 1986; Shioya et al., 1985; and Wu et al., 1985), and process optimization as practiced by life scientists in empirically determining optimal growth conditions (such as Peringer and Blachere, 1979). Optimal control applications in fermentation technology have varied considerably as to method applied and system addressed ; many of which serve as examples of exceptions to previously stated generalizations. For example, although this section began by describing a standard form of optimal control performance criteria, equation (2.1), Harmon et al. (1985) presented a general development of an optimal policy applying upon another index (an economics-based index) of performance; in this instance, an adaptive, point optimization for a chemostat, J = Dx - qDs (2.9) where D is the dilution rate, and q is an economic factor of relative cost between substrate, s, and biomass, x. And, although it was previously stated that dynamic programming methods are seldom applied to fermentation 36 processes, some investigators such as Alvarez and Ricano (1979), and Kishimoto et al (1981) have adopted such methods in establishing optimal temperature and pH, and optimal feed rate for batch single-cell protein culture, and a fed-batch glutamic acid fermentation, respectively. And, again, despite it being said earlier in this section that variational methods applying Pontryagin's principle are the most commonly adopted approach to obtaining analytic solutions for on-line implementation, researchers including Fishman and Biryukuv (1974), Rai and Constantinides (1973) (and, in a related paper, Constantinides and Rai (1974) ), and Cheruy and Durand (1979) have applied the approach off-line to generate trajectories for experimental implementation in erythromycin, gluconic acid and penicillin fermentations, respectively. With these exceptions, however, the remaining majority of the literature surveyed considered methods of applying Pontryagin"s principle to on-line fermentation process optimization. Of the optimal control papers collected, several were theoretical expositions of approaches to determining optimal flow rate profiles through application of variational calculus and Pontryagin's principle, and provided no demonstrations of the effectiveness of the approaches, nor any other significant link with any specific existent fermentation. San and Stephanopoulos (1984c) sought to maximize the index of performance. J = VfXf - cj ^ dt (2.10) '^0 subject to the fermentor dynamics, 37 dx/dt = kjj(s)x - (F/V)x; x(0) = x q (2.11) ds/dt = -k^(s)x/Y + (F/V)(sfggj-s); s(0) = Sg (2.12) dV/dt = F; V(0) = Vg; V(tf) = Vf (2.13) (where F is the constrained feed rate) to maximize biomass production. After applying Pontryagin's principle, they discovered that (i) for Monod kinetics, the optimal feed policy involves feeding at the maximum rate until Vf is reached, then halting the feed, (ii) for a specific growth rate that is a function of substrate concentration and that exhibits a maximum, the optimal feed policy consists of feeding at the maximum flow rate if the derivative of the specific growth rate with respect to substrate concentration is positive, of feeding at the minimum rate if the derivative is negative, or of feeding in accordance with, F = k^V/(Y(sfggj-s)) (2.14) if the derivative is zero. The flow pattern described by equation (2.14) exists during a singular period. The devlopment for this relationship appears in Chapter V. When Vf is achieved, then, the feed is halted. Upon reaching Vf, a batch operating mode is assumed until the final condition, k^(tf)x(tf)v(tf) = cj (2.15) is obtained. Modak et al (1986) sought to minimize the objective function, J = f(Xf,pf,Sf,Vf,tf) (2.16) subject to fermentor dynamics. 38 dX/dt = k^X; x(0) = Xq (2.17) dS/dt = -kgX + Fsfged? s(0) = Sq (2.18) dP/dt = kpX - cP; p(0) = p q (2.19) dV/dt = F; V(0) = Vq (2.20) and the constraints, V(tf) = Vf (2.21) 0 < F(t) < (2.22) where X is total biomass, S is total substrate, and P is total product, and kg and kp are the specific substrate utilization and product formation rates, respectively. In analyzing the problem of determining the optimal feed profile, Modak et al. classified possible situations into three nontrivial categories: (i) monotonie kg and nonmonotonic kp; (ii) nonmonotonic kg and monotonie kp; (iii) nonmonotonic kg and nonmonotonic kp. Based upon the conjecture that cells must be grown optimally before optimal product formation is pursued, they applied Pontryagin's principle and observed that the optimal feed profile is dependent upon the shape of k^ and kp and the initial conditions. For type (i) kinetics: (a) with low initial substrate and biomass concentrations, the feed rate initially is maximal for optimal biomass production, followed by a batch period to reduce the substrate concentration to optimize product formation, followed by a singular period that balances growth and production, followed by a batch period; (b) with high initial substrate concentration, a trajectory similar to (a) is followed, except there is no initial maximum feed rate period; (c) 39 with high initial biomass concentration and low substrate concentration, a trajectory again similar to (a) is followed, except the earlier batch period is eliminated; and (d) with appropriate initial substrate and biomass concentrations, the optimal trajectory once more follows (a), except the first two periods of maximum flow and batch operation are eliminated. For type (ii) kinetics: (a) with low S q and x q , a maximum flow period is initially instituted to reach the substrate concentration that provides the maximum specific growth rate, this is followed by a singular period which balances growth and production which, in turn, is followed by a maximum feed period to maximize product formation, which finally is followed by batch conditions; (b) with high Sq the optimal feed profile is the same as (a), except that the initial maximum flow period is replaced by batch operation; (c) with appropriate Sq and x q the feed pattern is similar to (a) except the initial period is eliminated and feed starts at the singular interval; and (d) for high X q and low Sq, the first two periods are eliminated and a period of maximum flow followed by the final batch growth results. For type (iii) kinetics: (a) with low S q and X q , the optimal trajectory consists of a maximum flow period to reach the optimal specific growth rate is followed by a singular period balancing growth and product formation which is followed by the final batch operation; (b) with high initial substrate concentration, the optimal trajectory is similar to (a), except a batch period replaces the maximum flow period; and (c) for appropriate S q and xq, the initial period of (a) is eliminated, leaving only the singular and final batch mode periods. With these sequences identified, Modak et al stated that the problem reduces to one of determining the switching times and 40 singular feed rate, which, in some instances, can be done analytically, but, in others, must be accomplished numerically, as they did in a subsequent paper (Lim, et al., 1986). Other papers presenting such theoretical expositions included D^Ans et al. (1971), Parulekar et al. (1985), and Weigand et al. (1979). Although there were several "theoretical" publications obtained in this survey of the literature, most papers applied their techniques to either process models or actual processes. In addition to simulations focusing upon optimization of biomass production by Hong (1986), Staniskis and Levisauskas (1984), and Yamane et al. (1979), simulations of profit optimization for fermentations producing valuable single-cell protein (SCP), and of product formation of penicillin, lysine, and alpha-amylase were presented by Choi and Park (1981), Lim et al. (1986), Ohno and Nakanishi (1976, and also with Takamatsu (1978) ) and Yoo et al. (1985), respectively. Out of the research surveyed, only two teams of investigators proceeded to test their techniques experimentally, as both D'Ans et al. (1972) applying their approach to coli K12 fermentation and Dairaku et al. (1982) implementing their method using baker's yeast concentrated upon biomass production. Interestingly, while all of the simulated processes but Yamane's et al. (1979) were applied to fed-batch fermentations, the two experimentally verified techniques were both applied to continuous cultures; specifically, to startup and transient periods. Two other comments seem in order concerning the optimal control papers collected. First, of the nineteen relevant reports only seven possess any adaptive character, and four of those fail to describe how state 41 variables that are difficult to measure, such as biomass concentration, would be measured. Second, a characteristic of applying variational calculus to fed-batch fermentation is that singularities appear due to the linearity of feed flow rate in the Hamiltonian. Although one paper avoided the problem by optmizing the specific growth rate, then related the feed flow rate to the optimal specific growth rate profile (Yamane et al., 1977), the majority approached the problem by use of either Green's theorem (five reports) or Kelley's theorem (four papers). A criticism of fermentation optimization applications leveled by Weigand (1978) was that these applications predominantly have been by analysis and simulation studies founded upon models that lacked the support of ". . .published experimental verifications with the actual fermentation systems upon which the models were based." A similar opinion was expressed by Wang and Stephanopoulos (1984) in relation to optimal control strategies when they stated that. The effectiveness of optimal control strategies are rarely verified through actual experiments. Many optimal problems are based upon highly hypothetical assumptions. For example, the validity of the starting model is often not established in advance. Many state variables included in the optimization are not practically measureable, and this prevents meaningful studies using closed loop feedback control from being actually carried out. Results of this literature review coincided with these sentiments as, of the relevant 24 optimal control papers collected, 5 papers presented theoretical analyses of optimal control approaches, 11 papers described results obtained from simulation studies, and only 8 reported results from any experimental (laboratory) research. In addition, of the 10 papers reviewed reporting 42 results from adaptive optimal control simulations or descriptions of optimal feedback controllers, situations that require on-line measurement of state variables, five present results that either explicitly assume all states are measurable or that ignore explaining how some measurements were acquired that could not be acquired by direct methods. This application of models beyond their valid range, adoption of questionable assumptions concerning the availabilty of measurements, and dearth of experimental verification, appears to be caused by investigators that are isolated from the experimental system they address, either by choice (as in the case of control engineers merely seeking novel model systems) or by the lack of access to adequately instrumented fermentation systems. In either case, the contribution of such research to the advancement of fermentation technology may be questionable; as evidenced by results obtained by Alvarez and Ricano (1979) which reported impressive performance improvements from simulations, but a mere one percent improvement experimentally due to the narrow range of conditions that the optimal trajectory covered (0.5°C and 0.25 pH), and evidenced by the insigificant, practical improvement of Rai and Constantinides' (1973) optimal control scheme over the best batch obtained during preliminary, data gathering experiments. Presently, in many ways, fermentation technology is as much an art as it is a science. Frequently, as Wang and Stephanopoulos (1984) relate, apparently identical fermentations will yield quite different results. Important growth related variables (such as pH and substrate and dissolved oxygen concentrations) are measurable and controllable; but, the more subtle variables that explain differences in identical fermentations, such as the 43 activity or concentrations of many chemical species that can affect the activity of the enzyme involved with the rate determining step of the organism's growth, are not accessible. Process optimization by life scientists and engineers is dependent upon knowledge of the important variables to measure over time, which is dependent upon understanding the organism, which is dependent upon the availability of adequate sensors, which, to a great extent, is dependent upon knowledge of which variables are important to measure over time (a vicious circle). Before effective optimal control methods can be developed for fermentation processes, significant, basic scientific research into understanding the behavior and chemistry of microorganisms must be accomplished; expectations otherwise would be premature. However, until then, optimal control techniques, employing information presently available, can be applied to reasonably improve the performance of present fermentation systems; control systems which, if they exist, are often founded upon heuristic principles and frequently lack adaptive characteristics. State and Parameter Estimation To perform effectively, a controller requires a precise understanding of the process, and accurate, timely information describing the state of the process. Application of such controllers to fermentation processes is severly handicapped by the existent limited understanding of such processes and lack of adequate sensors. To compensate for these multitudinous deficiencies, several techniques have been developed to provide information for optimal (and other) controllers. To increase the reliability of measurements, filtering and measurement error detection techniques have been 44 devised. To compensate for the nonexistence of sensors, indirect measurements and state estimation techniques have been created. And, to provide process dynamics information, model identification and parameter estimation techniques have been applied. Indirect measurement. Indirect measurements (or, as they are sometimes called, "gateway" sensors) are the most elementary approach for compensating for the limitations of present sensor technology. Indirect measurement involves the simple combination of two or more direct or raw measurements to form an additional measurement that has significance with respect to conditions surrounding or internal to the cells. For example, temperature, pressure, composition and flow rate measurements of the gas streams into and from the fermentor permit calculation of consumption and production rate of gases such as oxygen and carbon dioxide, and provide measures of cell respiration or of the specific growth rate of the culture (Park et al., 1983a, 1983b). Measurement of oxygen utilization rate and/or dissolved oxygen tension provide means for calculating the overall oxygen transfer coeffcient (Linek and Benes, 1977, 1978; Votruba et al, 1978; Merchuk, 1977; Tsao, 1978). Volumes of acid or base added to maintain a constant pH may be used to measure meatbolic product formation rates (San and Stephanopoulos, 1984d). And, other measurements may be combined to produce other indirect measurements, such as biomass yield. Filtering. Another elementary means for improving measurements transmitted to the controller is by filtering. Filtering can be accomplished by hardware filters, such as RC circuits, that reduce high frequency noise, or by digital filters, such as the calculation of a moving 45 average, that can reduce medium and low frequency noise. Unlike indirect measurement, some filtering approaches are quite complex and require information other than that immediately derivable from on-line measurements. In fermentation, the most popular of these appear to be techniques that combine filtering with estimation. Estimation. A third, more sophisticated approach to improving information sent to the controller is through the application of on-line estimation techniques. The purpose of estimation is to provide approximations of system factors that cannot be measured. These approximations are arrived at through the imposition of structure upon the system factors which, for fermentation systems, is usually in the form of a model based upon numerous biological and chemical principles. Factors are frequently classified as being of two types, either "parameters" (factors inherent or characteristic of the system), or "state variables" (fundamental quantities that, when taken together, describe the state of the system). It is the preference of this author, however, to adopt a simpler conceptualization of the types, with parameters representing very slowly changing factors (slow to change with time and with changes in the other system factors), and variables representing factors that tend to change more quickly. Beck and Arnold (1977) define six classes of estimation problems. The first class, or deterministic problem, consists of determining the system's state given known inputs into a known system; the classic engineering problem. The second type of estimation problem is the state estimation problem. As was the previous case, the problem is to determine 46 the system's state given a known system. However, unlike the previous type, the observed input to and output from, the system are corrupted by nonsystematic measurement errors (i.e., noise). It is to this problem that the appellation "filter" is attached. The parameter estimation problem occupies the third category of estimation problems. In this type of problem, the input is known, the output corrupted with noise is alsoknown, but the system is incompletely known: the structure of the system is known, and the initial and boundary conditions are known, but system parameters are not known. The objective, then, is to obtain an optimal estimate of the parameters. The fourth class of estimation problems is the optimum experiment problem. The objective in these problems is to make the output as sensitive as possible to the parameters by adjustment of the inputs over time, and the initial and boundary conditions. In this way the effect of the errors upon the estimations of the parameters is minimized. The fifth category is composed of problems of the "discrimination" problem class, and involves the design of experiments to select a correct model from a set of possible models. Problems of the final class, the "identification problem" category, are the most complex of all estimation problems because the structure of the model is unknown. To provide adequate input for the optimal controller, the research described in this dissertation had to address state and parameter estimation problems. To extract information from data, then, estimation techniques characteristically employ system models. Due to the complexity of fermentative processes, fermentation models cannot be comprehensive. Instead, model developers necessarily restrict their consideration to one of 47 four system levels (Humphrey, 1979; Votruba, 1985). The lowest level Is the molecular/individual reaction step level where enzyme activity is of principal concern. Domach et al. (1984) present a very limited example of such a model for Escherichia Coli B/r-A, and Papageorgakopolou and Maier (1984) present an approach to construction of such models that focuses upon a rate limiting pathway. The next highest level of modeling concerns metabolic subsystems in which the expressed rates are those of entire subsystems and the subsystems are interconnected by component flows. Votruba (1985) describes Roels (1980) work on the "Application of Microscopic Principals to Microbial Metabolism" as describing a modeling approach on this level. The second highest level of the microbiological process heirarchy is concerned with population subsystems; dealing with culture age distributions and the extent to which the culture has a given characteristic (such as morphological type). The highest level of the hierarchy addresses the macroscopic system formed by the biological subsystem and the support subsystem. The models of concern to this dissertation research are growth related models, and, therefore, are positioned in the highest and second highest levels of the hierarchy. Mathematical models have been classified in a variety of ways (Fasol and Jorgl, 1980): theoretical versus empirical; distributed parameter versus lumped parameter; discrete versus continuous; dynamic versus static; stochastic versus deterministic (which can be further divided into parametric and nonparametric models). The classification of a particular model, then, depends upon the source of information upon which the model is built and the assumptions made, among other factors. Obviously, the greater 48 the number of assumptions made the more tractable the model, but also the more limited and the less representative the model. Fredrickson et al. (1970) and Tsuchiya et al. (1966) described four common assumptions made in the modeling of fermentation processes. The first common assumption is the disregard of the distribution of states. Individual cells within a population differ from other members of the population in age and a host of other physiological, morphological and genetic characteristics. Yet, a typical assumption in modeling fermentations is that the properties of the culture can be adequately described by an "average" over the distribution of states. This assumption is common for two practical reasons : measurement (how are individual cells measured so as to obtain the distribution of interest); and manageability of the mathematics (the complexity added to the model by the introduction of the additional equations required to represent a distribution exceeds our present ability to solve such equations). The second assumption frequently made in the development of fermentation models is the neglect of the segregation of microorganisms into structurally and functionally discrete units. Under such an assumption the population is perceived as biomass that is continuously distributed throughout the culture, while cell numbers are ignored. Two explanations offered by Fredrickson et al. (1970) for the frequency of this assumption are, first, that often biomass, and not cell number, is the relevant quantity, and, second, (cell) proliferation and (biomass) growth are linked processes, theoretically maintaining perfect proportionality under balanced growth conditions. The third commonly adopted assumption is the neglect of stochastic phenomena; that is, fermentation processes are assumed to be 49 deterministic processes. This third assumption is commonly made to, again, maintain the manageability of the mathematics, and because it is quite accurate under conditions where the statistical law of large numbers applies. The last common assumption described by Fredrickson et al. is the disregard of biological structure. Models based upon this assumption do not recognize that the distribution of states for a population may change in response to changes in the environment of the population. Such models have been termed, "unstructured" models (Tsuchiya et al., 1966). The frequency with which these assumptions historically have been adopted is so great that Fredrickson et al. (1970) reported only a few unstructured or distributed or nonsegregated models, and those that were reported were too complex to be of practical value or simplified to the point of being of limited value. As has been stated, models of fermentation systems are founded upon basic biological, physical and chemical principles. Fredrickson et al. (1970) defines four biological principles especially relevant to fermentation process modeling. The first states that the behavior of an organism (specifically, its activities and the rates at which they are accomplished) is dependent upon the organism and its environment. The second biological principle states that the current phenotype (or state) of an organism is dependent upon its genotype and past history of environments in which it resided. Structured models incorporate this principle, while unstructured models ignore it. The third principle states that organisms may be classified on the basis of morphology, growth form, and mode of reproduction, implying that models should internalize the differences between classes or similarities within classes when representing different 50 microorganisms. The final principle recognized by Fredrickson at al. was that of the mutability of organisms which involves the modeling of mutation processes. Fredrickson et al. limit themselves to these four principles because their importance is generally recognized, but they are rarely accounted for fermentation models; a fact that highlights how limited the present understanding of microbial behavior (the biological subsystem) is, and one which limits the effectiveness of estimators based upon these models. In contrast to the infrequent adoption of biological principles, fermentation process models typically incorporate physical and chemical principles. In describing the latter principles, Fredrickson et al. (1970) have classified the physical and chemical principles as being conservative, thermodynamic, and constitutive. Conservative principles account for the transfer and transformation of an entity (such as mass, energy, or chemical species) across and within the boundaries of a system. Thermodynamic principles (which actually include only the second law of thermodynamics, since the first law relates to a conservative quantity) describe equilibrium states of the system and the efficiency of and extent to which processes may proceed. And, constitutive principles address the rates with which physical (such as transport phenomena) and chemical (such as chemical kinetics) processes occur. Of these, the conservative principles are those which have been most commonly and successfully adopted. Of the three classes of principles, conservative principles have been the most successfully applied because the available knowledge of and ability to measure relevant quantities have been the greatest. That is, it is much 51 easier to measure, for example, the concentration of a chemical species (which is used by conservative principles) than to determine the mechanism and measure the rate related quantities by which it is produced (which is relevant to constitutive principles). Although application of material and energy balances have been common in chemical process calculations for decades, their application to fermentation processes have been relatively recent. The suggestion for the employment of such approaches appears to have originated in 1977 with Cooney et al. (1977) and Wang et al. (1977) at the Massachusetts Institute of Technology. Others quickly recognized the value of these approaches, so that within two years many papers applying material and energy balances had been published (Bravard et al., 1979; Erisckson, 1979; Swartz and Cooney, 1979; Ho, 1979; and Madron, 1979). Today, the techniques are commonly applied to on-line computer monitoring of fermentation processes (Mou and Cooney, 1983a, 1983b; Constantinides and Shao, 1981; Stephanopoulos and San, 1984; San and Stephanopoulos, 1984a,b,c), and have been thoroughly delineated theoretically (Roels, 1980, 1981). The characteristic feature of the material balance method is the macroscopic description of the conversion of substrate to cell mass and other metabolic products. Ignoring elements that comprise only a small portion of the biomass, metabolic reactions are represented by the overall reaction, ^^t^u®v ^ > C^H^OyNg + dHgO + eOOg + gCpH^G^Ns (2.23) 52 where C^H^Oy, C^H^yN^, and CpHqO^Ng represent substrate, biomass and product chemical formulas. (Note that the stoichiometric coefficients are expressed on a mole of biomass basis, that the ammonia represents the nitrogen source which may also be nitrate, ammino acids or other nitrogenous compounds, and that only one substrate and one product are assumed.) Since the compositions for substrate, biomass and product are assumed to be known, elemental balances over carbon, hydrogen, nitrogen, and oxygen provide a system of 4 equations. C: at = w + e + gp (2.24) H: au + 3c = x + 2d + gq (2.25) 0; av + 2b = y + d + 2e + gr (2.26) N: c = z + gs (2.27) with 6 unknowns (i.e. a,b,c,d,e,g). To solve the system of equations, two additional equations containing only those six coefficients will be required. Wang and Stephanopoulos (1984) observe that oxygen uptake and carbon dioxide evolution rate measurements, along with an enthalpy balance, are frequently used to solve for the stoichiometric coefficients, but that the relationship between heat evolution and oxygen utilization creates a nearly singular set of equations. Similarly, nearly singular equations may arise if the degree of reductance of the substrate and the biomass (and/or the product) are equal or close. Another approach to solving the elemental balance set of equations was introduced by Erickson (1979a, 1979b), and involved inclusion of an electron balance (or, alternatively, energy balance) based upon three observed regularities: a "constancy" of the heat of reaction per electron transferred to oxygen (26.95 kcal/gram-equivalent electrons transferred to 53 oxygen); a consistency in the amount of carbon contained in biomass (approximately 0.462 grams carbon/gram biomass); and a regularity in the number of electrons available per a quantity of biomass containing one gram atom of carbon (4.291 gram-equivalents/biomass containing one gram-atom carbon). This work was worthy of mention because it highlighted the important interdependency of oxygen utilization, heat evolution and electron transfer to oxygen, emphasizing estimates resulting from the simultaneous application of these equations will be very sensitive to measurement errors. The second set of chemical principles, thermodynamic principles (i.e., the second law principle), rarely has been applied to fermentation process modeling. Although, for the sake of completeness in theoretical developments, the concepts of an entropy balance and thermodynamic efficiency appear frequently in publications summarizing the application of macroscopic principles to microbial metabolism (Roels, 1980, 1981), few papers have described its experimental application to processes. Grosz and Stephanopoulos (1983) detailed an approach to estimating the free energy of formation of biomass by a statistical mechanical method that modeled biomass as a system of biopolymer networks; however, no experimental work was described in the paper. Erickson and Oner (1983), and in similar papers Oner and Erickson (1983) and Oner et al (1984), employed free energy relations to estimate yield and maintenance parameters for several sets of experimental results, most of which were generated by other researchers. Constitutive principles are numerous and varied in modeling fermentation processes. These principles describe the rates and mechanisms by which mass, momentum and heat are transferred and the kinetics of growth. 54 In describing the specific growth rate parameter alone there are papers that model it during lag phase (Pamment, 1978), under high substrate concentrations (Edwards, 1970; Andrews, 1968), under multiple nutrient limitation (Chen and Christensen, 1985), and high population densities (Contois, 1959), to name a few. Takamatsu et al. (1981) discuss 23 unstructured growth models, listing numerous expressions relating the specific growth rate to state variables. These discussions do not even begin to touch upon modeling of other significant parameters such as yield and maintenance energy (Pirt, 1975, 1982; Lee et al., 1984; Verseveld et al., 1984; Beyeler et al., 1984; Stouthamer and Bettenhassen, 1973; Heijen and Roels, 1981; Oner and Erickson, 1983). To attempt to seriously discuss, even a portion of these observed relationships would be fruitless, since the vast majority were determined from specific situations, and no unifying structure has, yet, appeared. It is worthwhile, however, to note that although numerous relationships exist to estimate specific growth rate, the vast majority of research that focuses on modeling aspects of fermentation other than specific growth rate, has assumed, for lack of a better model, Monod (1949) kinetics to be applicable. The Monod model is similar in form to the Langmuir isotherm exhibited by monomolecular adsorption, K = k ™ * s (2.28) Kg + 8 where the specific growth rate, k^, is a function of substrate concentration, s, and the parameters, the maximum specific growth rate, k^^^, and the half-rate saturation constant. Kg. The lack of a unifying structure and common adoption of the Monod model, again, indicate the 55 limited level of understanding existent for fermentative processes. Having introduced some preliminary concepts (i.e. modeling), it is now possible to proceed with a discussion of parameter and state estimation techniques and how they have been applied to fermentation processes. Although this dissertation has described parameters and state variables as differing only in the rate with which they change relative to time and conditions (a view consistent with Astrom's (1983) interpretation), these factors traditionally have been treated quite differently. Historically, the inaccuracy and poor resolution of instruments have made parameters appear as constants. By filtering measurements (that is, by tradition, calculating the arithmetic mean), then solving the equations of simple models for their parameters, it was possible for early investigators to arrive at relations having predictive power. For example, averaging a series of p-V-T (pressure-volume-temperature) measurements for a given volume of gas would provide an estimate of the gas constant; which now is well known not to be a constant. Although the poor quality of researchers' instruments misled them to believe that parameters were constant, treating parameters as constant and differentiating between state variables and parameters permitted them to fully utilize the information of their slowly changing nature. To have done otherwise, and treated parameters as state variables would not have made as efficient use of the information obtained from measurements and would have complicated the interpretation of the data. The condition of having to estimate parameters and states separately continued until recently when estimation techniques were developed that permitted simultaneous estimation of both. 56 The first significant work in estimation theory was acomplished in the eighteenth century to assist astronomers in predicting planetary motion (Sorenson, 1980). The original dissatifaction with astronomical observations that Cotes in 1722, Euler in 1749, and Daniel Bernoulli in 1777 had was that slightly discrepant observations of the same event were averaged together equally to estimate the value of the quantity being measured. It was their opinion that estimates should be arrived at through a process that weighted the individual observations in relation to their perceived accuracy. Bernoulli propounded that the estimate should be chosen in such a manner so as to maximize the likelihood function. The likelihood function being the joint probability density function of the observations given the parameters, with its maximum determined by setting the differential of the density function equal to zero and solving for the parameters (Hogg and Craig, 1969). A second approach to parameter estimation has come from an extention of the work described in a 1763 essay by T. Bayes (Sorenson, 1980). This technique, termed Bayesian estimation, combined information about the parameters' prior distributions with direct sample evidence to generate posterior distributions. Symbolically expressed as. p(b|y) = h(b) ' f(b|y) (2.29) g(y) where b and y are the parameter and measurement vectors, and p, h, f, and g are the posterior conditional density, prior density, conditional density and density functions of the related parameters and variables, respectively. 57 In 1795, K. G. Gauss (and, independently, in 1806, A. M. Legendre) proposed another method of estimating parameters described as the method of least squares. The method essentially stated that, given M measurements that contain error, the best estimate of N parameters (N Gauss considered the approach a second time but from a probabilitistic perspective, assumed the measurement errors had a normal distribution. Over the decades since the original parameter estimation methods appeared, refinements and expansions of these techniques have been developed, as well as the introduction of other techniques such as minimum mean-square error, and stochastic approximation estimators. Recently, within the last fifty years, approaches to state estimation have emerged, the most important being the Kalman filter. Kalman's development in the late 1950's of the filter now bearing his name began with the assumptions that (i) the randomprocess to be estimated could be described by an equation of the form, x(k+l) = ë x(k) + w(k) (2.30) (where x and w are the state and process noisevectors, respectively, 5 is the matrix describing the relationship between the state vectors, in the absence of a forcing function, at two successive points in time, and the quantity in parentheses represents discrete time points), (ii) that process measurements were made at discrete points in time and conform to the relationship. 58 y(k) = M(k)x(k) + v(k) (2.31) (where y and v are the measurement and measurement noise vectors, and M is the matrix describing the relation between the state and measurement vectors in the absence of noise), (iii) that the noise sequences v(k) and w(k) have zero means, each is uncorrelated timewise, and there is no correlation between the noise sequences, (iv) that the second order statistics are known for all random variables (specifically, E[v.vî] = Rj, i=j (2.32) 0, ijÉj, E[w £w Î] = Qj, i=j (2.33) 0, ij^j, E[vjwP = 0, for all i, j) (2.34) (where R and Q are known process and measurement noise covariance matrices, respectively), and (v) that estimates are available for the initial state vector, X, and error covariance matrix, P. There have been several approaches applied in developing the Kalman filter, such as orthogonal projections which was used by Kalman in his original work (Kalman, 1960), recursive least squares, maximum likelihood, and linear minimum variance. Because they are so common (Jazwinski, 1970; Sage and Melsa, 1971; Brown, 1983; Sorenson, 1980), they will not be repeated here; instead, only the final result will be presented. The result is an algorithm for optimally processing sequential, discrete measurements. It is a two step process in which (1) a prediction (predicted state vector, R(k)~, and error covariance matrix, P(k)“) is updated with a measurement: 59 «(k) = %(k)- + K(k)(y(k) - M(k)«(kn (2.35) P(k) = (I-K(k)M(k))P(k)"[I-K(k)M(k)]T+K(k)R(k)KT(k) (2.36) where, K, the Kalman gain Is defined as, K(k) = P(k)“M(k)[M(k)P(k)“HT(k)4^^(k)]-l (2.37) and (2) estimates are employed to project ahead, X(k+1)- = J(k)X(k) (2.38) P(k+1)- = i(k)P(k) (k)T + Q(k) (2.39) Since its original exposition, the Kalman filter has become the foremost approach to states estimation. It has done so, not because it involved a complete departure from previous approaches (Sorenson (1980) compared the assumptions made by Kalman and Gauss and found the only difference to be that Kalman allowed the state to change over time), nor was it significantly more innovative (Sage and Melsa (1971) observe that the results of the two approaches are the same for the stationary estimation problem), but because the attributes of its solution were consistent with the technology of the age, that is, it was extremely convenient for digital computer implementation, and because its formulation occurred in a more general framework than previous estimators, so had a unifying effect on estimator theory (Sorenson, 1980). Its features of recursion, ability to handle multiple-input-multiple-output and discrete-data problems has made it the preeminent approach to on-line state estimation in some disciplines. And, has prompted reformulation of parameter estimators into more easily implemented recursive forms (Isermann, 1981, 1982; Astrom, 1983). 60 Interest In applying estimation techniques to fermentation processes has arisen only within the last two decades; appearing cotemporaneously with advances in computer technology and recursive estimation techniques. One common estimation approach has been to use measurements collected from previous experiments with the system under investigation to estimate the parameters of an assumed model (whether the model was a kinetic model derived from assumed process mechanisms, or empirically derived (Ong, 1983; Ollis, 1983), or was merely a power law model (Alvarez and Ricano (1979); Volt and Savageau (1982) ) using a nonlinear regression method (such as D. W. Marquardt's (1963) ). Estimates of process parameters or unmeasured state variables, then, were obtained by incorporating the previously determined parameters into the assumed model. Parameters obtained by this off-line method could be employed on-line in fermentations (Dairaku et al., 1982) or as part of a dynamic optimization scheme (Alvarez and Ricano, 1979; Cheruy and Durand, 1979; Constantinides and Rai, 1974; Kishimoto et al, 1981; Rai and Constantinides, 1973). Although off-line parameter estimation techniques possess many positive attributes, they also have a major limitation: their reduced reliablility during system transients that transgress their relevant range. For example, Rai and Constantinides (1973) and Constantinides and Rai (1974) obtained a general expression for parameters of a growth-production model they adopted, by applying the non-linear regression method of Marquardt (1963) to experimental data acquired from a batch gluconic acid fermentation. They, then, proceeded to determine and apply experimentally an optimal production policy in which pH and temperature were varied as 61 functions of time. The employment of pH and temperature to estimate growth and production parameters relied on the consistency with which the experimental fermentation reproduced the fementations upon which the estimates were based. Any deviation from the range of conditions of previous fermentations would decrease the reliability of the derived estimator relationships. Similarly, Kishimoto et al. (1981, 1982), and Churey and Durand (1979) rely on historically established estimator relationships to estimate process parameters for a glutamic acid and erythromycin fermentation. On-line estimation techniques can reduce the dependency of the estimator on how closely fermentor conditions approximate the historical conditions upon which the estimations were based. Wang and Stephanopoulos (1984) described a simple least-squares technique of estimating growth rate that was reported by Jefferis et al. (1977) in whicb Jefferis et al. smoothed optical density measurements through the application of a recursive least squares filter with exponential weighting to estimate the coefficients of a power series, X = 8q + ajt + (2.40) The growth rate was subsequently calculated by taking the derivative of the biomass concentration with respect to time. growth rate = ^ = aj + 2a2t (2.41) dt Jefferis later, 1979, goes on to apply a similar approach to the estimation of feed flow rates to a fermentor based upon feed vessel weight and feed flow rate measurements. However, in this case, since an accurate process 62 model existed, Jefferis also used a Kalman filter to provide least-squares optimal estimates of the feed vessel weight. In fermentation, on-line parameter estimation methods, typically, address much more extensive and complicated processes than the simple, small subprocesses that Jefferis considered. Although there are exceptions (such as the work of Staniskis and Levisauskas (1984) that simply used a recursive least squares parameter estimator technique to estimate process parameters, Rolf and Lim (1984, 1985) that applied a recursive least-squares technique that included a forgetting factor to a continuous yeast fermentation; Harmon et al. (1983) that implemented a UDU factorization of a recursive least squares estimator with variable forgetting factor, Wu et al. (1985) that developed a "moving identification" method involving successive least-squares estimations to estimate specific growth rate, and D'Ans et al. (1972) that minimized an error index to estimate substrate yield and Monod model kinetic parameters), based upon the literature reviewed by this (dissertation) research, the vast majority of fermentation process-related parameter estimation appears to have been performed by application of Kalman filter techniques. It also appears, based upon the literature surveyed, that a relationship exists between the amount of experimentation accomplished and the extent to which Kalman filter techniques are applied. Such an observation is not unexpected. Since researchers exclusively performing simulation studies can concentrate on parameter estimation and avoid difficulties associated with measuring state variables by assuming all state variables are measurable, but experimentalists cannot, researchers performing experiments who must estimate both state variables and parameters 63 tend to apply Kalman filter techniques that permit simultaneous estimation of both. Therefore, it is anticipated and appears to be the case that the greater the experimental emphasis of the research, the greater the expectation that Kalman filter methods would be adopted. Although Kalman's first paper on discrete-time, recursive mean-square filter was published in 1960, and its first application seems to have been to an aerospace system in 1961 (Sorenson, 1980), it appears that application to fermentation processes did not occur until the mid-1970's. One of the earliest fermentation applications was reported by Svrcek et al. in 1974 in which the response of cell mass to substrate concentration changes was tracked and in which estimates of three parameters and three state variables were estimated based upon measurements of biomass and substrate concentration. Wang and Stephanopoulos (1984) criticized the approach, however, by noting that the approach was essentially an open loop integration in which the initial estimates by Svrcek et al. were equal to the initial conditions. There was no justification that the filter would ever converge to the true condition given an incorrect initial estimate. Since 1974, the Kalman (or Kalman-Bucy, 1961) filter has been applied frequently to estimation of the parameters and state variables of fermentation processes. These applications have included, among others, Shioya et al. (1982) estimating biomass concentration and chemical oxygen demand from oxygen uptake rate for an activated sludge system, Dekkers (1982) employing measurements of oxygen uptake and carbon dioxide evolution rates to estimate biomass, biomass production rate and the specific growth rate for a fed-batch baker's yeast fermentation, Swiniarski et al. (1982) 64 using extended, stationary extended and adaptive (unknown process and measurement noise covariance matrices are identified) extended filters to estimate biomass and substrate concentrations in a batch cellulose degration fermentation, Yoo et al. (1985) estimating seven parameters of an alpha-amylase fermentation, Montague et al. (1986) estimating biomass from carbon dioxide evolution rate and fermentor volume for a fed-batch penicillin fermentation, Fawzy and Hinton (1980) using unspecified measurements to estimate unmeasurable biomass and substrate concentrations for a single-cell protein process, and Endo and Nugamune (1983) estimating the specific production rate of alcohol based upon unspecified measurement for a batch yeast fermentation. Perhaps the most concerted study by a single individual (or, at least, one of the most published) in applying the Kalman filter to fermentation processes has been that of G. N. Stephanolopoulos: Stephanopoulos and San (1982a,b, 1984), San and Stephanopoulos (1984a,b), Grosz, San and Stephanopoulos (1984), and Wang and Stephanopoulos (1984). Although application of Kalman filtering techniques to fermentation processes must address many problems associated with these processes (not the least of which Jefferis (1979) recognized as being our limited process understanding. Unfortunately, it has been shown that Kalman filter estimation of process states is seriously degraded by inaccuracies in the process model. Thus its use in control may be limited until more accurate models of fermentation processes are developed. The technique can be used with excellent results for the estimation of environmental variables where the processes are physical, rather than biologic, and the models are well known.). 65 Stephanopoulos and his collaborators have argued its superiority over other available methods (such as an integration technique that simply integrates the state equations, accepting RC data as input), and have applied the estimator, with varying degrees of success, to simulations of growth in a chemostat of an organism having assumed characteristics, and to the growth of Saccharomyces cerevislae in fed-batch and continuous culture. Their approach has been to apply an extended Kalman filter (that is, a filter that linearizes the nonlinear estimator model equations around the current estimate) that possesses an adaptive process noise covariance matrix to the estimation of parameters as well as state variables; treating parameters as state variables and, thereby, avoiding the difficulties associated with modeling the parameters in terms of state variables. While, in their development they listed a variety of variables that may be measured and serve as input into the filter, in their fed-batch laboratory study, San and Stephanopoulos (1984a) combined three output variables (oxygen uptake, carbon dioxide evolution and ammonia uptake rate) to obtain three measurements (biomass production rate and substrate and product yields) which were, then, used to estimate six state variables (biomass, substrate and product concentrations, specific growth rate and substrate and product yields). The results of their studies demonstrated good agreement between the estimated and actual (off-line measured/calculated) state variable values, but not significantly improved performance over the integration method that used RC data as input. However, the authors do observe that the simple integration method produces noisier estimates than the Kalman filter making it less suitable for control purposes. 66 Before concluding discussion of Stephanopoulos' and coworkers' study of the the Kalman filter a few additional apsects of their work should be highlighted. First, as originally modeled, parameters were assumed constant (that is, their derivatives with respect to time in the state equations were set equal to zero). The result, expectedly, was slow response in simulations where the parameters in the process model were time-varying. To improve the response of the specific growth rate, the researchers treated the specific growth rate noise as colored noise with a dampening factor (since colored noise alone produced a tendency for the estimate to overshoot). This was implemented by the addition of the state equations, = c + wi(t) (2.42) dt ^ = -CD + w f (t) (2.43) dt where w(t) were white noise processes and D was a dampening factor. (A similar study was accomplished for the yield parameter, but the response was believed adequate for the expected process conditions.) Second, while recognizing the value of including dissolved oxygen measurements into fermentation process estimators to provide mass transfer estimates and improve the accuracy of other estimates (specifically, biomass, substrate concentration, specific growth rate and yield), and having performed simulation studies incorporating suchmeasurements, Stephanopoulos and San (1984a) failed, for undisclosed reasons, to include these measurements in their experimental studies. Third, examination of the sensitivity of the state and parameter estimates with respect to changes in the biomass 67 composition during the growth phase of a cerevisiae fermentation revealed that the changes had little effect on the estimates (less than five percent), so a constant, average composition was assumed (San and Stephanopoulos, 1984a). Fourth, San and Stephanopoulos (1984b) reported that during a washout experiment of yeast from a continuous culture there was a brief period of time in which an instrument malfunctioned. Although the estimates of the Kalman filter appeared to be little affected by the problem, the integration technique that received RC filtered data as input exhibited a marked deviation from the actual biomass, substrate, and product (ethanol) concentrations. To protect the integration technique from similar, future problems, a "data window" was established in which a successive observation was rejected (and the previous substituted) if it differed from the previous by more than thirty percent. (Post-run simulations indicated the approach was effective as, again, the simple integration method's estimates were observed to be comparable to, but much more noisy than, the Kalman filter's estimates.) Fifth San and Stephanopoulos (1984b) provided a detailed study of the acid/base equilibria existent during fermentations that utilize substrates, or produce products that have acidic or alkaline properties (such as carbon dioxide in an aqueous medium). Since pH measurement and control is common in fermentations (often a nitrogen source having acidic/basic properties, such as ammonium hydroxide, is used in pH control and its rate of addition is applied to estimate growth rate), its inclusion in an estimator can be convenient, but can also produce erroneous estimates if the acid/base properties of all species in the fermentor are not considered. Finally, in 6 8 conjunction with Grosz, Stephanopoulos and San (1984) Investigated sensitivity problems associated with inclusion of respiratory and heat evolution measurements in the filter they developed. They confirm, as was previously observed, that singularities can exist in the macroscopic balances associated with these measurements that can eliminate any inherent usefulness. They noted that, because correlations between respiratory quotient and other state variables are close to being a linear combination of the elemental balances and respiratory quotient balance, when the degree of reductance of the substrate is identical to that of products formed or similar to that of the biomass, sensitivity problems arise. In one Escherichia coli fermentation in which acetic acid was a major product it was observed that small pH changes due to imperfect pH control produced oscillations in carbon dioxide measurements which, in turn, produced small (less than one percent) variations in the respiratory quotient that resulted in large variations in the calculated stoichiometric coefficients and estimated parameters (Grosz et al., 1984)! Likewise, the authors report sensitivity problems with the heat evolution measurements due to the linear dependence of the degree of reductance balance (NADH2 balance) and enthalpy balance caused by the fact that the degrees of reductance of most biologically-derived compounds are proportional to their heats of combustion. To avoid respiratory quotient sensitivity problems, the investigators suggested changing fermentor conditions in such a manner to induce production of a product having a degree of reductance dissimilar from the substrate's, and to avoid heat evolution sensitivity difficulties, they recommended substitution of an ATP balance. 69 Measurement error detection. Another approach to improving the quality of process measurements Is through the application of measurement error detection techniques. The application of one, very simple approach to measurement error compensation was described In the previous section as a "data window" (San and Stephanopoulos, 1984b) where deviations that exceeded established limits between two successive data points resulted In the elimination of the subsequent datum by substitution of the previous. Extending this Idea, to measurement error detection would only require generation of an alarm each time a data window Is transgressed. Much greater sophistication In measurement error detection was embodied In a technique proposed by Wang and Stephanopoulos (1983) In which (chi-square) statistical hypothesis testing Is applied to a test function (I.e., the weighted squares of the residuals of the macroscopic balance equations) to detect the existence of gross (as opposed to expected, random) measurement errors. Once detected, the proposal continues, an attempt Is made to Isolate the cause by sequentially deleting measurements to determine which measurement's deletion would have the greatest effect of reducing the test function's chi-square value; the measurement producing the greatest effect, being the most suspect. Beyond these approaches are techniques that apply expert system methods employing quantitative reasoning and knowledge-base heuristics for fault diagnosis (DeBemardez, 1986). CHAPTER III EXPERIMENTAL APPARATUS The experimental apparatus used in this research was an automated, 14-liter fermentor constructed as a part of this research from funds obtained from The Ohio State University Research Foundation by Dr. William R. Strohl of the Department of Microbiolgy and from resources existent within the Department of Microbiology. It is exhibited in Figure 1 of Appendix A. The apparatus had four primary subsystems: the fermentor; the microcomputer; its peripherals ; and associated sensors and actuators. Fermentor The central mechanical component of the fermentation system was a twenty to thirty year old Microferm fermentor (model MF-214, New Brunswick Scientific Company, New Brunswick, NJ). As purchased, the fermentor permitted manual control of agitation and gas flow rates, and temperature. Vessel. The vessel was comprised of a 14-liter glass cylinder (having a height approximately three times longer than its diameter), and a stainless-steel, head plate assemblage (from which extended a turbine shaft and series of metal fins and tubes). With filters attached to the air inlet/outlet lines, and steam-sterilizable probes, rubber stoppers. 70 71 and screw-on cap In place, the vessel became a self-contained unit that was autoclaved in this form. Head plate extensions into the glass container included fins through which cooling/heating water passed, a tube that terminated just below the turbine shaft that permitted the introduction of a gas stream into the vessel, two enclosed tubes for temperature measurement devices, a few, short, open tubes designed to end above the liquid level through which liquid streams may be introduced into the vessel, an open tube that terminated near the bottom of the the vessel, and a turbine shaft capable of accomodating several movable turbines that had a biological isolation coupling to reduce the possibility of contamination. In addition to these extensions, the head plate had an inoculation port (with screw-on cap), and several miscellaneous diameter holes for various probes. Agitation. The microferm fermentor, as originally configured, displayed agitation rate on a tachometer gauge located on the fermentor control panel and permitted manual control of the rate via a 3/4 turn, 0.5 watt, 10k ohm potentiometer also on the control panel. The output from the potentiometer went to an SCR motor controller which was connected to a 1/8 hp direct current motor that had a maximum revolution rate of 1150 rpm; however, the practical limit for the fermentor was closer to 750 rpm. A belt and pressure tubing connector system provided the mechanical connection between the motor and turbine shaft. Since the tachometer was attached to the motor, slippage of the belt or tubing introduced measurment error. Gas flow. To monitor and manipulate gas flow rate into the fermentor, the Microferm was originally equipped with a rotameter-valve 72 assembly that allowed gas rates of up to 20 llters-per-mlnute. One-eighth Inch inner diameter copper tubing conducted the gas from an external source to a port on the control panel. From there, 3/8 inch inner diameter pressure tubing, Goodrich MAXEOON 300, conducted the gas to a filter, then, to the gas port on the head plate. Temperature control. As originally received, temperature sensing and control was accomplished by a thermocouple in conjunction with an on/off relay control system. Output from a thermocouple, located in one of the wells extending from the head plate into the vessel, was directed to an on-off relay control unit attached to the control panel. The controller compared the thermocouple's signal to the signal that represented the desired temperature, as dialed into the temperature potentiometer on the control panel. If the temperature was above the desired, water from the local utility passed through the heat exchange fins in the vessel to provide cooling. If the temperature was below the desired, a solenoid closed off inlet and outlet water lines, a centrifugal pump forced recirculation of the trapped fluid, and a heating coil was activated to heat the circulating water. Microcomputer The central electronic component of the fermentation system was an Apple H e microcomputer (Apple Computer Corportation, Cupertino, CA). Through its particular hardware configuration and custom software, the Apple H e performed a variety of real-time data acquisition, manipulation, display, and storage activities, as well as telecommunication functions. 73 Microcomputer hardware. The Apple lie employed in this research was a 1 MHz, 6502A microprocessor based microcomputer with 128 kilobytes of random access memory (RAM). Although simple in architecture, being of a mid-1970's design with relatively few chips supporting the microprocessor, the microcomputer offered significant system expansion capability through eight slots on the mainboard that provided foreign devices with direct access to the system bus. To support input/output (I/O) through these slots, each slot had access to the two interrupt lines of the microprocessor's bilevel interrupt structure which included a regular interrupt (IRQ) and a higher priority, non-maskable Interrupt (NMI). The 6502 was a microprocessor with an 8 bit data space and 16 bit address space; implying that it was capable of accessing only 64 kilobytes of memory at one time. The computer utilized the 128 kilobytes of memory, 64 kilobytes on-board memory and 64 kilobytes adjoined through the mainboard's auxiliary memory slot, by switching between the two 64 kilobyte banks: viewing only one bank at a time. Additionally, a memory management chip permitted the computer to switch between 12 kilobytes of read only memory (ROM) and RAM, at memory locations DOOO-FFFF hexadecimal, if storage for small, machine-language routines was desired. Unlike many of Its contemporaries that had periodic, hardware-generated interupts to handle I/O, such as reading the keyboard buffer or performing the cursor flash on the monitor, the Apple lie had no such interrupt that could be accessed to provide timing capabilities. To provide such capability, this research designed and constructed a board that was based upon the 555-timer integrated circuit operating in an astable mode 74 with a frequency of 0.74 Hz and a duty cycle of approximately 0.44 percent. When placed in a slot, slot 5 was used in this configuration, and activated, the board would pull the microprocessor's IRQ lines low for approximately 6 milliseconds; forcing the microprocessor to peform a single interrupt whenever the interrupt-mask flag was clear and a non-maskable interrupt was not occurring. The schematic for this circuit is exhibited in Figure 2 of Appendix A. Microcomputer software. Software used in this research was of six, fundamental types: the operating system; the BASIC interpreter; firmware installed on peripherals ; the pseudo-interrpretter of the data acquisition and control unit; user machine language routines; and user BASIC programs. The operating system of the Apple lie, the collection of machine language routines that perform the fundamental operations of the computer (such as input/output activities), consisted of two parts: the system monitor, stored within ROM hexidecimal memory locations F800-FFFF; and the Apple Disk Operating System (DOS 3.3), downloaded from a disk drive into hexidemical locations 9600-BFFF. Portions of page 0, page 1 (the stack), and page 2, were reserved for operating system status and control variables. During bootup, the Apple lie automatically loaded the DOS from drive 1 of slot 6, then, from that drive, loaded and ran the first BASIC program on the disk. (This action was useful in automatic, unattended program restarts after temporary power failures, as will be described in a later chapter.) Apple-disk communications were performed using the non-maskable interrupt. The resident Applesoft BASIC interpreter, a version of Microsoft BASIC created in 1976, was stored in ROM within hexadecimal locations 75 D000~F7FF. It served as the higher-level language that interfaced user-written BASIC language instructions with the machine language routines of the operating system. The interactive interpreter, as compared to compiled or intermediate code, was advantageous in being compact, user-friendly and convenient to debug, but suffered from slow execution. The third type of software utilized in this research was firmware associated with the computer peripherals. The term, firmware, describes the machine language routines stored in ROM located on the peripherals boards that control the operation of the peripheral boards. In the particular instance of the Hayes Micromodem, many of the routines were directly accessible by the user. For example, transmission of specific codes to the modem commanded the modem to perform such activities as dial, wait for a carrier signal, answer a ring, hang-up, or permitted monitoring of transmissions by turning on the modem's speaker. Access to these routines and the soft switches that control the peripherals, and communications between the computer and these peripherals occurred through the CO - CF pages of memory by either BASIC or machine language calls. Firmware installed on the peripherals were not the only means of accessing routines that operated the peripherals, i.e. device handlers. The data acquisition and control device. Cyborg Corporation's ISAAC 91A (Cyborg Corporation, Newton, MA), stored many of its routines in the Apple lie's RAM. Specifically, in the switchable bank of RAM that occupies the same memory space as the Apple's ROM; it occupied hexadecimal locations DOOO-FFFF. Operation of the ISAAC through Applesoft BASIC involved a pseudo-interpreter written for the ISAAC by Cyborg called LABSOFT. LABSOFT 76 commands were "appended" to Applesoft via the ampersand (&) wedge built into Applesoft. Any command that began with an ampersand forced the computer to divert from Applesoft routines to a specially designated section of memory into which were placed user-written extensions to the Applesoft language. Direct access to the primitives that operated the ISAAC was possible through the use of machine language subroutine calls (JSR's). Machine language routines written for this research were developed to support the interrupt generator board, to drive the glucose analyzer, and to provide certain, other timing functions. Interrupt handling routines of the sort necessary to support the interrupt generator board required careful attention to detail, as competition with other IRQ interrupts and with NMI interrupts, suspension of interrupts by routines that disabled interrupts, and bank swapping became inescapable traps for handling routines that lose track of status. The ultimate result of falling victim to such pitfalls included improper program functioning, premature program termination, or, even, complete loss of computer functioning. And, since the IRQ handler was designed to operate the feed pump via the ISAAC binary output device, it was necessary for the handler to kep track of other system components that were connected to the binary output: specifically, the agitation and temperature set-point; stepping-motor controllers ; the acid and base pumps; and the glucose analyzer solenoids. The IRQ handler and other, user-written machine routines were protected from BASIC program and variables space by reducing the size of that space; routines were placed in hexadecimal memory locations 8FD0-95FF. 77 Detailed discussion of other user-written, machine-language routines and Applesoft BASIC programs employed in this research will be deferred to a later chapter. Suffice it to say that, for this research, the BASIC program and variable space has been reduced from its standard 38 kilobytes to approximately 36 kilobytes, due to the reserving of space for machine language routines. BASIC memory, after the modification, extended from 0800 to 8FC0 hexadecimal. Peripherals Five peripherals were attached to the Apple microcomputer for data acquisition, display and storage, and for telephonic communication. For display of current fermentor status, a video monitor was incorporated into the system. For display and storage of historical data, a printer was Installed. Another means of data storage was provided by the two disk drives. A modem and a data acqusition and control unit provided communications to other computers and to system sensors and actuators. The video monitor incorporated into the computer system was an Apple III monitor. Although capable of displaying 80 columns of text, due to the 80 column display and memory expansion card in the microcomputer's auxiliary slot, only 40 column text displays were utilized in this research as a result of limitations of the 80 column mode. Likewise, while graphics displays of 560 by 192 pixels were possible because of the presence of the forementioned card, only displays of 280 by 192 pixels were adopted by this research. Data transmission to the monitor interface had a maximum rate of approximately 1200 characters per second (cps). 78 Hard copy output was provided by a BUFFERED GRAPPLER+ (Orange Micro, Incorporated, Anaheim, CA) Centronics compatible parallel interface with a 16 kilobyte buffer and Okidata Microline 92 dot-matrix printer (Okidata Corporation, Mt. Laurel, NJ). The printer interface occupied expansion slot one in the Apple lie. The data transfer rate to the BUFFERED GRAPPLER+ interface was approximately 1200 cps, while the printer output was approximately 160 cps in the normal printing mode. Data display consisted of standard text characters in a stripchart format. A reduced character size was adopted in which characters were compressed to provide 136 columns of text with line advances of 4/144 inch. Access to telephonic communication was made possible by the addition of a Hayes Micromodem lie (Hayes Microcomputer Products, Incorporated, Atlanta, GA) into expansion slot two. The modem supported many of the standard handshake protocols and could operate in either a half or full duplex mode. While capable of transmitting at several different baud (bits per second) rates, its maximum rate was 300 baud (or 30 to 40 cps). Permanent data storage was provided by an Apple DuoDisk (Apple Computer, Incorporated, Cupertino, CA). The DuoDisk was a two, 5-1/4 inch, single sided-single density, floppy disk drive unit that had a storage capacity of approximately 160 kilobytes per drive. The controller card for the disk drives was located in expansion slot six of the Apple lie's mainboard and was capable of transferring a maximum rate of 9600 cps to the disks. The DOS 3.3 operating system was a rudamentary operating system limiting the storage capacity of an individual file to a maximum of 32 kilobytes and not providing error checking services for many disk problems 79 such as bad sectors. Data acquisition and control was accomplished by the ISAAC 91A (Cyborg Corporation, Newton, MA), that Interfaced the fermentation system's sensors and actuators with the Apple lie through the Apple's number three expansion slot. The ISAAC was an expansible, flexible, moderately high-speed data acquisition and control device that was capable of accessing and generating a variety of analog and binary signals, and provided calendar and tlme-of-day functions to the microcomputer. Physically, the ISAAC consisted of an Interface card that was connected to the main card cage from which extended a smaller card cage that housed a low-level signal conditioning unit; all of which were connected by ribbon cable. (Sensors and actuators, subsequently, were connected to the card cages by RG type 58/U coaxial cable or stranded 18 guage, shielded cable In lengths of less than fifteen feet.) An additional connection to the Interface card was a line that provided battery backup to the tlme-of-day clock/calendar. Other than this battery power to the clock/calendar, all ISAAC power came from the Apple lie. In the configuration adopted for this research, the analog-to-dIg1ta1 converter (ADC) of the ISAAC mainboard provided sixteen single-ended, 0 - +5 volt analog Inputs. The ADC performed Its conversion by successive approximations, having a maximum sampling rate of approximately 600 Hz with a 12-blt (0.025 percent of full scale) resolution and accuracy of +0.05 percent of full scale. Low level, -100 - +100 millivolt, signals were acquired by an I-130/I-140A preamp expansion to the ISAAC. The I-140A channel selects one of four differential Inputs and amplifies the Input 80 signal to a -5 - +5 volt signal which is, then, converted by the 1-130 to a digital signal and transmitted on the ISAAC data bus. As did the main unit, the low-level signal conditioner subsystem accomplished its conversions by successive approximations and had a 12-blt resolution. However, unlike the central unit, the subsystem had a maximum sampling rate of approximately 280 Hz with an unspecified, greater then j^.03 percent, accuracy. The ISAAC mainboard contained four ladder-type, 12-blt resolution dlgltal-to-analog converters (DAC) that had j^.05 percent accuracies over their 0 - +5 volt ranges. The maximum current these DACs were capable of outputting was +5 mllllamperes. Although capable of transmitting and receiving digital (0 - +5 volt, transistor-transistor level, TTL) signals, this research utilized only the binary output subsystem (to activate relays). The ISAAC provided two output stages each of which had eight binary outputs In the subsystem. Each output carried a maximum of 2.6 mllllamperes at 3.1 volts for binary high signals and 20 mllllamperes at 0.5 volt for low binary signals. Transition time between the two states was less than fifty nanoseconds. One additional subsystem was used in this research: the counter subsystem. The counter subsystem was capable of accepting seven channels of TTL Input and one channel of ^100 millivolts to +50 volts of input, which were multiplexed Into a single counter. The TTL channels required +2 - +5 volts/20 microamperes for a high and 0 - +0.8 volt/400 microamperes for a low. Acceptable count frequencies ranged from 0.5 Hz to 10 MHz (fifty percent duty cycle); however, the maximum counter value was 65535. The counter was somewhat unusual among the ISAAC devices In that, since the only 81 software-directed operations the user could perform was to select a channel or reset the counter, the counter continued to collect and store information, counts, after the LabSoft commands had been accomplished. For completeness it should be mentioned that the ISAAC had other subsystems. It had a battery powered clock/calendar that provided hour, minute and second, and year, month, day-of-week, day-of-month information that was used by this research. It also had a millisecond timer, audio generator and Schmitt trigger subsystems that were not utilized by this research. The functioning of the Apple-ISAAC 91A system may be described by a simple command-wait-respond model. That is, the Apple transmits a command to the ISAAC, then, if the command requires a response (as it does for binary and analog input). It suspends program execution and waits for the ISAAC'S response. For most activities, this wait is only a few milliseconds; however, for triggerred ("&LOOK FOR...THEN...") actions this wait may be hours. Although simple, this approach is potentially inefficient, especially when compared to command-continue-interrupt-respond or command-continue-store response models in which the computer continues its execution after sending the command, stopping to receive its response only after the response has been prepared. The only ISAAC devices that are capable of collecting data simultaneously with Apple program execution are the real-time clock, Schmitt trigger, and the counter subsystems, but these only maintain simple time, and change of state data. It is apparent, then, ISAAC functioning is capapble of placing a heavy load on the Apple. 82 Sensors and Actuators As described previously, the MicroFerm fermentor, in its purchase configuration, had three sensors and three control elements. Two of the sensors, a gas flowmeter and agitation tachometer, had outputs that were accessible to the operator, while the third sensor, a thermocouple, sent its output to the temperature controller exclusively. Similarly, only two of the three control elements could be manipulated directly (manually); those were a valve on the flowmeter and a potentiometer (connected to the motor control circuit) that manipulated the revolution rate of the turbine. The third control element, the heating coil of the temperature control system, could not be manipulated directly, but was adjusted by the temperature controller. Of course, however, the operator was able to manipulate the setpoint of the temperature controller. To further instrument and automate this fermentor, this research added several new sensors and actuators. Off-gas analysis was made possible by the addition of oxygen and carbon dioxide analyzers, mass flow meters and a manometer. Instrumentation to provide liquid analysis included pH, foam, glucose, turbidity, dissolved carbon dioxide and dissolved oxygen probes and meters. Devices to measure temperature, agitation and glucose feed flow rates were also included. Actuators that were added included: stepping motors and stepping motor controllers to automatically manipulate the agitation rate and the temperature controller setpoint; air flow rate controllers ; and eight solid-state relays to power various liquid feed pumps. Performance characteristics of these devices are presented in Table 1 at the end of this chapter. 83 Oxygen off-gas analysis. Analysis of the oxygen concentration in the inlet and outlet gas streams was performed by Sybron's Servomex^^) model llOOA Oxygen Analyzer (Sybron Corporation, Boston, MA). The analyzer was comprised of two flowmeters (one for dry sampling, the other a bypass), a transducer unit, and a pressure compensation device. Oxygen concentration measurement by this analyzer was based upon the paramagnetic property of oxygen; a property that it shares with only three other common gases: nitric oxide (NO); nitrogen dioxide (NO2); and chlorine dioxide (CIO2). The oxygen transducer contained two glass spheres filled with nitrogen that were attached to the ends of a bar, positioned in a symmetric, non-uniform magnetic field. In such a configuration, the diamagnetic nitrogen impelled the spheres away from the strongest part of the field. This displacement increased when the spheres were surrounded by a medium with paramagnetic properties, as the attracted paramagnetic medium would concentrate in the field, inducing the spheres to move farther from the field. The strength of the torque created by the presence of the paramagentic fluid was a function of the paramagnetism, i.e. oxygen partial pressure, of the medium. The Servomex Oxygen Analyzer measured this torque by means of a null balancing technique, in which it created a counteracting torque to restore the bar to its original position and, concurrently, measured the strength of that reverse torque. Since such analyzers measure oxygen partial pressure, not concentration, the units used in this research had pressure compensation devices installed to account for changed in barometric pressure. In addition, the analyzers had internal temperature sensors and heaters maintained a thermal equilibrium within the units. 84 Carbon dioxide off-gas analysis. Carbon dioxide off-gas analysis was accomplished by HORIBA's MEXA 211E Carbon Dioxide Analyzer (HORIBA Instruments, Incorporated, Irvine, CA). The principle underlying the operation of the carbon dioxide analyzer was non-dispersive infrared absorptiometry. Specifically, pulsed, infrared radiation from dual infrared sources passed through juxtaposed cells: a sample cell; and a reference cell. Each cell was fitted with a solid filter that removed interference from sample gas components that absorbed at wavelengths close to those being observed for carbon dioxide. At the end of the cells, a condenser microphone detector measured the energy difference between the radiation reaching it from the sample cell and the reference cell; this difference signal was proportional to the carbon dioxide concentration in the sample cell. Beyond these devices, the carbon dioxide analyzer had circuitry that provided additional compensation for Interference from coexistent gases and external influences, such as vibration, and it had an internal pump to promote movement of gases through the sample cell. This pump was never used, however, as the pressure from the fermentor was adequate to move the off-gas stream through the analyzer. Fermentor pressure measurement. To provide an estimate of the pressure within the fermentor head space, a mercury manometer was connected at times to a glass T-tube located just upstream to the inlet air filter and at other times to the exhaust of the hypochlorite, outlet gas sterilization solution flask just downstream of the condenser. The manometer was constructed simply of a meter stick, two, one-quarter inch straight glass tubes connected by synthetic tubing, an overflow bottle, and a wooden 85 support. To prevent possible mercury contamination, the manometer was connected to the fermentor only when pressure measurements were taken. Connection and measurement, of course, was accomplished manually. Gas flow rate measurement. The fourth and final gas stream sensor of the automated system was the Tylan Mass Flowmeter (Tylan Corporation, Carson, CA). The operation of the Tylan Mass Flowmeter was based upon thermodynamic principles. A portion of the gas passing through the meter was diverted through the flow sensing element. The flow sensing element consisted of a stainless steel sensor tube around which was wound two, heated, resistance thermometers, each capable of dissipating 40 milliwatts. As gas passed through the sensor element, heat was transferred from the upstream to the downstream thermometer. The temperature difference between the two thermometers was a function of the flow rate and physical properties (specific heat capacity, and viscosity, among others) of the gas stream. Each thermometer, then, was a component within a bridge and amplifier circuit that output a 0 to 5 volt direct current signal that was proportional to the gas flow rate. The units used in this research were calibrated to air under conditions of standard temperature and pressure in units of liters per minute. The properties of nitrogen and oxygen are quite close to those of air, so that, for streams containing essentially nothing except these gases, no adjustment of the meter output was required. However, other gases, such as carbon dioxide, or water vapor had significantly different properties which required adjusting the meter reading. For example, carbon dioxide had a correction factor of 0.74 compared to nitrogen. Meter output went to both an ISAAC analog-to-digital converter 8 6 channel and to a Tylan PS-14 Readout Box which provided power to the meter and a digital, light emitting diode display of the gas flow (expressed in standard liters per minute). The mass flow sensor was constructed of 316 stainless steel. pH measurement. Several probes and meters were incorporated into the experimental apparatus to monitor conditions within the fermentation broth. To measure the pH of the medium, the system employed a Fisher Scientific Gel-Filled pH Electrode (Fisher Scientific, Lexington, MA) coupled with a B. Braun Instruments MRRl pH Meter Module (B. Braun, South San Francisco, CA). The probe's structure consisted of an interior glass element containing a silver/silver chloride electrode that had an exterior epoxy sheath which held, in a gelled 4M potassium chloride medium, another silver/silver chloride electrode. The pH sensitive glass membrane projected through the epoxy sleeve at the tip of the probe to provide contact for it with the broth, while a porous plug in the side of the probe permitted contact for the other electrode. The pH probe was sterilized by immersion in a hypochlorite soluion prior to installation in the fermentor. The signal from the pH probe was amplified within the Braun pH meter by two, sequential, fully integrated operational amplifiers. Manual temperature compensation, as well as slope and offset correction were provided by the meter through potentiometers on the front panel of the pH meter module. The design of the Braun unit was based upon technology available in the late-1970's. 87 Dissolved oxygen measurement. Measurement of the dissolved oxygen tension of the fermentation broth was accomplished by an Instrumentation Laboratory Oxygen Sensor (Instrumentation Laboratory, Incorporated, Andover, MA) coupled with a Braun MRRl Oxygen Meter Module (B. Braun, South San Francisco, CA). The dissolved oxygen probe was a constant potential, polarographic oxygen sensor containing a silver/silver chloride anode and platinum cathode surrounded by a semipermeable membrane. The stainless steel mesh, reinforced composite membrane permitted oxygen transfer from the fermentation broth, while prohibiting the movement of proteins, ions and other chemical species that could have interfered with the measurement. A common, interfering molecule that it was not capable of excluding, however, was sulfur dioxide. The stainless steel encased sensor sensor was designed to be steam sterilizable at 120°C for 20 minutes. Current from the dissolved oxygen probe was amplified by a multistage, monolithic integrated operational amplifier within the Braun Dissolved Oxygen Meter Module designed in the late-1970's. The front panel of the module contained potentiometers that allowed for manual zero point adjustment and slope (gain) adjustment and a switch to select from three measurement ranges. In addition, the module's circuitry provided temperature compensation. Dissolved carbon dioxide measurement. A steam-sterilizable Ingold Type 780 Carbon Dioxide Probe and complementary Type 781 OO2 Amplifier (Ingold Electrodes, Incorporated, Andover, MA) made possible measurement of the carbon dioxide partial pressure of the fermentation broth. The carbon dioxide probe was, essentially, a potentiometric electrode consisting of a cylinder within a cylinder. The inner cylinder was a silver/silver 8 8 chloride, glass membrane pH electrode, while the annulus contained a silver/silver chloride reference electrode In a bicarbonate solution. A gas-permeable, silicone membrane at the tip of the probe permitted transfer of gases between the fermentation medium and the electrolyte In the annulus. In operation, to equilibrate with the broth, carbon dioxide diffused through the membrane to/from the bicarbonate-contalnlng electrolyte. The effect of this transfer was to shift the C02/HC03~,H"'’ equilibrium of the elctrolyte towards the right/left In accordance with the following reaction, COg + HgO ^ HCO3 + H"'" (3.1) thereby, altering the pH of the of the electrolyte. The consequent change In pH was measured, then, by the pH electrode. The design of the probe permitted convenient, on-line recallbratlon of the probe (I.e. pH electrode) by permitting the electrolyte within the annulus to be easily removed and replaced by standard buffer solutions. The carbon dioxide meter was an Ion meter calibrated In mlllbar carbon dioxide with three potentiometers on Its control panel for manual temperature compensations, slope adjustment (mllllvolt/pH) and slope asymmetry. In addition, a switch provided for scale (range) selection from four ranges. Measurement "Interference" to this probe originated from two sources : the presence of free ammonia or volatile organic acids In the broth that could pass through the probe's gas-permeable membrane and shift the electrolyte equilibrium; or changes In the fermentation medium that could Influence the broth's [pCX)2]/[CX)2]/[HC03] relationships. This second source of "Interference" relates to the fact that the carbon dioxide probe measures the partial pressure, not 89 concentration, of carbon dioxide. Partial pressure and concentration are related by Henry's law, [COg] = a • pCOg (3.2) (where, a, is Henry's law constant). Since the coefficient, a, is dependent upon temperature and solution components and concentrations, and since the composition of the fermentation medium and bicarbonate-containing electrolyte are not the same, the values of the coefficients of the two solutions differ. As a result, this difference and changes in it over time must be accounted for when determining the carbon dioxide concentration in the broth. An advantage of the design of this probe is its relative insensitivity to membrane deposits, in that such deposits may reduce its respone time, but will have little influence upon the accuracy of its measurment. Foam control. Foam control was achieved independently of the system computer by Braun foam probes and MRRl Foam Control Module (B. Braun, South San Francisco, CA). Two stainless steel, autoclavable foam probes provided contacts for the Foam Control Module through which conductivity measurments of the medium were made. The controller within the module was an electronic pulse interval controller. Module operation was modified by three potentiometers (or, "pots") on the module's frontplate: one pot input a selectable delay into the controller (the delay required foam to be present at the beginning and end of a finite delay, to prevent antifoam addition due to momentary splashes); another pot provided for insertion of a preset interval between antifoam addition and resumption of foam monitoring (since 90 the antifoam required a significant amount of time to act upon the foam); the third pot established the duration that the antifoam pump would operate (the antifoam pump received power from a 120 volt electrical outlet at the back of the MRRl unit). Glucose analyzer. Automatic glucose analysis was performed by a prototype glucose ana'.yzer being developed by Yellow Springs Instrument Company (Yellow Springs, OH) in collaboration with W. R. Strohl (Department of Microbiology, The Ohio State University, Columbus, OH). The analyzer was based upon the YSI Model 27 Industrial Analyzer, incorporating the same probe, stirring pump, signal conditioner, buffer pump, and sample chamber/temperature block as the Model 27. In addition to these components, however, the automatic analyzer included a sample/calibration-standard withdrawal pump, a pulse dampener, and a two position/two chamber valve having three inlet and three outlet ports. The three ports were connected to the carrier buffer stream, the sampler, and the calibration standard reservoir. The valve was designed so that both chambers had a volume of 75 microliters which, when filled by the withdrawal pump and switched into the carrier stream, delivered the correct volume of sample or calibration standard solution to the probe. Power for the solenoids that drove the pumps was provided by an ac/dc Electronics (Emerson Electric Company, Oceanside, CA) Model ECV12N1.7, 12 volt, 1.7 amp regulated power supply. Power for the valve solenoids came from a 48V, 2.0 amp brute-force power supply constructed as a part of this dissertation research. Each solenoid received its power by route of a Potter & Brumfield (Princeton, IN) 0DC5 solid state relay in the form of 1 Hz, 10 percent duty cycle pulses that 91 orginated In signals from the ISAAC binary output subsystem. Since the machine language program controlling the relays was written based upon a positive true logic assumption, but the 210-4A had negative true logic, 2N2222 transistors were employed to invert the control signal from the ISAAC. Output from the glucose analyzer was in the form of an 0-200 millivolt signal (over 0-20 grams glucose per liter) from the signal conditioner. Adjustment of the gain of the conditioner's amplifiers, however, resulted in a 0-70 millivolt signal that was acceptable to the ISAAC'S low-level ADC. There were two major design problems that had to be resolved before this research was able to use the glucose analyzer. The first was construction of an improved pulse dampener in the carrier line. The dampener that was received with the instrument was nothing more than a length of wound tubing, and was relatively ineffective. Evidence of this was provided by measurement errors of 25 percent with ADC conversion rates of 20 Hz, due to sample peaks passing too quickly to be consistently captured by the ADC. To provide increased dampening, a small piece of sponge from a household dish-cleaning implement was placed inside a one-inch length of 1/8 inch inner diameter, 1/16 inch wall, amber latex tubing (VWR Scientific, San Fransisco, CA). Measurement errors of less than one percent were observed immediately after incorporation of the new dampener. The second major design problem involved construction of a sampler from which the analyzer would receive samples to be analyzed. The design adopted was comprised of three principal elements: a recycle stream with a high flow rate; an aseptic filter; and a small-volume reservoir that would 92 permit escape of gas bubbles and from which the analyzer would sample. To generate the suction required to draw and recycle broth from the fermentor, a Harvard Model 1203 Peristaltic Pump (Harvard Apparatus, South Natick, MA) was used in conjunction with 1/4 inch inner diameter silicone tubing (Cole-Palmer Instrument Company, Chicago, IL). Reservoir construction simply consisted of a 10 ml vial with three lengths of 1/8 inch inner diameter (ID) glass tubing protruding down from its cover. One tube reached the bottom of the vial and provided filtrate to the reservoir, another also reached the bottom and led to the analyzer, while a third terminated ca. 1/4 inch below the cover and was connected to a Masterflex (Cole-Palmer Instrument Company, Chicago, IL) model 7543-30 peristaltic pump which withdrew excess fluid to protect the vial from overflow. The third component, the filter, was the most difficult to select. The first filter tested was a 0.2 micrometer pore size, Minikros Model S314, KF-200-003 Hollow Fibre Microfiltration Module (Microgon, Incorporated, Laguana Hills, CA). Since it was not autoclavable, sterilization consisted of rinsing the filter with a hypochlorite solution. Unfortunately, the small radius of the hollow fibers was unable to accommodate C5 pellets and the filter quickly clogged. The second filter evaluated was a Nuclepore 90 millimter Radial Flow Cell (Nuclepore Corporation, Pleasanton, CA) with a 10 mil gap and holding a 0.45 micrometer pore size cellulose nitrate membrane (Micro Filtration Systems, Model A045A090C). Although apparently capable of handling dilute C5 suspensions, it seemed to have difficulty with air bubbles which resulted in shunting of fluid through the membrane. Ultimately, the recycle loop required much pressure, but gave little recycle 93 as most of the fluid appeared to move from the filter inlet to the filtrate, and not to the filter cell-side outlet. A third filter was devised based upon the hydrophobic Aero 50 (number 4251), 20 square centimeter, 0.2 micrometer pore-size filter (Gelman Sciences, Ann Arbor, MI). A 3/8 inch glass T-tube was inserted into the fermentation broth recycle line. Onto the T-tube, an Aero 50 filter with a cloth, "prefilter" over its inlet was connected using silicon tubing. The filter outlet was, then, connected to the sample reservoir. After autoclaving, but before connection to the system, the Aero 50 was rinsed with an organic solvent (specifically, ethanol) to permit its use with the aqueous fermentation broth. Pressure required to force fluid through the filter was provided by a screw clamp located downstream side from the filter. Since only moderate pressures were required, the recycle flow rate was relatively high, of the order of 100 milliliters a minute. Although placement of the T-tube with the right-angle leg pointing towards the ground essentially eliminated bubbles reaching the filter, cells tended to accumulate in the space between the filter and T-tube. These were eliminated by squeezing the silicon tubing connecting the T-tube and the filter. Results obtained from use of the Aero filter indicate that elimination of the sample reservoir (and with it an estimated 6 minutes of dead time) might be possible, and that a smaller, hydrophilic filter might be preferable. Turbidity measurement. Turbidity measurements taken at 600 nanometer wavelength were automatically accomplished using a Spectronic 21 spectrophotometer (Bausch & Lomb) with a 1 milliliter flow cell. 0 - +1V output from the spectrophotometer was acquired from recorder jacks at the 94 rear on the instrument. C5 pellets tended to clog the flow cell. Glucose feed rate measurement. Although automatic gas flow rate measurement devices were available for incorporation into the fermentation system, no such device was available for liquid flow rate measurement. To provide an estimate of the glucose feed flow rate, a 5 millilter graduated pipette was placed on the glucose feed line through the use of a glass T-tube. Flow rate measurements, then, were accomplished by removing the clamp on the latex tubing that connected the T-tube and pipette, drawing feed into the pipette using a pipette bulb, clamping off the upstream feed line, turning on the feed pump and measuring the rate at which fluid was drawn from the pipette. After the measurement, the clamp was removed from the feed line and replaced on the pipette line. Temperature measurement. Although broth temperature could have been acquired from an existent device, the thermocouple of the fermentor"s temperature controller, a simpler and more flexible approach was adopted: an Analog Devices (Norwood,MA) AD592CN precision integrated chip, temperature transducer was incorporated into the system. The chip, which provides an output current proportional to absolute temperature, was placed in series with a 1 kiloohm resistor. With the chip's (+) terminal connected to the ISAAC'S +5 volt source by route of an eight foot long, shielded cable and its negative terminal connected to the resistor which was connected to the ISAAC analog ground, an ISAAC analog-to-digital converter channel was connected to the junction of the chip and resistor. Voltage measurements at the chip-resistor junction, then, were proportional to medium temperature changes with a one degree Celsius temperature change resulting in 95 approximately a one millivolt potential change. Physical protection of the chip from the environment of the thermometer well in which it is seated during fermentations is provided by a thin silicon sealant coating. With an maximum error of one degree Celsius over the range -25®C to 105°C, the accuracy of the chip exceeds the resolution of the supporting devices. Agitation rate. Monitoring of the agitation rate was accomplished through the application of a device custom-designed for this research. The device utilized a transparent disk that has an 1/8 inch opaque strip extending from its center to its edge to break the infrared beam of an optical switch which, thereupon, sent a signal to the ISAAC'S counter. The disk was placed on an short extension to the drive element that coupled the belt to the impeller of the fermentor; thereby, making the sensor immune to belt slippage error, but not to error cause by slippage of the impeller's coupling. The optical switch, consisting of a light emitting diode/phototransistor pair, Honeywell (Minneapolis, MN) SPX1873-11, acted in such a manner that, when the opaque strip transits between the emitter/detector, a low voltage is indirectly transmitted to activate a 555 timer (Radio Shack 276-1723). The timer output changes state for approximately 20 milliseconds (to lock out possible, erroneous, multiple activations), then returns to await another transit. This action permits the sensor to detect rotation rates in the 50 - 1000 rounds-per-minute (rpm) range. Noise from the drive motor at rotation rates greater than 400 rpm, on occasion, have produced erroneous agitation rate measurements, so that shielded cable was required to protect the device's signal. 9 6 Stepping motor actuators. Essentially three types of actuators were incorporated into the experimental apparatus; they included; two stepping motors and controllers; air flow meters ; and a "relay box" containing eight solid state relays. Prior to this research, manipulation of the agitation rate was accomplished by Titus et al. (1984) through the use of a servo (of a type commonly found in radio-controlled model airplanes boats and so on) attached by latex tubing to the fermentor's motor-control potentiometer. Although a creative, inexpensive solution to automating the motor-controller, the servo had two major deficiencies: it only had a 120° angle of rotation (which was equivalent to about a 200 rpm agitation range); and its coupling to the motor-controller's potentiometer exhibited considerable "play" (that is, when the servo would reverse direction, the elastic tubing would require some rotation just to increase its tension to the point of overcoming the pot's internal resistance). A search for a computer controllable, solid-state device to replace the potentiometer was fruitless, due in part to the unusual, alternating-current signals passing through the pot. So, as an alternative, it was decided that a stepping motor with an inelastic, tight coupling would be added to the system. The ElectroScience Laboratory of The Ohio State University was called upon to construct a suitable device. And, since the additional cost for another such controller was relatively small, it was decided that a similar unit would be prepared for the set point potentiometer of the temperature controller. Ultimately, the ElectroScience Laboratory created two stepping motor units that were attached to ten-tum potentiometers of the appropriate resistance range and Wattage, that, in turn, were connected in parallel to 97 the existent pots on the fermentor's control panel. Selection of manual (fermentor control panel) or automatic (computer) control was available for each unit through a double pole, double throw switch. The stepping motors, controllers, power supply, potentiometers and switches were placed In/on a metal housing. Computer manipulation of the stepping motors occurred through the use of three binary Input/output lines for each stepping motor: the voltage level of one line determined the direction of turn; a rising edge on another line latched the direction; and a pulse train on the third line stepped the motor. Gas flow controllers. The experimental apparatus Incorporated two different devices for controlling gas. I.e., air or oxygen, flow through the vessel. The first device was a needle valve driven by a synchronous motor located In the Braun MRRl Oxygen Control Module. The Oxygen Control Module was Initially configured to take 0 -- 5 volt output from the Oxygen Meter Module, compare It to the set point set In on a dial on the front of the Oxygen Control Module, and, through the application of a proportional-integral scanning controller, vary the valve position In response to the observed error. In operation, the valve's motor would turn at a constant speed. In the appropriate dlrecton, for a duration that was a function of the observed error. Unfortunately, the unit's operation suffers from two serious deficiencies: the flow response Is not linear to the error (ten seconds of valve movement In the lower range may result In a 0.5 llter/mlnute change In flow at the lower extreme, while providing a 10 llter/mlnute change at the upper extreme); and mlcroswltches Installed to protect the valve from damage due to excessive turning, prevent the unit 98 from operating in both directions at its extreme positions (for example, the valve will not permit a direct one liter/min decrease in flow at its upper extreme; instead, it requires a transition down three liters/minute then an increase of two liters/minute to accomplish the change). The needle valve's major advantage, however, is its ability to maintain its last position during a power failure. The Oxygen Control Module's front panel provides two features in addition to set point selection: manual control of valve position through the use of two pushbuttons; and a potentiometer that permits adjustment of the unit's sensitivity. The valve was constructed of acid-resistant, stainless steel, and, provided a flow rate range of 0 to 14 liters/min at one atmosphere (with a maximum input pressure of 6 atmospheres). To match the voltage level of the computer interface and permit its insertion into the Braun's dissolved oxygen control loop, a voltage inverter was installed in the Oxygen Meter and Control Modules (Titus, et al.; 1984). The second type of gas flow controller installed in the experimental apparatus was a Tylan Mass Flow Controller, model FC261, 0.4 - 20 standard liters/minute. The Tylan controller functioned by comparing the signal from its flowmeter, previously described, with a 0 - +5 volt set point signal on pin A of the AMP583853-5 connector. Normally the value of this voltage was manually asserted through the R020A Readout Box; however, in constructing the experimental apparatus that line was broken and substituted a control signal from an ISAAC digital-to-analog converter line. The error signal from the comparison varies the voltage supplied to the heater element of a thin-walled tube that had a ball (or cone) at the end. Increases in 99 temperature caused the tube to expand; thereby, forcing the ball (or cone) into the surrounding tube and decreasing the gas flow. This thermal expansion design, involving maximum ball travel of 0.003 inch, effectively eliminates deadband and hysteresis effects common to other gas flow controllers. Unfortunately, a disadvantage of this approach was that power failures resulted in the valve movement to a maximum gas flow position. Power for the operation of the valve was provided by the +15 volt power supply of the Tylan Readout Box. Relay box. Several liquid streams were introduced into the experimental apparatus during the course of a fermentation. Despite alternative means, flow rate manipulation of these streams by the computer was accomplished by eight solid-state relays contained within a single enclosure or "relay box" (Titus et al., 1984). Manipulation of acid and base addition to control pH was available through the pH Control Module of the Braun MRRl, or through use of a solid-state relay. The pH Control Module, as modified by addition of a voltage inverter by Titus et al. (1984), accepted a 0 - 5 volt, direct-current input signal, compared the signal with a set point value dialed in on a potentiometer on the front of the module, and would activate an internal relay to provide 115 volt line current to the appropriate (acid or base) pump. Manual activation of either relay/pump also was available via two pushbuttons on the face of the module. With potential equivalents of 0, 1.5 and 5 volts for pH values of 2, 7 and 12 from the set point potentiometer, the controller acted in a proportional-integral mode to add acid if the control signal from the computer was greater than the potential 100 from the set point potentiometer and to add base if the signal was less. Unfortunately, this design had two significant flaws: first, the gain of the controller was excessive, which resulted in excessive volumes of acid and base soution being added; and, second, the controller acted in such a manner that the appropriate pump was activated for variable durations (short for small errors, longer for large errors), but the integral action of the controller made it impossible to estimate how long the pumps were on or how much solution was added. However, calibration of the acid and base pumps and use of two relays from the relay box permitted the computer to manipulate acid and base solution additions with a more correct estimate of the volumes that had been introduced into the fermentor. Nutrient feeds, including carbon source, nitrogen source and salts, and magnesium sulfate, that were autoclaved and maintained separately to prevent complexing and caramelization prior to introduction into the vessel, could have been fed either through emloyment of a variable speed pump or by variable-duratlon, on-off control of a single speed pump. Two Masterflex (Cole-Palmer, Chicago, IL) Model 7534-30 variable speed pumps having a 0 - 5 volt input range and providing ca. 0 - 400 milliliters/minute flow rate range were available to provide variable speed facility, while several Harvard (Harvard Apparatus, South Natick, MA) Model 1203 pumps having manually selected rates of 0 to 200 milliliters/minute were available for relay control. The Harvard pump/relay alternative was chosen for this research because of reported (Gregory Luli, personal communication) recalibration requirements of the Masterflex during fermentations due to ground drift problems. 101 The relay box was of local design and fabricaton (Titus et al., 1984) consisting of eight Potter & Brumfield (Princeton, IN) 0AC5 solid-state relays on a 210-8 mounting board. Normally capable of being driven by the binary I/O channels of the ISAAC, the light-emitting diodes (LED) on the mounting board were replaced by LED's that were mountable on the front of the enclosure. Due to an internal resistor, the new LED's required more power than the ISAAC'S binary I/O could provide, so the binary channels were used to drive transistors that switched on/off current from a Emerson Electric Company (Oceanside, CA) AC/DC Model ECV5N6-1 5 volt, 6 amp power supply. The power supply, then, drove the solid-state relays. To permit manual control of the relays, each relay had, in parallel to the binary I/O-transistor line, a direct line to the power supply. Selection of an open circuit, binary I/O, or direct connection to the power supply was provided by a double pole, triple pole switch mounted on the face of the enclosure, under the related LED. Use of the Potter & Brumfield solid-state relays having a maximum input rating of 35 railliamperes at 32 volt direct-current and a maximum load rating of 3 amperes at 140 volt alternating-current provided significant protection for the ISAAC circuitry: >3000 volts peak-to-peak noise immunity and isolation of 4000 volts root-mean-square. Auxiliary Devices In addition to the devices already described, the experimental apparatus was comprised of several other miscellaneous pieces of equipment such as an air conditioning subsystem, and various tubing, pumps, stir plates and so on. 102 Air conditioning subsystem. The humidity of the air passing through the experimental apparatus was Important for two reasons. First, compressed air entering the fermentor was cooler and less humid than that exiting the fermentor; typically entering with a relative humidity of ca. 60 percent, while leaving the fermentor nearly saturated. At a flow rate of ten liters per minute over the period of twenty-four hours such conditions resulted In a two to three tenths of a liter water loss from the fermentor each day. Second, the Instruments performing off-gas oxygen and carbon dioxide analyses were adversely affected by high humidity. To reduce the water loss from the fermentor and the effects of humidity upon the off-gas Instruments a simple air conditioning system was Installed. To Increase the temperature and humidity of the air entering the fermentor, the air was first bubbled through a sterile, heated, dlstllled-water reservoir consisting of a 4 liter pyrex bottle with rubber stopper closure seated on a Fisher (Springfield, NJ) Thermlx Model 2101 stirring hot plate that was positioned to Its lowest heat setting. Contrarlly, to decrease the moisture content of the off-gas stream before reaching the Instruments, a sterile, 18-lnch glass condenser fitted with rubber stopper closures at both ends and connected to a Haake Model G cooler with Model G1 recirculator (Haake, Berlin, Germany) was placed at the exit gas port. Condenser cooling fluid was maintained by the recirculator at 15°C. Condenser condensate was collected In a 500 mlllllter flask, which. In turn, was connected to a flask containing a hypochlorite solution from which a small side stream of gas escaped. For additional humidity protection, a twelve-inch long, one-inch diameter tube of deslccant was also placed In the off-gas line. 103 Miscellaneous components. Although less desirable than stainless steel tubing, all gas lines to and from the fermentor were composed of synthetic tubing. The reasons for this were expense and convenience. Stainless steel tubing of the appropriate size could only be purchased in quantities far in excess of the laboratory's needs, which, considering the expense of the material, was unacceptable. Although stainless steel is rugged, the connections to the fermentors and the instruments are frequently broken to permit autoclaving of the fermentors and reconfiguration of the instruments. Under these conditions, standard stainless steel connectors would be inconvenient to use, install, and replace, and would be subject to damage from inexperienced users. Unfortunately, as a result of using synthetic tubing air lines (principally, 1/4 inch ID, amber, latex tubing from VWR Scientific, San Fransisco, CA, and Tygon tubing from Norton Company, Akron, OH) and rubber stopper closures in the fermentor head plate, gas leaks of more than 10 percent have been observed between the inlet and outlet gas flow meters. Attempts to reduce the air loss by sealing the rubber closures with silicone cement, and by seeking other leak sites did not eliminate the leaks. Downstream of the outlet gas flow meter, additional sites at which losses were possible included junctions with instruments, and connections with glass T-tubes, teflon valves and the desiccant tube. Several types of pumps, at various times, were incorporated into the experimental apparatus. As was previously stated, the Harvard Apparatus (South Natick, MA) Model 1203 Peristaltic Pump and Masterflex (Cole-Palmer Instrument Company, Chicago, IL) Model 7534-30 Variable Speed Peristaltic m Pump were both considered for use as the feed pump and the recyc.le pump for the glucose analyzer; with the Harvard pump ullmately being chosen due to Its greater speed and the greater number of lines It could handle simultaneously. The smaller, single speed, Masterflex Model 7543-30 Peristaltic Pump, however, was chosen to provide the drive for the acid and base addition and for the glucose analyzer overflow. The system's feed reservoirs consisted of 4 liter, autoclavable, glass bottles that had 1/4 Inch ID glass ports near the base of each bottle. Each reservoir had a one-hole, rubber stopper closure with a Gellman Bacterial Air Vent filter (Gellman Sciences, Ann Arbor, MI) extending through the hole, and was stirred by a magnetic stir bar with a Fisher (Springfield, NJ) Thermlx Model 120M Stirrer. Lines from the feed reservoirs to the fermentor were constructed of 1/4 Inch ID amber, latex tubing (VWR Scientific, San Fransisco, CA) except for a 12 Inch piece of 1/4 inch ID Cole-Palmer Series 6411-slllcone tubing at the feed pump. The silicon and latex tubing were connected by stainless steel connectors. Continuous Culture Apparatus Although the vast majority of the research reported herein was performed using the 14 liter Mlcroferm experimental apparatus, some continuous culture experimentation was accomplished using a Vlrtls Omniculture Model 6701-10I0-0C fermentor (The Vlrtls Company, Gardiner, NY). A 1 liter, autoclavable, glass vessel with an overflow port at the 600 milliliter level was chosen for the particular experimentation performed. The Omniculture provided manual manipulation of agitation rate, temperature set point, and air flow rate. A light emitting diode display provided a 105 switch selectable read out of agitation rate (in revolutions per minute), temperature, or temperature set point (in degrees Celsius). An internal pump provided an air supply, the rate of flow of which was measured by an internal rotameter and adjusted by a valve at the base of the rotameter. In addition to the Omniculture instrumentation, a Virtis Dissolved Oxygen Indicator, and Horizon Model 5997 pH controller with an expanded scale (Horizon Ecology Company, Chicago, IL) were included as part of the continuous culture apparatus. Output from the dissolved oxygen meter included a light emitting diode display and recorder jacks, while the pH controller had a meter and recorder output available. The pH controller functioned in an on/off manner: if the pH decreased below a value dialed into a potentiometer a 115 VAC output for a base pump would be activated; similarly, if the pH rose above another preset value, a second 115 VAC output would be energized for an acid pump. A Cole-Palmer (Chicaogo, IL) ISMATEC Multichannel Peristaltic Model J-7611-00 Metering Pump served as the feed pump from a 10 liter autoclavable carboy. Overflow from the fermentor was collected in a similar carboy which, like the feed carboy, had a rubber stopper closure with Gellman Bacterial Air Vent Model 4210 filter (Gellman Sciences, Ann Arbor, MI). Feed flow rate measurements were accomplished through use of a pipette-meter similar to that described previously. Table 1 Instrument Characteristics Measurement Variable (output) Response Accuracy Repeatability Drift range (%FS/time) PH 0 - 1 2 (0 - +5 V) 90% FS in 10 s 440.05 0.05 / year Temperature 0 - 50°C (25 - 10k ohms) Solution oxygen 0 - 145% (0 - +5 V) 90% in 40 - 70 s Solution carbon dioxide 0 - 100 mBar ( 0 - 2 0 mA) +1% FS 40% FS in 31 Off-gas oxygen 0 - 25% (0 - 20 mV) 90% in 5s 0 - 50% (0 - 20 mV) Off-gas carbon dioxide 0 - 2000 ppm (0 - lOOmV) 90% in 10s +5% FS 0 - 6000 ppm (0 - 100 mV) 0 - 5 % ( 0 - 1 0 0 mV) 0 - 25 % ( 0 - 1 0 0 mV) Air flow rate in 0 - 2 0 sim (0 - +5 V) 98% in 6 s +1% FS +0.2% FS Air flow rate out 0 - 2 0 sim (0 - +5 V) 98% in 6 s +1% FS +0.2% FS Turbidity 0 - 100 % T (0 - +1 V) 3 min dead time +1% FS 4-1% FS Glucose 0 - 3 5 g/l (0 - 100 mV) 23 min dead time +0.2 g/l +0.2 g/l Agitation 50 - 1000 rpm A - ampere FS - full scale ■ Ô ' ^ w i i w h - hour min - minute ppm - parts per million rpm - revolutions per minute s - seconds sim - standard (1 atm pressure, 0°C) liter per minute T - Transmittance o V - volt CT> CHAPTER IV ORGANISM, MATERIALS AND METHODS This chapter describes the microorganism chosen to serve as the biological subsystem of this research, Streptomyces strain 05, and materials and methods related to culture maintenance, growth media, preparation and performance of shake flask studies and continuous, batch, and fed-batch fermentations, and off-line assays applied in conjunction with these studies. Although, ideally, conditions created by the support subsystem are intended to provide for the needs of the biological subsystem in some optimal fashion, in practice, deviations from optimal conditions frequently occur to satisfy limitations of the support subsystem. For example, the application of material balances to fermentation processes requires information describing the composition of the medium, and of liquid and gas streams entering or leaving the fermentor. As a consequence, fermentations to which such techniques are applied must involve defined media. This can pose a serious limitation for high cell density fermentations because determining and supplying the individual requirements of the microorganism is more difficult than supplying a suitable rich, complex medium. Furthermore, complex media have the potential -to segregate materials, such as metabolites, that might inhibit or 107 108 otherwise reduce growth. Another example, relating to available sensor technology, Is that when substrate measurements are required, substrates often must conform to the available sensors. The effects of both of these situations upon this research are described In this and the following chapters. Microorganism The microorganism studied In this research was an anthracycllne-preducing, unspeclated streptomycete, designated Streptomyces C5, obtained from the Frederick Cancer Research Center, Frederick, MD (White and Stroshane, 1984; McGuire et al., 1980a,h,c). Streptomycetes are Gram-posltlve, soil-dwelling, filamentous bacteria that are commercially significant due to their ability to produce a variety of secondary metabolites having therapeutic properties (Demain, 1981). Although of commercial Interest, relatively little Is known about the , behavior of the microorganisms as Indicated by the comment of Hlrsch and McCann-McCormlck (1985) that, "Despite the considerable body of knowledge that has accumulated over the past 30 years or so on the secondary metabolism of Streptomyces, comparatively little Is known about other aspects of their biology." Streptomyces C5 was obtained from ultraviolet-induced mutation of a natural variant of an unspeclated streptomycete (McGuire e^t al, 1980a). When grown In a well-aerated GNFS (glucose-nltrate-phosphate-trace metals) medium, the only slgnfleant product observed was a red, secondary metabolite, e-rhodomyclnone, which It Is capable of excreting Into the 109 medium. On occassion, however, melanin production also has been observed. During Its growth on GNPS In a well-agitated submerged culture, the microorganism undergoes a complex, morphological change from large, diffuse floes to tight pellets. The organism was chosen for four principal reasons. First, It possessed characteristics of many commercially Important microorganisms. Including production of an antibiotic having potential therapeutic value. Second, It was readily available, as coworkers with W. R. Strohl In the Department of Microbiology at The Ohio State University had been studying It for several months before this research began. Third, some expertise from Strohl's colleagues was available from experience acquired In growing It to high density In complex media (Blackwell, 1987) that was believed could aid In learning to grow on It In a defined medium. And, fourth, despite Its commercial significance, no control and few engineering-related studies of streptomycetes could be found In the literature, which presented a substantial opportunity for contributing to the streptomycete knowledge base. Culture Maintenance During the course of this research, two 05 cultures were obtained. The first was contaminated by a faster growing, but poorer producing mutant which was detected by M. L. Dekleva, a coworker with W. R. Strohl. The second culture was acquired from Dekleva after careful screening. Both cultures were obtained In the same form, a plate, and maintained In the same manner, a frozen stock. 110 Each frozen stock culture, was prepared from a plate by transfer of several loops of cells to a 250-ml Erlenmeyer flask containing 80 ml of medium consisting of (per liter); glucose, 30 g; cottonseed flour (Proflo, Traders Protein, Memphis, IN), 10 g; NaCl, 3 g; CaCOg, 3 g; and a solution of trace metals, 10 ml. The trace metals solution contained (milligrams per liter): ZnClg, 40; FeCl^'bHgO, 200; CuCl2*2H20, 2; MnCl2*4H20, 2; Na2B^Oy'10H20, 2; (NH^)^Moy024'4H20, 10; NiCl2*6H20, 7 (Dekleva et al., 1985). The pH of the medium was adjusted to 7.0 and a stainless-steel spring was added to the flask prior to autoclaving. After four days of growth in a 27°C to 30°C rotary shaker at 200 rpm, a second transfer to 800 ml of the same medium in a 2 liter flask was performed. After three additional days of growth, cells were transferred to 1 dram vials and stored at -20 °C, for the original, contaminated culture, and -70°C, for the second culture. Media Although experimentation described herein demonstrated the potential superiority of other defined carbon sources, instrumentation limitations required that, for implementation of the estimator, C5 be grown on glucose. The medium ultimately adopted was similar to one developed for peucetius (Dekleva et al., 1985) composed of (per liter): cerelose (industrial grade glucose. C o m Products, Englewood Cliffs, NJ), 21.5 g; NaNOg, 0.85 g; K2P0/,*3H20, 1.14 g; MgS0^'7H20, 0.123 g; 3-(N-morpholino)propane sulfonic acid (MOPS buffer), 4.19 g; MAZU DF-60P antifoam (Mazer Chemicals Co., Gurnee, IL), 0.2 ml; and trace metals solution, 20 ml. The medium components were autoclaved in three separate Ill vessels containing the glucose and antifoam, the buffer, trace'metals, nitrate and phosphate salts, and the magnesium salts to reduce caramelization of the glucose or precipitation of the salts. Combined, the component solutions had a pH of 7.3 prior to autoclaving. It is this medium that is referred to as the GNPS (glucose-nitrate-phosphate-trace metals) within this dissertation. Acknowledging that preliminary fed-batch experiments used several different feed media, the adaptive fed-batch experiments had a feed stream composed of two streams: a glucose and magnesium salt stream that was fed from a 1.7 liter reservoir containing (per liter) 410 g of cerelose and 2.46 g of MgS0^*7H20; and a salts stream that was fed from a 1.5 liter reservoir composed (per liter) of 9.7 g of NaNOg, 23.3 g of K2HP0/^'3H20 and 120 ml of trace metals solution. When fed in equal proportions before autoclaving, the feed streams had a combined pH of 7.1. The magnesium salts were autoclaved separately from the glucose to reduce caramelization. The medium optimization that was performed as a part of this research obviously used different media than those just described. However, description of their composition will be postponed until a later chapter when the results of the medium optimization studies are discussed. Fermentation Preparation and Performance Four types of liquid cultures were used during this research: shake-flask; continuous; batch; and fed-batch. Each began by inoculation of a 250-ml Erlenmeyer flask containing 80 ml of medium 112 with 1 to 2 ml of frozen stock. Shake-flask culture. Preparation of shake-flask experiments and seed cultures for larger scale fermentations followed the same procedure. Flasks in which medium components would be autoclaved were rinsed with 6 N HCl, and the stainless-steel springs that were used to disperse the cells during shaking were placed in a NO-ŒROMIX solution for one to three hours. Medium components were generally autoclaved in three flasks: glucose in the first; magnesium salts in the second; and the remaining components (i.e. nitrate, phosphate, trace metals, and buffer) in the third. After autoclaving for 23 minutes at 121°C, components were allowed to cool, combined, inoculated with 1 to 2 ml of cells from a recently thawed vial of frozen stock, then placed in a 27®C to 30°C rotary shaker (200 rpm; amplitude approximately 2 cm). Under these conditions, C5 cultures typically completed growth within four days after inoculation, depending upon the medium. When the shake-flask culture was to serve as a seed for a larger scale fermentation, the same procedure was followed, except that a 2 1 flask containing 800 ml of medium accepted the 81 ml inoculum. Two to three days, then, were required for the culture to complete its growth in this larger volume. When inoculating the larger vessel, a few milliliters of broth was typically withheld for microscopic (lOOOx) examination and a pH measurement. Continuous culture. A single continuous culture was accomplished to observe the effect of dissolved oxygen level upon the specific growth rate of 05. Preparation involved growth of an 81 ml seed which inoculated a 2 1 vessel containing 500 ml of GNPS medium that lacked MOPS buffer, but had elevated NaNOg, K2HP0^ and MgSO^ concentrations, 5.29, 1.74, and 0.246 g/1. 113 respectively. The initial glucose (cerelose) was autoclaved in the culture vessel separately from the other contltuents of the initial medium. Also autoclaved separately to reduce precipitation was the magnesium sulfate. After inoculation, the culture was permitted to grow in a batch mode for twenty-four hours prior to commencement of the feed. Agitation, temperature and pH controllers maintained conditions of 160 rpm, 28°C and 7.1 throughout the fermentation, while the air flow rate was adjusted periodically in an attempt to maintain a 50 percent of saturated air dissolved oxygen condition during the first phase of the fermentation. pH control involved introduction of pulses of 1 M solutions of sodium hydroxide and hydrochloric acid. After twenty-four hours, a feed having a dilution rate of 0.0277 h~^ was begun. The feed consisted of a single stream from a 12 1 carboy containing (per liter): cerelose, 297 g; NaNOg, 63.5 g; K2HP0/^, 20.9 g; MgS0^*7H20, 2.95 g . As usual, the cerelose, the magnesium sulfate, and the remaining feed components were autoclaved in three separate vessels. Culture volume was maintained nearly constant at 600 ml during the fermentation by an overflow port that led to a sterile, 12-1 collection carboy. Deviations from that volume occurred only at sampling instants, every eight to twelve hours, when 20 ml of broth were aseptically withdrawn. Samples were stored at -20°C for later analysis. Eight days after inoculation the air flow rate was decreased to produce a dissolved oxygen concentration that was 30 percent of saturated air. 114 Batch and fed-batch fermentations. Preparation for batch and fed-batch fermentations were very similar, differing principally In the amount of Instrumentation that was used to monitor and control the fermentations and In the existence of a nutrient feed stream for the fed-batch vessels. Despite the vessel's Initial medium composition, glucose (cerelose) and magnesium sulfate were usually autoclaved In separate vessels from the remaining constituents. Most commonly, the glucose was autoclaved with the antifoam In the fermentation vessel Itself. After cooling, the components were combined In the fermentor (typically to a volume of 7.2 1), and all Instrumentation and feed lines were Installed prior to Inoculation of the vessel. The seed culture usually had a volume of 880 ml, resulting In an 11 percent Inoculum. As a rule, batch cultures had little. If any. Instrumentation attached. As the fermentations progressed, samples were withdrawn periodically, examined microscopically (lOOOx) for contamination, their pH measured, and stored at -20°C for later analysis. In some Instances, especially during fermentations In which ammonia served as the nitrogen source, periodic, aseptic additions of medium constituents were performed. Typical conditions for batch and fed-batch fermentations Involved agitation rates of 400 to 550 rpm, air flow rates of 2 to 5 1/mln, temperatures of 28 to 30 °C, and pH In the range 6.5 to 8.5. Since most batch runs were accomplished early In this research with media possessing little buffering capacity, manual acid additions were common to maintain the pH In the desired range. 115 More extensively instrumented batch fermentations and all fed-batch fermentations involved additional activities in preparation for fermentations. Prior to autoclaving, all autoclavable probes (i.e., dissolved oxygen probe, antifoam probes, and so on) had to be installed. Since the fermentors lacked proper couplings for such probes, probes were run through one-hole rubber stoppers of the appropriate size and placed in holes in the fermentor head plate. The interface between the stopper and head plate, then, was sealed with silicone glue. Probes that could not be autoclaved (i.e., pH probes) were sterilized in a hypochlorite solution and washed with sterile, distilled water prior to insertion into pre-installed, foil-covered stoppers that were autoclaved with the vessel. Acid, base, nutrient feed lines, air lines, and broth recycle lines (for the on-line turbidity and glucose concentration sensors) that were detached from the vessel during autoclaving where aseptically connected to the vessel's lines through use of stainless-steel quick-connect connectors. In addition to installation of physical components, sensor and actuator calibration and computer set-up were required for the more instrumented fermentations. Oxygen and carbon dioxide off-gas analyzers were calibrated by adjusting the zero of each instrument to a high purity nitrogen stream and adjusting their respective spans to a 21.35 percent oxygen stream and a 1610 parts per million carbon dioxide sample. (The carbon dioxide span gas is injected directly into the sample chamber through a special calibration port.) The dissolved oxygen probe is electronically zeroed and its span is adjusted by creating high agitation conditions within the fermentor that approach saturated air conditions. Increased air flow 116 cannot be used to assist in attaining saturated conditions because of pressure changes within the vessel that alter the saturated concentration. The pH probe is calibrated through a one-point calibration using the pH of the medium as the standard. The pH of the medium is obtained from an off-line measurement during the calibration procedure. The feed pump is calibrated prior to autoclaving the nutrients. Since pumping is based upon a fixed speed, variable duration pulse technique, calibration at only one speed was required. Completion of preparation activities involved creation and storage of a feed pump schedule for open loop conditions or telephonic connection of the Apple microcomputer to the supervisor computer, and initiation of the control program. Adaptive control fermentations differed from other fed-batch fermentations in that monitoring and control was started after lag phase was completed for the adaptively controlled fermentations, while monitoring and control began immediately for other fed-batch fermentations. Not including the waiting period for lag phase to conclude, preparation for an adaptive fed-batch fermentation required more than 15 man-hours. After inoculation or completion of lag phase, there was little difference between the lesser and more extensively instrumented fermentations, since the computer and instrumentation required little attention. Samples were drawn, microscopically examined for contamination and stored at -20°C for later analysis in both situations. However, if pH was not monitored, off-line pH measurements were made of samples. And, if off-gas analysis was accomplished on-line, desiccant changes and condensate removal from the condenser system were required twice a day. 117 Off-line Analyses and Assays Over the course of this research, ten different off-line analyses were performed of samples drawn during the fermentations and immediately stored at -20°C. Approximately half were of biomass constituents, while the remainder assayed for broth components. Dry weight. The most common off-line biomass measurement was of the concentration of dry biomass, or, "dry weight". This assay began, as did all other assays, by the separation of biomass from a known volume of broth by centrifugation. Cells were twice pelleted at 10,000 x g for 10 minutes and washed with distilled water, resuspended in a small volume of distilled water, then, dried at 90°C for one day in tared predried aluminum pans. Optical density. Optical density measurements provided an indirect means of measuring biomass concentration. Optical density measurements were accomplished by transferring 4 ml from samples withdrawn from the fermentor to an appropriate, low optical distortion tube. After vortexing, the tube was quickly placed in a Bausch & Lomb Spectronic 21 spectrophotometer and an absorbance measurement was made at 600 nm. After repeated mixing and measurements, a representative absorbance was selected. A similar procedure was followed for measurements of cultures grown in side-arm flasks using a Klett-Summerson photometer. In this instance, however, mixing occurred in the body of the flask before transfer to the arm, and subsequent measurement. Each measurement involved a thirty second observation in which bubbles were observed to escape and cells accumulate in the bottom of the arm. A representative value was then assumed which, when combined with several measurements for each flask, provided a final 118 measurement. Springs in the flasks maintained cell dispersion., A red filter (ca. 640 to 700 nm) was installed during measurement. Protein assay. When protein assays were accomplished in addition to dry weight measurements, a slightly different procedure was followed to concentrate cells. After the second wash and resuspension, instead of transfer to drying pans, homogenization of the cells using a Potter-Elvehjem tissue homogenizer was accomplished. Cells were, then, divided between the dry weight and protein assays in a 12:1 ratio. Prior to performing the protein assay, however, lysing of the cells had to be performed. This was accomplished (Dekleva, personal communication) by boiling 1 ml of cells in 1 ml of 0.1 N aqueous sodium hydroxide solution for 3 minutes. After boiling, the mixture was neutralized by 1 ml of an aqueous O.IN HCl solution and sonicated for 1 minute. The product was, then, diluted and assayed using the Bio-Rad (Bio-Rad Laboratories, Richmond, CA) protein assay. A standard of 25, 12.5, 6.25 and 3.13 mg/1 of bovine albumin (Sigma Chemical Co., St. Louis, MO) was prepared following the same procedure. The Bio-Rad protein assay procedure involved gently mixing 0.8 ml of sample with 0.2 ml of dye, then waiting ten minutes to measure absorbance (at 595 nm) against a reagent blank. A Bausch & Lomb Spectronic 2000 spectrophotometer was employed for this purpose. Protein concentration was, then, read from the bovine albumen standard curve. Elemental biomass analyses. The final analyses of biomass were elemental analyses performed by Galbraith Laboratories (Knoxville, TN). One liter samples taken during mid-exponential growth and at the end of two 119 different fermentations were centrifuged and washed twice, then, lyphilized over a period of 48 hours, and sent to Galbraith Labs for analysis of carbon, hydrogen, nitrogen and oxygen. The first analyses were single analyses of C5 that were later found to be contaminated with a faster growing, lower producing mutant. The second analyses involved duplicate analyses of C5 mid-log cells and a single set of analyses of producing cells. Galbraith Labs apparently used Perkin-Elmer automatic carbon, hydrogen and nitrogen elemental analyzers along with a LEGO oxygen analyzer to perform the analyses. Glucose analysis. The most common analysis performed on broth constituents was glucose analysis employing a YSI model 27 glucose analyzer (Yellow Springs Instruments, Yellow Springs, OH). Sample preparation involved centrifuging ca. 5 ml of fermentation broth, transfer of 0.1 ml of supernatant to a test tube and dilution with 4.9 ml of distilled water. A precalibrated syringe, then, permitted injection of a correct volume of sample into the glucose analyzer which presented the results in the form of a digital readout. Calibration of the instrument with a 2.00 g/1 glucose standard was accomplished every ten samples, or more often if drift in the calibration was observed. Nitrate analysis. Nitrate analysis was performed using a technique described by Hanson and Phillips (1981). The method essentially involved conversion of nitrate to nitrite, which is subsequently converted to a diazo compound which reacts with N-(l-naphthyl)-ethylenediamine to form a dye whose absorbance is measured at 543 nm. After removal of cells by centrifugation, nitrate in the broth was reduced to nitrite through the 120 addition of 0.06 ml of 2 percent aqueous NH^Cl solution and 0.12 ml of a KCl-HCl buffer (at a pH of 1.5) to 1.5 ml of supernatant. After addition of 0.2 g zinc powder to the mixture and a wait of 30 minutes, the zinc was removed by filtering and nitrite analysis was performed. 1.25 ml of reduced supernatant was combined with 0.025 ml of an acidified 1 percent sulfanilamide solution. After five minutes, 0.025 ml of a 0.1 percent N-(l-naphthyl)-ethylenediamine dihydrochloride solution was added with mixing to the mixture and permitted to sit for 15 minutes. At the end of that time, the absorbance of the mixture was measured at 543 nm using a Bausch & Lomb Spectronic 2000 spectrophotometer. The nitrate concentration, then, was determined from a standard curve obtained from application of the same procedure to nitrate samples of known concentration. Phosphate analysis. Phosphate analysis was accomplished through application of a method reported by Heinonen and Lahti (1981). The technique involves reaction of phosphate with (NH^)Moy02^"4H20 to produce a colored compound, phosphomolybdate, whose absorbance is read spectrophotometrically. Specifically, 0.38 ml of supernatant was combined with 3 ml of a solution containing 1 volume of 10 mM aqueous (NH^)Mo7024*4H20, 1 volume of 5 N H2SO4 and 2 volumes of acetone, and mixed thoroughly. Immediately after mixing, 0.3 ml of an aqueous 1 M citric acid solution was added to the reaction mixture and mixed. The absorbance of the resulting mixture was measured using a Bausch & Lomb Spectronic 2000 spectrophotometer at 400 nm against a phosphate-free blank. Phosphate concentration was obtained from a standard curve prepared just prior to the fermentation broth analyses. 121 Organic acid analysis. Analysis for organic acids was accomplished through application of HPLC techniques by P. L. Lorensen-Kretz of the Department of Microbiology, The Ohio State University based upon methods reported by Guerrant et al. (1982). Approximately 5 ml of fermentation broth was centrifuged to remove cells, and the supernatant was removed and added to 5 ml of an aqueous 0.013N H2S0^ solution. After thorough mixing and sitting for 5 minutes, the mixture was, again, centrifuged and the supernatant filtered with a 0.45 micron filter. 50 mlcrollters of filtrate was Injected Into an HPLC possessing a Bio-Rad Amlnex HPX-87H organic acids analysis column. Retention times of peaks were then compared to the observed times of nineteen commonly occurring organic acids. AnthracyclIne analysis. Anthracycllne analysis was performed using a modification of a technique reported by Dekleva et al. (1985). 10 ml of broth was mixed with an equal volume of a 9:1 chloroform-methanol mixture. The organic phase was saved and the extraction repeated a second time with the aqueous phase. After mixing, the organic phases from the two extractions were combined and dried under nitrogen. The remaining solid was resuspended In methanol, and Its absorbance measured by a Bausch & Lomb Spectronic 2000 spectrophotometer at 495 nm. Anthracycllne concentration was calculated based upon an extinction coefficient of 220 (1%, 1 cm). Ammonia analysis. Ammonia analysis of cell-free broth was accomplished through application of a technique described by Hanson and Phillips (1981) In which ammonia, hypochlorite and phenol react to form a colored product. After preparation of ammonia-free water by distillation of 500 ml of distilled water containing 0.1 ml of concentrated H2SO4, two 122 reagents and an ammonia standard were prepared using the ammonia-free water. One reagent was a mixture of 10 ml of 5 percent hypochlorite solution (commercial bleach) and 40 ml of ammonia-free distilled water which had a pH of 6.7 after adjustment with concentrated sulfuric acid. The other reagent contained 2.5 g NaOH and 10 g phenol in 100 ml of ammonia-free water. The assay involved adding 1 drop of an aqueous, ammonia-free 0.003 M MnSO^ solution to 10 ml of sample. With continuous mixing, 0.5 ml of the hypochlorite reagent was added to the reaction mixture, followed by dropwise addition 0.6 ml of the phenate reagent. After ten minutes, the absorbance was measured using a Bausch & Lomb Spectronic 2000 spectrophotometer and the ammonia concentration read from a standard curve. An additional analysis was performed upon one sample to which was added a known amount of NH^Cl to serve as an internal standard. CHAPTER V ESTIMATOR AND CONTROL SCHEME DEVELOPMENT The general approach taken by this research has been to limit the required amount of process modeling by applying overall material balances to perform on-line state and parameter estimation. The reason for this is that little information presently exists about streptomycetes that could contribute to such modeling, and the effort required to acquire such information about microorganisms that are as difficult to grow consistently as Streptomyces C5 are to grow in a defined medium exceeds that available for this dissertation. The consequences of such a limited understanding of the process are modeling inaccuracies and the existence of unknown parameters which combine to make optimal controller development difficult. The approach taken to estimator-controller development has also emphasized separating the estimation activity from that of the controller so as to make state and parameter estimates accessible to elements outside of the controller. This modularity, then, permits independent application of the estimator for other purposes, if so desired. 123 124 Estimator Development The estimation technique adopted by this (dissertation) research was the extended Kalman filter; a well-known, recursive minimum variance (or least-squares) filter technique. The discussion that follows parallels that presented by Jazwinski (1970), Brown (1983) and many other authors. Starting with (i) a continuous nonlinear system with discrete observations, and (ii) the discrete Kalman filter, this discussion will proceed by developing the linearized Kalman filter (where the process model is linearized about a nominal trajectory) before arriving at the extended Kalman filter (where linearization is performed around each new estimate as each becomes available). Given the nonlinear process model, dx = f(x,u,t) + w(t) (5.1) dt and the measurement relationship, y = h(x,t) + v(t) (5.2) where x is the state vector, y is the measurement (observation or output) vector, w and v are the process and measurement (independent white) noise vectors, u is the process input vector, and f and h are nonlinear functions, and given a nominal trajectory and nominal measurement, dx* = f(x*,u,t) (5.3) dt y* = h(x*,t) (5.4) 125 variations from the nominal trajectory and nominal measurement are defined, Sy = y - y* (5.6) In this way equation (5.1) becomes, d((Sx) = f(x,u,t) - f(x*,u,t) + w(t) (5.7) dt Assuming the variations, x, are small, a linearized Taylor series expansion gives, f(x,u,t) = f(x*,u,t) + F[x*,u,t]Sx (5.8) where F[x*,u,t] Is the matrix of partial derivatives, a f 4(x*,u,t) (5.9) The linearized process equation, then, becomes, d(jx) = F[x*,u,t]éx + w(t) (5.10) dt the solution for which can be discretized (following Van LandIngham, 1985) to give, ^x(tfc+i) = $ (tj^+i,tk;x*(tj^))5 x(ti^) + w(tk+i) (5.11) where f Is the state transition matrix. The linearized, discrete measurement equation becomes. 126 «î y(tk) = M[x*(tk) ]^x(tk) + v(tk) (5.12) where M[x*,k] is the matrix of partial derivatives, 3h^(x*,u,t|^) (5.13) d Xj Equations (5.11) and (5.12), are incorporated into the discrete, linear filter: a filter defined by the following algorithm, 1. Based upon the state vector, SKt^), and error covariance matrix, P(tk), at time, t^, project the state vector, H(tk+i)~, and error covariance matrix, P(bk+i)~ at time, t^+i, ~ ^(*^k+l'^k)^(^k) (5.14) P(tk+l)" = ^ 2. Applying the Kalman gain matrix at time t^, ^(^k+l) “ ^(^k+l)"^^(*^k+l)[^(tk+i)P(tk+i)"^^(tk+i)+R(tk+i)] ^ (5.16) correct the projected state vector and error covariance matrix to arrive at the estimated state vector, &(tk+i), and error covariance matrix, P(tk+j) at time, t^+j, ^(*^k+l) = ^(tk+i) + K(tk+|)[y(tk+i)-M(tk+i)îl(tk+i) ] (5.17) P(Ck+l) = [I-K(tk+i)M(tk+i)]P(tk+i)" (5.18) or P(tk+i) = [I-K(tk+i)M(tk+i)]P(tk+i)"[I-K(tk+i)M(tk+i)]T + (5.19) K(tk+i)R(k+l^k+ 1) where, for the linearized filter, X is replaced by the variation and 127 where Q and R are the process and noise covariance matrices, respectively. The linearized filter functions by calculating the measurement variation (or deviation) from measurements and the nominal trajectory, then enters the result into the above algorithm. The product of the algorithm, the state variation, is then used in conjunction with the nominal trajectory to calculate the estimate. Two forms of the estimated error corvariance matrix are presented in equations (5.18) and (5.19). The latter has been referred to by Bierman (1976) as the Kalman stabilized form because it better maintains the positive definiteness and symmetric nature of the error covariance matrix. Using the structure of the linearized filter, then, it is possible to create a more sophisticated algorithm by linearizing about each new estimate as it appears, instead of around a nominal trajectory. The development of the extended Kalman filter begins with the recognition that, since linearization occurs at the latest estimate, the estimated state variation (deviation) at any sampling time, tj^, is zero; symbolically, <^X(tk|tk) = 0 (5.20) Applying equation (5.14) to the rfx(tk|tk) variations reveals thatR(tk+iItk) are also zero for all discrete, tk. Consequently, the best state estimate between observations is the most recent estimate, so that. d(R(t|tk)) = f(X(t|tk),t), tk of the nonlinear process model, equation (5.1), with w(t) = 0. ' With the integration of equation (5.21) replacing equation (5.14) as the state projection equation, the remaining filter equation expressed in variational variables is the state correction equation, equation (5.17), = SHty,+i)- + K( tk+i ) [6y ( tk+l ) -M( tk+l )^&( tk+l ) -] (5.22) However, since, ~ ^(^k+l) ^ ^^^k+l)iy(^k+l)"^(^(^k+l) )) (5.24) Therefore, the extended Kalman filter (algorithm) is comprised of (i) a state vector projection, equation (5.21) integrated, (ii) an error covariance matrix projection, equation (5.15), (iii) calculation of the Kalman gain, equation (5.16), (iv) a state vector correction, equation (5.24), and (v) an error covariance matrix correction, equation (5.19). The process model adopted by this research, and upon which the estimator was based, consisted of four material balances representing the four significant state variables: biomass concentration; substrate concentration; dissolved oxygen concentration; and volume. These variables were significant because they are either factors in the index of performance (biomass concentration), factors that determine the rate of biomass production (substrate and oxygen concentrations are assumed to be the only 129 substances to have a significant effect upon the biomass production rate) or factors that are related to the control variable (volume). All other variables, such as pH, temperature, other nutrient concentrations (nitrate, phosphate and so on), and concentrations of toxic or Inhibitory substances, were assumed to be In ranges that had no significant effect upon growth. Thus, the process model was. dx = lev - (F/V)x (5.25) dt ds = -(k^/Yg') +(F/V)(sf-s) (5.26) dt ^ = -(k^x/Yo') + k^a(o*-o)- (F/V)o (5.27) dt ^ = F (5.28) dt As will be demonstrated later In this chapter, the optimal controller requires estimates of three state variables and five parameters. By treating the parameters as state variables, the Kalman filter Is used to estimate the parameters as well as the state variables. In this manner, the elements of the state vector, x, were defined as follows: x(l biomass concentration (x); x (2 substrate concentration (s); x(3 dissolved oxygen concentration (o); x(4 specific growth rate (k^); x(5 overall substrate (glucose) yield (Yg'); x(6 oxygen mass transfer coefficient (kj^a); x(7 overall oxygen yield (Yq '); x (8 saturated dissolved oxygen concentration (o*), To these were added three state variables, x(9) through x(ll) which are described by equations (5.32) through (5.39), to Improve the dynamic 130 character of slowly converging variables (specifically, specific growth rate, overall substrate yield, and oxygen mass transfer coefficient). This results in an ultimate process model of. dx(l)/dt = x(4)x(l) - ux(l), u = F/V (5.29) dx(2)/dt = -x(4)x(l)/x(5) + u(sr-x(2)) (5.30) dx(3)/dt = -x(4)x(l)/x(7) + x(6)(x(8)-x(3)) - ux(3) (5.31) dx(4)/dt = Cjx(9) (5.32) dx(5)/dt = CgxUO) 0.33) dx(6)/dt = cgx(ll) 0.34) dx(7)/dt = 0 (5.35) dx(8)/dt = 0 (5.36) dx(9)/dt = 0 (5.37) dx(10)/dt = 0 (5.38) dx(ll)/dt = 0 (5.39) Of the variables that were acquired by the experiments, five were orginally selected as raw measurements that would serve as input to the estimator. These included dissolved oxygen concentration, carbon dioxide and oxygen off-gas concentrations, and inlet and outlet air flow rates. From these, and information about the overall stoichiometry of the glucose to biomass conversion, the biomass production rate, oxygen uptake rate, dissolved oxygen concentration, and glucose and oxygen yields were to be computed to provide input to the filter. However, it was discovered that gas leaks in the apparatus and air flow rate meters of insufficient accuracy would not provide adequate measurements of the oxygen uptake rate. These were, then, eliminated and replaced by on-line glucose concentration measurements and substrate concentration was added to the five other filter measurements. In this manner, the filter's measurement equations became. biomass production rate, y(l) = k^ (5.40) oxygen uptake rate, y(2) = k^^a(o*-o) (5.41) dissolved oxygen concentration, y(3) = o (5.42) 131 overall substrate yield, y(4) = Yg' (5.43) overall oxygen yield, y(5) = (5.44) substrate concentration, y(6) = s (5.45) The remaining information necessary to complete the estimator is that describing how the measurement vector, y, was obtained. As was stated, the raw, on-line measurements acquired included air flow into the fermentor (in units of liter/minute at standard temperature and pressure), concentration of carbon dioxide in the off-gas (which, when combined with air flow rate into the fermentor, gave the carbon dioxide evolution rate), oxygen tension (in units of percent of water saturated with air), vessel pressure and off-gas oxygen concentration (which were used to convert the oxygen tension measurement to dissolved oxygen concentration using Henry's law constant of water), and glucose concentration. These raw measurements directly provided only two filter measurements y(3) (dissolved oxygen concentration) and y(6) (glucose concentration). To obtain the remaining measurements knowledge of the overall biomass synthesis reaction is applied. From elemental analyses, it was determined that the weight percent composition of the biomass was approximately 46.26 percent carbon, 7.25 percent hydrogen, 30.92 percent oxygen, and 9.55 percent nitrogen. When converted as an (ashless) biomass expression, the molecular formula, CHi .8677%.5018%.1770 obtained. This, then, gave an overall glucose to biomass conversion equation of, ^^6^12^6 + b02 + c N03~ > (5.46) (^1.8677% .5018%. 1770 + ^^2^ + eC02 + fOH" To solve for the stoichiometric coefficients of the above reaction, a system of five equations (ion, carbon, hydrogen, oxygen and nitrogen balances) with 132 six unknowns, at least one additional relation was required. Originally, when oxygen uptake rate was to be measured, the ratio of the oxygen uptake rate to the carbon dioxide evolution rate to be equated with the b/e ratio. However, when it was learned that oxygen uptake rate could not be adequately measured, the glucose uptake rate to carbon dioxide evolution rate was equated with the a/e ratio. (Measuring the glucose consumption rate by taking glucose concentration measurements over time was very undesirable, but, as it turned out, the measurement exhibited much less noise than was anticipated.) From the stoichiometric coefficents and the molecular weights of the chemical species, the biomass production rate was obtained by dividing the carbon dioxide evolution rate by the value of the coefficient, e, in equation (5.62) and adjusting the units with the molcular weights of biomass and carbon dioxide, the oxygen consumption rate was computed by multiplying the carbon dioxide evolution rate by the b/e ratio and adjusting with the carbon dioxide and oxygen molecular weights, and the overall glucose and oxygen yield were calculated by adjusting the inverses of a and of b with the biomass molecular weight and glucose and oxygen molecular weights, respectively. Additional parameters that may be generated by this estimation technique are the substrate and oxygen maintenance requirements, mg and m^. In addition to growth and metabolite production activities, microorganisms require energy and material to maintain themselves. These maintenance operations have an energetic aspect in providing energy for cell motility, turnover of cell materials and maintenance of concentration gradients between the cell and its environment (Pirt, 1973), and a structural aspect 133 in providing new material to replace that turned over. The relationship between maintenance and overall yield is expressed by, 1/Y' = 1/Y + m/k^ (5.47) where Y is the "true" yield (defined by Pirt (1975) as being the maximum possible for the given system, or casually defined as being that occurring when growth is at its maximum). The typical decreases in overall yield over the course of a fermentation is usually attributed to this factor. Optimal Controller Development Formulation of the optimal control problem required specification of the process model, the initial and final conditions, the available measurements, the control variable(s), physical constraints upon the state or control variables, and the performance criterion. The process model that was ultimately adopted by the optimal control scheme was also that used in the estimator, excluding the oxygen balance, equations (5.25), (5.26) and (5.28). The initial conditions, or initial state, varied between fermentations, and so was whatever state was observed at the beginning of a fermentation. The final condition was the final, desired biomass concentration, x^. The available measurements were those provided by the estimator. The control variable was defined to be the nutrient feed flow rate. Two physical constraints observed included minimum and maximum feed flow rates of 0 and respectively, and a maximum glucose concentration due to glucose sensor limitations, s'*". During the development 134 of the first version of the controller, measurement of substrate concentration was not required because it was assumed that oxygen uptake rate could be measured. However, after it was discovered that the oxygen uptake rate could not be accurately measured at the expected cell densities and that substrate uptake rate measurements would be required, a physical constraint was established at the limit of the glucose sensor. The objective function adopted by the following development is the time optimal criterion. 1) dt (5.48) ■ tn0 where the performance measure is to be maximized. Development of the first version of the controller was based upon the assumption that high cell densities would be achieved that would depress dissolved oxygen concentrations to an extent that the growth of the culture would be affected; a common occurrence in high-density fermentations. This assumption required inclusion of an oxygen balance, equation (5.27), in the controller model, and created a situation that, apparently, had not been addressed in the literature: development of an optimal controller operating under double substrate limitation conditions in which one substrate was a gas. Since the inaccuracy of the oxygen uptake measurement had not been discovered at that time, the necessity of the substrate measurement did not exist, so no physical constraint assumption was necessary. In attempting to determine the optimal trajectory, two approaches were considered: Miele's (1962) method; and application of Pontryagin's maximum principle (1962). 135 Because Miele"s method, based upon Green's theorem, can only be applied to two dimensional systems, further consideration was postponed until some means was uncovered of reducing the system's dimension by two. Application of Pontryagin's principle requires that the Hamiltonian, H = -1 + PjdCjçX-Fx/V) + p2(-kjjX/Yg'+F(sf-s)/V) + (5.49) P3(-kjjx/Yo'+kLa(o*-o)-Fo/V) + p^F = Hj + H2 (5.50) (where p is the costate vector), be a maximum along the optimal trajectory and that. dx = 9 H(x*(t),u*(t),p*(t),t) (5.51) dt Ô P dp = -a H(x*(t),u*(t),p*(t),t) (5.52) dt ^ X and H(x*(t),u*(t),p*(t),t) = 0 (5.53) where the asterisk associated with state, costate and control vectors designates the optimal condition. The final equation (condition) follows by transversality and the facts that the final time is not fixed and the Hamiltonian is not an explicit function of time. As a result the optimal feed pattern becomes. F = pnax «2 > 0 (5.54) F = F = Fg, ' H2 = 0 (5.55) F = 0, H2 < 0 (5.56) where Fg denotes the feed flow rate during a singular interval. One approach that was applied to solving for the optimal feed flow rate profile 136 was based upon recognition that H2 and all its time derivatives are zero. Elimination of the costate variables and determination of F would have required a system of five equations, H2 and four derivatives equated with zero, which was a mathematically Intractable problem. Stanlskls and Levlsauskas (1984) solved a four equation system for the optimal feed profile to provide optimal product production. In this instance the oxygen balance equation was replaced by a product balance, dP/dt = xe(x,s,K) - FP/V (5.57) where e Is the specific product production rate and P Is the product concentration. Their approach Involved reducing the four dimensional system to a two dimensional system by eliminating the product balance, equation (5.57), and applying Kelly's theorem (1965). The product balance could be eliminated because explicit expression of P was unnecessary for the objective function or other state equations. Kelly's theorem, then, transformed the three dimensional system with feed rate as the control variable to a two dimensional system with volume as the control variable. The costate variables were eliminated and the optimal control profile determined by equating the Hamiltonian and derivative of the Hamiltonian with respect to the control variable of the transformed system equal to zero, then solving the transformed equivalent of equation (5.50). Applying a similar approach to a system of equations containing an oxygen balance equation would have required either using an additional derivative of the Hamiltonian to solve for the additional state variable or applying Kelly's theorem twice. Two unacceptable alternatives. 137 Hong (1986) followed a similar approach, beginning with the same system of four dynamic equations, but kept the product equation and eliminated the substrate equation by combining the substrate and biomass equations and integrating to obtain substrate concentration as a function of biomass concentration, volume and substrate yield, (x + Yg's)V - (xj + Y/si)Vi = SfeedY/(V - V^) (5.58) in which subscript i denotes the initial value of the variable. The transformation is performed by setting zi = In(xV) (5.59) zg = In(PV) (5.60) Z3 = V (5.61) resulting in a transformed Hamiltonian, H = e(exp(zj)) + Pgi(k^) + P22e(exp(zi-Z2)) = 0 (5.62) in which e is the specific production rate. Elimination of the costate variables and solution for the optimal feed flow pattern resulted from applying the following conditions 3H = d^a H \ = 0 (5.63) ~Sz2 dt àz2 in conjunction with (5.62). A limitation in Hong's, and Staniskis and Levlsauskas' approach to maximization of product formation is that it fails to explicitly account for substrate conversion to product in the substrate balance. Although the form of the substrate balance may have been made to simplify the mathematics, the biomass yield term must somehow absorb any 138 substrate to product conversion. While more complex than Hong's system of equations, due to the existence of the oxygen mass transfer term in the oxygen balance, Hong's approach was under consideration for use to determine the optimal profile for the model of equations (5.25) to (5.28). Use of equations (5.58) to (5.61) is possible if the transformed product variable, equation (5.60), was replaced by a transformed oxygen variable, %2 = In(oV) (5.64) Application of a transformed Hamiltonian, H = -1 + P2i(kjç) + Pz2[kxexp(z2-Z2)/Yg' + (5.65) kLa(o*Z3/exp(z2) - 1)] = 0 in conjunction with equation (5.64) followed by reverse transformation would permit solution for the flow rate in a manner similar to that followed by Hong if the oxygen mass transfer term did not make the mathematics too unwieldy. This approach was never completed, however, because it was at this time that experimentation indicated that the organism grown in a defined medium would never reach densities where oxygen depletion would affect growth. Since the dissolved oxygen concentration was no longer believed to affect growth, it was eliminated from the optimal controller model. And, since it was determined that oxygen uptake rate could not be measured with sufficient accuracy, substrate concentration measurements were included which, consequently, required imposition of the substrate state constraint. Optimization for the new conditions, again, involved the application of 139 Pontryagin's principle, but to the Hamiltonian, H = -1 + Pi [kjjX - (F/V)x] (5.66) + P2 [-k^x/Yg' + (F/V)(sfeed-s)] + P3 [F] - P4 [s‘^-s]2 flCs-s'*') = Hi + H2 F (5.67) in which II denotes the unit Heaviside step function as defined by, H (-f) = To, for f 2 0 (5.68) ^ 1, for f < 0 and where the costate variables must satisfy, d(Pi)/dt = -aH/3x = Pi[(F/V)-kx] + (5.69) P 2 [W ] d(p2)/dt = -3H/0S = -pi[xkjj®] + (5.70) P2[(V^s'>^^ + F/V] - p^[2(s'*'-s )H(s-s+)] d(p3)/dt = -àH/3v = -pi[xF/v2] + (5.71) P2[(sfeed-s)F/v2] d(P4)/dt = 0 (5.72) in which superscript s represents differentiation of respect to s. On the optimal trajectory, which is denoted by an asterisk, the Hamiltonian is zero, H(x*,s*,V*,Pi*,p2*,P3*,p4*,F*) = 0 (5.73) Maximization of the Hamiltonian, again, results, in the feeding policy, of 140 equations (5.54) through (5.56). Assuming the substrate constraint is satisfied and the overall substrate yield is constant, the feed flow profile during the singular interval can be obtained by recognizing that H2 and all its derivatives are zero, *2 = -Pix/V + P2(sfeed-8)/V + Pg (5.74) = 0 d(H2)/dt = x(sfgg^-s)/V [p2*Sc®/Yg' - (5.75) = 0 d^(H2)/dt^ = x(s£ggj-s)/V (5.76) [(k^^^(P2/Yg'-pj)ds/dt + (kx®)/Ys'(-kx®^l + P2F/V + P2kx®x/Yg') + lSc®(pi(kx - F/V) - P2V V > ] = 0 Combination of equations (5.26), (5.75), and (5.76) to eliminate the costate variables results in the following expression, Fg = kxXV/[(sfged-s)Yg'] (5.77) Equation (5.75) reveals that, on the optimal trajectory, = 0 (5.78) implying that during the singular interval, the specific growth rate is maintained at its maximum. Experiments indicate the specific growth rate of C5 increases with increased substrate concentration, but the penalty imposed upon the Hamiltonian by the constraint is such that any substrate concentration above the constraint would not be optimal; therefore, its 141 maximum growth rate is limited to that at the constraint. The optimal trajectory that results is s t^t2 The first switching time, tj, occurs when the substrate concentration reaches the substrate constraint, s'*", and the second occurs when the final condition, x^, is attained. CHAPTER VI SOFTWARE DEVELOPMENT Computer software developed for this research were prepared for three purposes: to perform simulations to test estimator and control schemes under consideration; to accomplish the on-line fermentation control experiments; and to assist in the analysis and display of data after its collection from simulations and experiments. Listings of programs written in conjunction with this research, along with variable/label/memory location definitions appear in Appendix B. Simulation Software Simulations performed by this research were accomplished for three purposes: to develop and validate the process model; to develop and test estimator and control schemes; and, in conjunction with results from on-line experiments, to refine the estimator and controller. Software utilized. Depending upon the computer(s) installed at The Ohio State University's Koffolt Computer Graphics Laboratory (KCGL), simulations were performed at various times upon DEC VAX 11/750, VAX 11/780, and VAX 8500 minicomputers (Digital Equipment Company, Maynard, MA). User programs were written in the FORTRAN computer language and compiled and linked using the VAX FORTRAN compiler (version 4) and VAX/VMS Linker. Two software packages were accessed in creating the simulation programs. The 142 143 Advanced Continuous Simulation Language (Mitchell and Gauthier Associates, Inc., Concord, MA), ACSL, assisted in preparing the process simulator code, while the IMSL (IMSL, Inc., Houston, TX) library of mathematical subroutines contributed to the estimator-controller software. In addition to the user-written FORTRAN programs, command files were prepared to ensure the accuracy, consistency and speed of data entry and program execution of the simulation programs. Program descriptions. The simulation software consisted of two user-written programs : a process simulator written in the ACSL simulation language; and a control program written in FORTRAN that performed the estimator and controller functions. The former program is designated as FD_0F8 in Appendix B, while the latter is named KNF028. The program simulating the process was based upon an process model that assumed an exponential growth law. The mathematical model consisted of a system of four, simultaneous, differential equations representing biomass, substrate, and oxygen concentrations, and volume balances. The model conformed to the stoichiometry aCrHi oO^ + bOo + cNOo — -- > ^ ^ ^ ^ (6.1) ™1.8677°0.5018^0.1770 + ‘^^2° + ^^2 + which assumed a substrate yield of 0.5 and a biomass composition representative of those obtained from elemental analyses of four C5 samples by Galbraith Laboratories of Knoxville, TN. For most of the simulations accomplished, process parameters, such as specific growth rate, yields and the oxygen mass transfer coefficient, were constant. During 144 these "standard" simulations, the output from the process simulator, which included carbon dioxide evolution rate, dissolved oxygen concentration and substrate concentration, were corrupted by white noise having a standard deviation equal to ten percent of the value of the output, except for the substrate concentration which had white noise superimposed that possessed a constant standard deviation of 0.5 grams/liter. Other, non-standard, simulations introduced changes to the process model and parameters that reflected a cube root growth law, Contois kinetics, oxygen limitation, process noise, and a several other effects. A fourth order Runge-Kutta integration with a 1/120 hour step size was adopted by the process simulator. Communication with the estimator-controller program occurred every 1/6 hour, at which time the process simulator exchanged its output for the value of the up-dated control variable: feed flow rate. Additionally at this time, state and parameter information was stored in a data file for later analysis. The estimator-controller program was designed to separate the estimator and controller into two modules; thereby, permitting independent application of the estimator or easy substitution of other controllers. The incorporated estimation and control algorithms are those that have been previously discussed. Program execution proceeds by acquiring the noisy output from the process simulator, averaging the substrate concentration datum with previous data, then, based upon the stoichiometry described above, estimating the overall yields. Following this, the Kalman filter processes the measurements, providing estimates of eight parameters and state variables to the controller which, in turn, calculates an optimal flow 145 rate, and transmits that flow rate to the process simulator at the next communication. Integration applying Gear's method, and several, simple matrix functions within the estimator routine were accomplished by subroutines from the IMSL library. To increase the precision of the calculations, thereby reducing divergence problems due to round-off error, double and quad-precision arithmetic were performed by the estimator-controller program. Software design. Two concepts central to the design of the simulation software were those of modularization and physical separation. Modularization simplified the debugging and testing of the software, increased the ease with which the simulation programs could be modified and expanded, improved the comprehensibility of the source code, and maintained the distinctness and independence of the estimator from the controller. Similarly, physical separation of the simulated process from the estimator-controller simplified the debugging and testing of the simulated process and the estimator-controller, but it also provided a closer emulation of the physical arrangement and communication links of the experimental system being simulated. In an attempt to approximate communication conditions expected during experiments, several types of links between the process simulator and the estimator-controller programs were created. First, to emulate the modem-based supervisor-DDC communications of the on-line experiments, a task-to-task link between the simulator and estimator-controller was sought. Unfortunately, unlike UNIX, VAX/VMS does not provide such a facility. However, during the early simulation studies, there were two VAX 146 minicomputers available in the KCGL that were connected by a DECNET. With the VAX 11/780 running the process simulator and the smaller VAX 11/750 executing the estimator-controller software, task-to-task communication over the network was possible. The slower VAX 11/750 ran the estimator-controller because, of the two computers, it was the machine designated for real-time process control, and would be the minicomputer executing the estimator-controller during the on-line experiments. Unfortunately, the DECNET running between the computers was not a Digital Equipment Corporation-installed product, but, rather, was an invention of the KCGL staff, and was incapable of efficiently handling the simulator communication with the estimator-controller without system degradation. The next approach adopted also made use of both computers by recognizing that each had read privileges to the other's user disk. The software was, then, modified to transfer data by writing onto the user disk associated with that computer and to read from the other computer's user disk. Before this research was complete, however, the VAX 11/780 minicomputer was removed from KCGL; requiring that the software be rewritten again so that both program resided in a single machine, the VAX 11/750 (and, later, the VAX 8500). Although, by necessity, the estimator-controller became a subroutine of the process simulator, some separation was maintained by editing and compiling the routines separately, bringing them together during the linking process. Despite these attempts to establish communication links that approximated those of the experimental system, over the course of this simulation research, the communcations similarity between the simulated process the experimental system decreased. Initially, the simulations' communication 147 links were device-based. Later, communications were through common statements and subroutine call arguments; communication links least similar to those existent during the experimental research. Obstacles. In addition to the problems already mentioned, several other obstacles had to be addressed during the course of the simulation studies. The most important was the calculation of the state transition matrix. Following the development by Van Landingham (1985), given the continuous time state model. x(t) = Ax(t) + Bu(t), x(tm) (6.2) y(t) = Cx(t) + Du(t) (6.3) the general solution of equation (6.2) is, x(t) = exp(A(t-tQ)) x(tg) + ^ exp(A(t-w))Bu(w) dw (6.4) If measurements are made only at discrete times, the solution appears as. ckT+T x(kT+T) = exp(A(T)) x(kT) + \ exp(A(kX+T-w))Bu(w) dw (6.5) '^kl where T is the sampling interval. The exponential factor of the first term of the right-hand side of equation (6.5) is the state transition matrix; a calculated quantity required for the implementation of the Kalman filter. Calculation of the state transition matrix is common in the application of linear system theory and many convenient techniques have been developed to accomplish this. Melsa and Jones (1973) described a method based upon the 148 Sylvester Expansion Theorem in which the matrix coefficients of the series, exp(At) = FjexpCljt) + F2exp(l2t) + Fgexpdgt) + . . . + Fj^xp(l^t) (6 .6) are calculated, given the N simple eigenvalues, 1^, of the A matrix. Zadeh and Desoer (1963) also described methods of calculating the matrix function exp(At), which they defined as f(A). In the first method they described, the interpolation method, f(A) was determined by the series. s fdk) f(A) = s TT (A - iji) (6.7) E 1 7 d k - ii> i=l k=l i=l i?*k # k where s is the number of distinct eigenvalues. The second method they presented, a method based upon the formula. (6.8) inserted appropriate trial functions of f into the above equation to solve for the Z matrices. The f functions are defined as. f(lk) - p(lk) k = 1, 2, . . . , s (6.9) f(j)(lk) = p(k)(lk) k = l , 2, . . . , s (6 .10) j=l,2, . . . , m^—1 where m^ is the multiplicity of the k eigenvalue, and p is the polynomial. 149 N p(l) = ' ^ V k (6.11) k=0 Another approach to calculating the state transition matrix simply Involves summing the series, exp(At) = I + (l/l!)At + (l/2!)(At)2 + (l/3!)(At)^ + . . . (6.12) terminating the summation when the contribution of the next term for each element was less than a preestablished value. Additionally, the IMSL library contained routines that calculated this exponential function. Ultimately, application of each of these methods failed because the eigenvalues of the matrix were not simple, because zero eigenvalues existed, or because of round-off error due to the A matrix containing elements that differed by five orders of magnitude. It became apparent that calculation of the state transition matrix required development of a technique that took advantage the specific characteristics of the process A matrix. Manual calculation of A^ revealed that a maximum of only twenty elements were non-zero. Further, when placed into the summation representing exp(A), equation (6.12), it was revealed that it was necessary to calculate a maximum of only sixteen elements, which are listed in Table 2 at the end of this chapter. To avoid the problems that occurred previously when attempting to sum series, all series were expressed as exponential functions. In accomplishing this, summations for each element of the state transition matrix, such as element (3,9), were rearranged from simple power series. 150 <4,9>[ <3,4>(1/2!-K3,3>/3!-K3,3>2/4!+. . .) + <3,1X1,4> (6.13) [1/3!+«1,1>-K3,3»/4!+(<1,1>2+<1,1X3,3>+<3,3>2)/5!+. . .] ] to power series containing exponential terms, <4,9> [ <3,4>(exp<3,3>-<3,3>-l)/<3,3>2 + (6.14) <3,1X1,4>/<3,3>3 ( (exp<3,3>-l-<3,3>-<3,3>2/2!) - r ( exp<3, 3>-l-<3, 3>-<3, 3>2/2 ! X3 , 3>3/ 3 ! ) - r2(exp<3,3>-l-<3,3>-<3,3>2/2!-<3,3>3/3!-<3,3>V4!) -...)] where the triangular brackets, <>, denote elements of the original A matrix and where r Is the quotient of element <1,1> divided by element <2,2>, when the magnitude of element <2,2> Is greater than that of element <1,1>. In this form, a rapidly converging, recursive algorithm for the summations was created. To Increase the accuracy of the calculations the subroutine that calculated the state transition matrix, EXPAQ, performed Its calculations In quadratic precision (REAL*16). On-line Experimentation Software prepared to perform the on-line fermentation experiments were of two types; supervisory programs. I.e. software related to the estimator and controller, that executed on the VAX 8500 minicomputer; and direct digital controller (DDC) software that ran on the Apple lie microcomputer. Software utilized. The software Involved In the development of the fermentor control system Included that mentioned previously In the estimator/controller simulation studies, the VAX FORTRAN compiler, the 151 VAX/VMS linker, the KOGL management system, IMSL, and user-written FORTRAN programs, plus the software associated with the Apple lie's DDC function: Apple DOS3.3, the Apple monitor, the Applesoft BASIC interpretter, user programs written in BASIC, the 80 column/64 kilobyte memory expansion card, and various machine-language device drivers (the BUFFERRED GRAPPLER+ firmware for the printer interface, the resident firmware on the Hayes Micromodem lie, the LABSOFT version 2.0.3 software for ISAAC interface, and the user-written drivers for the interrupt generator board, the glucose analyzer and some program cycle timing). In addition, the DDC software had to communicate with the The Ohio State University's Instruction and Research Computer Center's 300 baud network switch to gain access to the network and the VAX computer. The complexity of the system becomes apparent when it is realized that, at any one time, at least five programs are executing concurrently. Program flow. Program flow for the supervisor program, listed in Appendix B as SUPERV8, is essentially the same as that of the supervisor in the simulation studies. Under normal conditions, the program flow for the three Applesoft programs was from the initialization program, denoted FEDBATCHO in Appendix B, to the preparatory program, FEDBATCHl, to the control program, FEDBATCH2. The initialization program loaded the device drivers, set actuators to a neutral state and, during restart, established communication with the VAX minicomputer. The preparatory program assisted the user in configuring the system, calibrating the instrumentation, and setting system parameters, such as PID controller parameters, sampling frequency, and so on. The control 152 program performed the DDC functions of monitoring and controlling the system, and accomplished various data logging and communication activities. During restart of the system, the program flow changed, proceeding from the Initialization program directly to the control program. This was possible because the three programs were designed to communicate through data files stored on disk, and once the preparation program was run and the system parameters were stored, the preparatory program was no longer required to regenerate the system parameters. Execution of the control program began with the setup portion of the program. This section of the program went to the RUN NAME file to obtain the name of the data file that contained the system parameters stored by the most recent preparation program. After loading the system Information and configuring the system accordingly, the program commenced Its repetitive monltor-control-communlcate cycle. Each cycle began by acquiring data from each designated device and converting the Information Into appropriate units. Based upon this Information, the program, next, performed the required control actions. Upon completing those actions, the program updated the data display on the computer monitor, and communicated with the disk drive (storing the average value of the monitored variables every seven cycles), the printer (printing. In a strlpchart format, the average value of monitored variables every five cycles), and the supervisor (transmitting monitored data and receiving the new, optimal flow rate every ten minutes). After completing Its communications, the Apple waited for the next cycle to begin. The duration of a cycle was normally three minutes, except when communication with the supervisor occurred. In which case It was extended to 153 four minutes. The wait was accomplished by a short, machine-language routine due to the inability of BASIC to repeatedly access the ISAAC'S real-time clock from LABSOFT without conflicting with the interrupt handler. During the wait routine, the keyboard buffer was frequently read to determine if the operator wished to modify the system through the system's on-line facility that performed reconfiguration, and parameter alteration. A three key code of "CTRL", and shifted signaled the user's intention to access the facility. Software design. The estimator-controller software was essentially the same as that developed during the simulation studies, with six important differences: communication with the data source was through a device instead of subroutine call arguments; intermediate results were stored onto disk in place of common statements; all transmissions received from the Apple were stored for later recall by simulation studies recreating the on-line experiments; capabilities were added permitting on-line alteration of parameter and state variables values or selection of a different estimator model (exponential and cube root growth laws were available); error recovery/program restart facilities were introduced; and estimator-controller output was appended to a specific file instead of just being sent to a logical device. The DDC software was considerably more complex than that of the supervisor. There were, essentially, three layers of software, each possessing great potential for interaction with the other levels. The highest layer consisted of the user-written BASIC-language programs that were described above. The middle level was composed of the machine-language 154 device driver routines which included the on-board firmware resident in the GRAPPLER printer interface and Hayes Micromodem lie boards, LABSOFT that was loaded into RAM during initialization, and user-written, machine-language device drivers for the feed pump, for the glucose analyzer, and for control program loop timing. The lowest level of software included the Apple DOS and monitor. Conflict between the highest and midddle levels existed because the control program and IRQ interrupt handling routine competed for access to the ISAAC binary output system. Conflict between the middle and lowest layers existed because access to the disk drive by the operating system overrode the IRQ interrupt. Conflict within the middle level existed because LABSOFT and the interrupt handler routine both accessed LABSOFT primitives. And, conflict between the user-written machine language programs and all other software existed because each machine language program accessed LABSOFT routines that were located in segments of memory that required the swapping out of an important bank of ROM to access. These and other conflicts were managed through the creation of buffers and status registers, and by temporarily disenabling IRQ interrupts during strategic portions of conflicting software. Several important design concepts were emphasized during the preparation of the supervisor and DDC software. First, of paramount importance was the immunity of the software to failure and, collaterally, its recovery from a failure if one occurred. The three principal sources of error expected to affect the DDC software were programming errors, entry of erroneous information during on-line modification of the system by the operator, and either a lack of response or receipt of improperly formatted 155 information over the Apple-VAX communication link. The result of these errors were expected to be premature termination of the BASIC control program or the complete loss of computer control. Four actions taken to avoid such situations included: designing all routines as modules that could be individually tested in detail before incorportation into the larger program; careful screening all user entered data to ensure the information being entered was consistent with the activity being modified; institution of a unique communication protocol between the Apple and VAX; and use of a simple, dependable, interrupt-driven, machine-language program to operate the feed pump. (Use of an interrupt-driven routine to manipulate the feed pump provded immunity to BASIC program failures because such routines are independent of BASIC and continue to execute even after termination of BASIC programs.) Additional system protection was provided by the ability to restart the program, automatically after a power failure or manually by recycling the computer's power switch. Restart was made possible through the storage of all system configuration information and parameters, and all intermediate results in disk files for recovery after restart. The second design concept incorporated into supervisor and DDC software, was inclusion of the ability to change or modify, on-line, any estimated state variable or parameter of the process or any system configuration information; thereby, permitting recalibration or substitution of instruments or incorporation of more accurate, off-line measurements. A third concept adopted by this research was the types and extent of linkages used between programs and between modules within programs. Disk storage provided permanent storage for file pointer and system configuration information for the Apple, and 156 state variable, parameter and Intermediate calculation Information required by the estimator-controller on the VAX. This storage served to link different programs (such as the preparation and control programs on the Apple) or restarts of the same program (such as the control program on the Apple or estimator-controller on the VAX). Registers In Apple memory were used as temporary storage for concurrent modules or programs that competed for system resources, such as the nutrient feed pump contending with the acid pump for the ISAAC binary output subsystem. The fourth Important concept Integrated Into the software design was that the DDC control communications between the DDC and supervisor and not the supervisor. The reason for this was related to the heavy load carried by the Apple and to Its responsibility for the timing control of system events. The fifth major design concept adopted was the extensive and redundant storage of results by the Apple and VAX. The extensiveness of the data was to permit detailed post-experIment data processing and simulation while the redundancy was to assist In recovery of data If one of the storage devices would fall, and lose Information. The final, important, but somewhat Incompatible design concepts were the comprehensibility and efficiency of the code and of program operation. Since It was anticipated that Individuals other than the programmer would be operating and modifying the software, some consideration had to be given to software comprehensibility both by operators and programmers. To this end, the preparatory program was extracted from a software package produced In conjunction with this research (Schlasner and Strohl, 1987) which utilized menus and default values to create an Inefficient, but very user-friendly environment. The extent of 157 user-friendliness on the part of the DDC control program, however, was limited only to the fact that the program would restart merely by recycling the Apple power switch if the operator recognized that the program was executing incorrectly. Although all programs were written in modular form, the complexity of the programs, the deviations from the modular form for the sake of execution speed, the lack of internal documentation for reason of program compactness, and the use of logical statements and other "tricks" to increase execution speed, make understanding the programs inconvenient at best. Obstacles. In addition to the problems identified previously in the software design section, there were many other problems that had to be resolved during the course of the software development. One set of problems related to limitations imposed by the KOGL system management. For example, inactive terminals were automatically logged out after fifteen minutes. Because of this, supervisor-DDC communication had to occur at least every fifteen minutes. Likewise, because a system purge of previous versions of files was accomplished each night, all information to be stored had to be appended to a single file, instead of appearing in multiple versions of a file. (As originally programmed, a new version of the data file was created each time a restart occurred. This served as a convenient, but dramatic means of identifying gaps in data due to restarts.) Another set of obstacles related to accessing the Micromodem lie. Access to the modem was possible either through firmware or direct register communication. Through firmware, BASIC commands were able to conveniently accomplish many communication actions, but by machine-language, direct-register access even 158 greater facility could be obtained. One action BASIC was unable to accomplish was an automatic restart If the carrier "was lost or If the Apple or VAX became hungup waiting for a correct response after receiving a correct, but garbled transmission. A machine-language program, theoretically, would have been able to eliminate this difficulty, but would have required considerable time for Its development and more Information than was available in the manual that came with the Micromodem lie. As a result. It was decided that, since an operator had to be present at all times to maintain the glucose analyzer, the operator could also be ready to restart the system If a hangup or other communication trap occurred. Although there were many other obstacles addressed In developing the on-line experimentation software, a final problem to be mentioned here Is filtering of measurement noise. Although the estimator was. Itself, a filter, all monitored signals were filtered. Attached to the glucose analyzer, the only device to have such a filter, was a (RC) hardware filter that had a 0.1 second time constant. Instead of a hardware filter, all other monitored devices were sampled using digital filters performing 100 conversions In ca. 1 second. The average value of the 100 samples served as the measurement for the cycle. These measurements were, then, averaged In sets of three, five and seven for communication and storage to the VAX, printer and disk drive, respectively. Data Analysis and Display Software written for the analysis and display of data obtained from simulations and experiments performed two principal functions: data file size reduction; and the display of any type of data collected with respect 159 to any other type. Software utilized. Most of the software used in the simulation studies, was also accessed by the data analysis and display programs, i.e. VAX FORTRAN compiler, VAX/VMS Linker, and the KCGL management system. In addition, however, one other software package was accessed: QWIKPIDT, a graphics package written by KCGL staff member James McDowell and based upon the Precision Visuals' (Boulder, CO) DI3000 graphics package. Software design. It was the primary purpose of the data analysis and display software, first, to provide quick, graphical descriptions of the change in important state variables and parameters with respect to time, and, second, to provide comparisons of estimated data with actual data (i.e., data obtained off-line or output from the process simulator). To accelerate the plotting process, data files larger than 2000 blocks were generally reduced to one-quarter their original size prior to plotting. In addition to quick, post-run plots, the software was also used for detailed analysis of specific estimator factors (such as specific elements of the Kalman gain matrix or values of error covariance matrix elements) over time. The software was also employed in preparing the higher quality plots such as those appearing in this dissertation. Obstacles. Although well done, QWIKPLOT was not a professionally produced package and suffered from inadequate documentation and serious limitations as to the format of the axis labels, the choice of axis length, the information permitted to be displayed in the legend, and so on. 160 Table 2 Expressions for the Series of Each Element of the State Transition Matrix (STM) SIM elements (1,1), (2,2), (3,3): 1 + STM elements (4,4), (5,5), (6,6), . . ., (13,13): 1 STM elements (4,9), (5,10), (6,11), (7,12), (8,13): 1 STM element (1,4); <1,4X1 + STM element (1,9): STM element (2,1), (3,1): (<1, 1>^+<1,l>^"ki,i>+< 1,l>^"^ SIM elements (2,4), (3,4): <1,1X1,4X1/2! + ( « 1 , 1>^-K1,l>k"ki,i>-Kl,l>'""^ SIM element (2,5): <2,5X1 + <2,2>/2! + <2,2>2/3j + . . . + <2,2>k/(k+l)i + . . .] 161 Table 2 (continued) STM elements (2,9), (3,9): (<1,1>^-Kl,l>*'"^ STM element (2,10): <2,5X5,10>{l/2! + <2,2>/3! + ... + <2,2>V(k+2)« + . . .] STM elements (3,6), (3,7), (3,8): <3,l>tl + <3,3>/2! + . . . + <3,3>V(k+l)! + 1=6,7,8 STM elements (3,11), (3,12), (3,13): <3,lXl,l+5>[l/2! + <3,3>/3! + . . . + <3,3>k/(k+2)! + ...], 1=6,7,8 STM elements not listed above are zero. Round brackets, parentheses, contain locations of STM elements. Triangular brackets, <>, contain locations of elements of original A matrix. Square brackets, [1, contain series that are expressible Is terms of series having exponential terms. CHAPTER VII PRELIMINARY EXPERIMENTATION This chapter describes all laboratory experimentation accomplished prior to the fermentations that applied adaptive control on-line. These experiments include growth of 29 shake-flask cultures, of a 600 ml continuous culture, of 18 9-liter batch and 8 9-liter fed-batch fermentations. Originally, there were several, varied purposes underlying this experimentation. In relation to the medium, the purpose was to optimize the glucose-nitrate-phosphate-trace metals (GNPS) medium, or some variation thereof, so that it was capable of consistently producing high-density C5 cultures. A collateral purpose was to determine if fed-batch was required at all; that is, if the additional expense of adding a nutrient feed was justified by the improved performance of a fed-batch configuration over a batch. In relation to the apparatus, experimentation was a means to evaluate the performance of the experimental apparatus and acquire experience in its operation. In relation to the simulation studies, although the preliminary experiments were not designed to provide a detailed model of the microorganism's behavior, they were intended to provide some order of magnitude parameter estimates, some estimates of instrument noise level and other input for the process model. And, in relation to the 162 163 adaptive control experiments, it was hoped that preliminary, fed-batch experiments that were based upon preestablished feed schedules would provide a performance benchmark against which the adaptive fermentations could be compared. Since preliminary experimentation was performed in parallel with simulation studies, early simulation studies were based upon previous, fed-batch experiments in which C5 was grown in complex media (Blackwell et al., 1987). As the preliminary experimentation progressed, assumptions that were discovered to be erroneous were modified which had profound effects upon the development of the estimator and optimal controller. Ultimately, the preliminary experimentation became a medium optimization study focusing upon a glucose-nitrate-phosphate-trace metals (GNPS) medium similar to one developed by M. Dekleva and colleagues (1985) for Streptomyces peucetius. The research progressed in three phases. The first phase involved the same constituents in the same proportions as Dekleva's medium, but increased their concentration. The second phase varied the individual proportions of medium components. And the third phase investigated the effect of the addition of small amounts of a complex nutrient, Proflo (Traders Protein, Memphis, TN), upon growth. In addition to these GNPS experiments, a few related experiments were performed to compare carbon sources, the adoption of ammonia as a nitrogen source, and the effect of low dissolved oxygen levels upon growth. Phase One The initial phase of experimentation involved 12 batch fermentations in which medium components and their proportions were the same as those of a 164 medium optimized for growth and anthracycllne production In peucetius by Dekleva et al. (1985). The Dekleva medium had the following composition, per liter: glucose, 22.5 g; sodium nitrate, 0.85 g; dlpotasslum phosphate, 0.174 g; magnesium sulfate heptahydrate, 0.123 g; and trace metals, 20 ml. (The composition of the trace metals solution Is described In Chapter IV.) Since 05 Is not peucetius (White and Stroshane, 1984) and since the purpose of this (dissertation) research did not encompass optimizing anthracycllne production. It was felt that the Dekleva medium could be Improved upon. The pupose of Phase One experiments, however, was not so much to optimize the medium as It was to observe the effect of higher concentrations of medium components upon the organism's growth rate and final biomass, and to determine what were the maximum concentrations the organism could tolerate. Batch fermentations were performed at the Ix (22.5 g glucose/llter), 2.22x (50 g glucose/llter), 4.44x (100 g glucose/llter), and 6.67x (150 g glucose/llter) concentration levels. With the exception of two, simultaneous, Ix batch fermentations that were performed to evaluate the performance of the experimental apparatus, no substantial biomass measurements were accomplished during this phase because the results were clearly evident: 05 did not grow In medium concentrations at the 6x level, or. If It did. Its lag phase lasted longer than 130 h. This Implies that. If the proportions of the Dekleva medium are maintained and a substrate yield of 0.5 Is assumed, achievement of biomass densities greater than 75 g dry blomass/llter would require a fed-batch mode of operation for the carbon source, and, based upon the available nitrate from a 6.67x medium 165 and upon biomass composition information, any biomass densities above 15 g dry biomass/liter would require fed-batch operation for the nitrogen source. In addition to evaluation of the performance of the experimental apparatus, the dual batch fermentations were intended to provide process information for the simulation studies. Augmenting on-line measurements of dissolved oxygen concentration, pH, off-gas oxygen and carbon dioxide concentrations and inlet air flow rate, off-line measurements of dry weight, optical density, and anthracycllne, protein, glucose, phosphate and nitrate concentrations were accomplished. Also, at the conclusion of the fementations, the oxygen mass transfer coefficient was measured for each fermentor applying the dynamic degassing method (Wang et al., 1979). Although intended to be identical, the two fermentations behaved quite differently. For example, optical density measurements of the first fermentor depict nearly linear growth commencing at the time of inoculation, while those of the second indicate a 42 hour lag phase followed by exponential growth having a specific growth rate of 0.04 h~l. Measurements of pH supported this observation as the pH of the first culture rose steadily after seven hours from 7.3 to 9.5, while that of the second culture rose slightly at seven hours, but did not rise substantially until 42 hours reaching a value of only 8.5 at 141 hours, the termination of the fermentation. Phosphate assays also indicated linear growth for the first culture between 30 and 120 hours as phosphate concentrations fell at a nearly constant rate of 0.0032 mM/h. Dry weight and protein concentration measurements exhibited too much scatter to confirm the other observations. At the conclusion of the fermentation, the first culture appeared to be 166 further into idlophase than the second as anthracycllne concentrations of 1.18 mg/1 and 0.22 mg/1, respectively, were observed. The oxygen mass transfer coefficient at the end of the fermentations were 132 and 142 h“^, which were close to a literature value of 108 h”l for a viscous streptomycete fermentation (Tufflie and Plnho, 1970). Phase TWO After Phase One demonstrated that merely Increasing the concentration of all medium components would not produce significantly higher cell densities. Phase Two began studying the effect of Individual components on £. 05 growth. The early research consisted of shake-flask studies observing the effect of glucose on growth. The first set of 8 250-ml side-arm flasks contained 80 ml of the Dekleva medium with a modification In the glucose concentration. Glucose concentrations ranged from 0.4 to 30 g/1 In the flasks. Only two flasks exhibited growth after 183 hours; they were flasks containing 10 and 16 g/1 glucose. The accepted explanation for this was an unsuitably small Inoculum; three loopfuls of cells from frozen stock. Part of the reason for the Inconsistent behavior also Involved the discovery that the original plate from which the frozen stock was grown was contaminated with a mutant. To a limited extent, this can explain some of the Inconsistencies that were observed during Phase One. With a pure stock culture, and a 1 ml Inoculum In each side-arm flask, the test was repeated; only, In this Instance, with 44, 33, 22, 11 g/1 (glucose equivalent) of cerelose, and. In a later experiment, 110, 88, 66, 44 g/1 (glucose equivalent) of cerelose. The results Indicate that. 167 In shake-flask culture, the duration of lag phase and the specific growth rate appear to Increase with glucose concentration. A difference of 6 percent In the maximum specific growth rates of the 44 g glucose/1 cultures was observed which was attributed to temperature effects, since the shaker's temperature control was Inconsistent, Care must be exercised In extrapolating these results to 14-1 fermentations, since 05 Is under relatively reduced dissolved oxygen tension In shake flasks and produces acids under these conditions. The final pH's of the first experiment were 4.6, 4.8, 4.9 and 5.1, In decreasing order of original glucose concentration. Prior to the first 14-1, batch fermentation of the second phase, results of elemental analyses of S^. 05 biomass were received. Interestingly, red, Idlophase cells ware observed as containing slightly more (0.16 percent) nitrogen that mid-log phase cells, an unexpected finding since e-rhodomyclnone, a major component of the stationary phase cells, contains no nitrogen. (This observation was disputed some months later by the second elemental analysis that Indicated a decrease of 1.8 percent In nitrogen between mid-log and stationary phase cells, from 9.2 percent to 7.4 percent.) These results Indicated that the maximum expected biomass that could be produced from 0.85 g/1 of sodium nitrate was ca. 1.4 to 1.5 g dry blomass/1. Implying that towards the end of fermentation the culture Is likely to be nitrogen limited. In preparing the first 14-1 fermentation of Phase Two, the phosphate concentration was Increased five fold to 0.87 g/1 (5 mM) K2HP0^ to provide additional buffering capacity and reduce the possibility of phosphate 168 limitation. Additionally, In comparison to previous fermentations, the air flow rate was decreased from 8 to 5 1 (STP)/mln, and agitation was decreased from 500 to 300 rpm. Growth In this first Phase Two fermentation, commenced soon after Inoculation and proceeded very quickly. At twenty-four hours, when It appeared that the carbon dioxide evolution rate may be declining, a pulse of 20 g of NaNOg In 250 ml of distilled water was added aseptlcally to the fermentation: an addition of 2 g NaNO^/l. From 0.36 g dry blomass/1 at the beginning of the fermentation the culture grew to attain 1.6 g dry blomass/llter at 43 hours, 2.7 g/1 at 70 hours, to 4.4 g/1 at 115 hours. Meanwhile, at these same times the glucose concentration fell from 21.7 to 17.3 to 12.8 to 4.5 g glucose equlvalent/llter and the Incremental yield declined from 0.27 to 0.25 to 0.21 g dry blomass/g glucose equivalent. The average yield was ca. 0.23 g dry blomass/g glucose equivalent. The fermentation was terminated at 123 hours because a significant fraction of the culture appeared to have concluded growth and was producing antibiotic. On the basis of elemental analysis, the 2.85 g NaNO^/l Introduced Into the fermentor would have been expected to produce a maximum of 4.9 g dry blomass/1 If all nitrate nitrogen went Into biomass formation. Since only 4.4 g dry blomass/1 was observed, ca. 0.3 g NaNO^/l remained as nitrate or was converted to a nitrogen-containing compound. At the conclusion of the fermentation an ammonia analysis was performed In addition to the glucose and dry weight analyses, the results exhibited an Increase In NH^CI-N from 1.51 to 4.8 to 7.2 to 10.9 mg/1 at 0, 43, 70 and 115 h, respectively. Indicating some nitrate nitrogen was converted Into ammonia and excreted, but much of the remaining nitrogen was probably still In nitrate. 169 The success of this early defined fermentation, which was never exceeded, greatly Influenced the design of successive fermentations by leading to the superficial conclusion that maintaining a moderate concentration of glucose and Increasing nitrate to Its stoichiometric ratio with glucose would result In optimal fermentation conditions. Three batch fermentations were Immediately performed that Increased nitrate level nearly to Its stoichiometric ratio with glucose. The first fermentor contained the standard amount of glucose, capable of producing 11.3 g dry blomass/1 given a substrate yield of 0.5, and 6.2x the standard amount of nitrate, capable of producing a maximum of 9.1 g dry blomass/llter given that nitrogen comprises 0.0955 percent of dry cell mass. The second and third fermentors had the same concentration of nitrate, but 3.6x (ca. 80 g glucose equlvalent/1) and 5.3x (ca. 120 g glucose equlvalent/1) the standard concentration of cerelose, respectively. All three fermentors contained lOx and 2x the standard levels of phosphate and magnesium sulfate, respectively. (lOx phosphate was only twice the level of the previously successful fermentation.) Assuming phosphorus comprised 2 percent of dry cell mass (Wang et al., 1979), the level of phosphate employed In these fermentations would have been capable of producing a maximum of 15.5 g dry blomass/1. And, given that the standard concentration of magnesium sulfate supported 4.4 g dry blomass/1, doubling the concentration was expected to support a minimum of 8.8 g dry blomass/1. Concentrations were not Increased more because of concerns that excessive levels might be reached, producing unexpected results. Within twenty-two hours after inoculation, more than twenty hours earlier than any other fermentations, the first two fermentors 170 exhibited anthracycllne production. This prematurely high level of production continued throughout the remainder of the fermentation until, at the conclusion of the fermentation seven days later, the color appeared to be the deepest red of any fermentation performed by this research. Although there was little growth, the pellets In the two fermentors seemed to be Intact and mechanically strong; somewhat unusual, considering that they had been producing for such a period of time. Production In the third fermentor began approximately 70 hours Into the fermentation and followed a similar path of little growth, but good antibiotic production. Since Improved growth, not anthracycllne production was the purpose of these experiments, anthracycllne assays were not accomplished. The rapid transition of these two fermentations from lag phase to Idlophase was believed to be due to the elevated nutrient concentrations. To avoid these concentrations, a fed batch fermentation was performed. The Initial medium was the Dekleva medium containing a 5x concentration (5 mM) of phosphate and 0.1 ml MAZU antlfoam/1. Two nutrient feeds were prepared with 700 g glucose/1 In one and salts In the other (NaNO^, 280 g/1; K2HP0^, 65 g/1; MgS0^.7H20, 9.2 g/1; and trace metals, 250 ml/1). The proportions of glucose to each salt was the same as those of the successful batch run, except an additional 20 percent of each salt was added. A malfunctioning pH controller required that pH adjustments be accomplished manually. The feed curve was designed assuming a twelve hour lag phase, but when growth did not commence at that time, nutrient feed addition was changed from automatic to manual. At the end of the fermentation, despite the addition of 800 ml of glucose and 600 ml of salts feeds, only nominal growth was observed. 171 Additionally, some melanin production seemed to have occurred due to the uncharacteristic blackness of the final broth. The ensuing fermentations were a dual fermentation: a fed-batch using essentially the same initial medium and feeds as the previous fermentation; and a batch employing the same medium as the initial fed-batch medium. The initial media were different from the previous fed-batch initial medium in that they included 20 mM (4.18 g/1) MOPS buffer. This was done to reduce the difficulty of controlling the pH encountered during the previous fermentation. The feed curve was also shifted backward 6 hours to provide for a longer lag period. As in the case of the previous fed-batch fermentation, feeding commenced prior to growth, so automatic feeding was suspended and manual feeding instituted. At the conclusion of the fermentations, even though the fed-batch medium had received an additional 250 ml of glucose and 600 ml of salts feed, the batch fermentation exhibited an average specific growth rate of 0.027 h“^ while the fed-batch exhibited an average rate of 0.020 h“l. Both final dry weight measurements were 1.0 - 1.2 g dry biomass/1. The subsequent fed-batch fermentation was designed to reproduce the previous fermentation. As before, due to the slow growth of the microorganism, automatic feed addition was eliminated in preference to manual addition. No significant growth appeared until 85 hours after inoculation (23 hours after automatic feed addition was terminated). To extend the growth of the culture beyond the conclusion of the 96-hour, normal feed schedule, the feed schedule was reset to start at the 60 hour point, and automatic feed control was begun. The result of this action was 172 that growth continued at a nearly constant specific growth rate of 0.014 h~l for the first 200 hours of the fermentation, and reached a dry weight of ca. 2.9 g/1 before the rate slowed. At 286 hours, the fermentation was concluded and the dry biomass concentration was 3.6 g/1. The final fermentation of Phase Two was a fed-batch fermentation that, again, reproduced the previous two fermentations, except that magnesium sulfate was fed in a separate, third stream. The purpose of this fermentation was to determine if the precipitation of the magnesium sulfate with the other salts in the feed reservoir had any effect upon growth. At 50 hours no effect was observed, as the 0.54 g/1 dry weight measurement for this fermentation compared favorably with the 0.52 g/1 measurement at 59 hours of the previous fermentation. At 65 hours, 0.5 g of Proflo was introduced aseptically into the fermentor. It appeared to have little effect as at the end of the fermentation, 167 hours, the dry biomass of 2.23 g/1 was very close to the previous fermentation's measurement of at 177 hours of 2.32 g/1. Phase Three The results of the second phase appeared to indicate that the maximum biomass concentration that could be obtained from the GNPS medium was probably 5 to 6 g dry biomass/1. Since limitations of the support subsystem required that glucose be the carbon source, three fermentations were accomplished to determine if small amounts of Proflo could increase the final biomass concentration. Proflo was chosen since research by J. V. Blackwell (1987) and other coworkers of W. R. Strohl had already demonstrated that increased densities could be achieved with yeast extract. 173 and soybean meal. However, in obtaining increased densities, they demonstrated that increased amounts of the complex nutrient were required, amounts which would have transgressed the carbon source constraint of this research. All three Proflo augmented fermentations used essentially the GNPS medium of the final fed-batch runs of the previous phase, except approximately 5 percent more sodium nitrate was added to the salts feed and the separate magnesium sulfate feed was eliminated by adding it to the glucose feed after autoclaving. The first Phase Three fermentation acquired its Proflo through 4 g that was added to the 880 ml seed flask. Although exhibiting a specific growth rate approximately four times greater (0.0508 h~^) than those of the later Phase Two fed-batch fermentations, the final dry weight measurement at 93 hours was ca. 4.6 g/1 only a little improved over the best fermentation without Proflo. The second fed-batch fermentation received Proflo both from 4 g that were added to the 880 ml inoculum and from 8 g that was introduced as a separate, third feed stream. In this instance, the specific growth rate was closer to the fermentations lacking Proflo, at 0,0197 h“^. After 140 hours of growth, the final dry weight measurement was 4.0 g/1. The final fermentation differed from the second only in the amount of Proflo in the feed, 27.5 g/1. It exhibited a specific growth rate intermediate to the previous two fermentations, 0.026 h~^, and reached a final biomass concentration of 4.3 g dry biomass/1 after 185 hours. 174 Feed profiles for these fed-batch runs assumed a 6 hour lag phase. Although the feed pump was allowed to operate automatically for the most part during these fermentations, several, large manual additions were made during the third fermentation when it appeared that the feed may not have been adequately following the fermentation. An assumption underlying the modeling of this process is that balanced growth occurs during log phase. That is, components of biomass and metabolites are produced in proportion to each other. Such behavior would be reflected by equal specific production rates of all products, as appeared to be observed for a defined medium fermentation when a specific growth rate of 0.0135 h“^ was observed with a specific carbon dioxide production rate of 0.0117 h”^. However, the first two. Phase Three fermentations exhibited specific growth rates of 0.0508 and 0.0197, while having specific carbon dioxide production rates of 0.0979 and 0.0374 h“^, respectively, during the initial stages of the fermentation when the effect of the feed is small. The ratios of the carbon dioxide specific production rate and that of biomass were 1.927 and 1.898, a difference of less than 1.5 percent, and deviating considerably from unity. Data from the third fermentation was not included because the high range carbon dioxide meter was used, and its results possess significant scatter. Related Research Three experiments were conducted that were a part of the preliminary experimentation and were related to nutrient optimization. Ammonia nitrogen source. In studying peucetius, Dekleva et al. (1985) reported, "Ammonia alone did not support the growth of 175 S^. peucetius. . In contrast, a 14-1 batch experiment with C5 growing on GNPS medium in which nitrate was replaced by 10 mM ammonia, demonstrated that C5 can utilize ammonia as a nitrogen source. Growth over 103 hours on an initial ammonia concentration of 10 mM that was supplemented by two additions at 7 and 61 hours of sufficient NH^Cl to increase the ammonia concentration to 30, then, 50 mM, resulted in a growth rate of ca. 0.037 h“^ and a final dry biomass of 0.94 g/1. Two major differences observed between growth in ammonia and growth in nitrate were that the cells formed pellets much more slowly in ammonia than in nitrate, and the cells excreted very little of the anthracycline they produced. Instead of pellets, the cells tended to remain in finely, dispersed floes, and, instead of excreting anthracycline, the cells that produced anthracycline, appearing to be only those cells that formed pellets, maintained the product in their bulk, becoming extremely red. Other carbon sources. Shake-flask experiments were performed to observe the effect of other carbon sources on growth. Optical density measurements were used as indirect means of measuring biomass in 250 ml side-arm flasks. Using the GNPS medium as a basis, the effects of growth on cerelose, mannose, and dextrin were observed by replacement of the cerelose by identical amounts of the other carbon sources. To another flask was added equal quantities of dextrin and cerelose which bad a combined weight equal to that of the single carbon sources. To additional flasks containing the same materials was added 0.66 g (8.3 g/1) yeast extract (Amberex 1003, Amber Laboratories, Milwaukee, Wl). And, to one other flask that contained 176 cerelose, but lacked nitrate, 10 M of ammonium chloride was added. The cultures were prepared by transferring 1 ml of frozen stock to each seed flask containing 80 ml of the appropriate growth medium. Then, after four days, 1 ml of cells were transferred from each seed flask to a side-arm flask containing 80 ml of the same medium. The best growth appeared in the cerelose and yeast extract flask where, within 23 hours after inoculation the optical density was 475 Kletts (as measured with a Klett-Summerfield photometer using a red filter, 640 to 700 nm). The second best culture was the mannose and yeast extract culture which had a 280 Klett absorbance at 23 hours (and, ultimately had a biomass density of 4.35 g dry biomass/1). The third best culture was the dextrin, cerelose, and yeast extract culture reaching 550 Klett units after a longer lag phase of 97 hours. Growth for the ammonia and nitrate-containing flasks were very similar, beginning by 72 hours and reaching final absorbances of 183 and 214 Klett units, respectively. The remaining cultures showed little or no growth: mannose (31 Klett units after 216 hours); dextrin (18 Klett units after 216 hours); dextrin and yeast extract (83 units after 216 hours); and dextrin and cerelose (20 Klett units after 167 hours). The results indicate that, of the media tested, C5 cultures grow most quickly and to the highest biomass concentration in cerelose and yeast extract, and mannose and yeast extract media. Both grew very quickly initially, producing a viscous slime that later disappeared. Growth under oxygen limitation. Observation of growth under low dissolved oxygen concentrations was attempted applying continuous culture techniques. However, it was discovered that the air pump of the continuous 177 culture system was Insufficiently accurate to maintain a constant dissolved oxygen concentration, especially for levels at or below 30 percent of air saturated water. Summary of Preliminary Experimentation Preliminary experimentation indicated that, given the restrictions imposed by the support subsystem, the medium developed by Dekleva et al. (1985) for peucetius in many respects is optimal for batch C5 growth. Studies described herein, observe that the duration of lag phase and the specific growth rate may increase with increasing glucose concentration, up to a limit of between 80 and 150 g/1 glucose where growth does not occur. The glucose concentration of the Dekleva medium is within a range of concentations exhibiting a high specific growth rate and short lag phase. Experimentation appears to indicate that high levels of nitrate, phosphate, and magnesium sulfate may promote anthracycline production. The Dekleva medium has concentrations below these levels. Research discussed in this chapter has observed that, while ammonia and nitrate promote similar levels and rates of growth, ammonia depresses anthracycline production. The Dekleva medium uses nitrate as the nitrogen source. However, the Dekleva medium has little buffering capacity and, due to low nitrate concentrations, cannot support cell densities beyond ca. 1.5 g dry biomass/1. To compensate for these inadequacies, a GNPS medium using a MOPS buffer and having five times the amount of phosphate was adopted (as an initial medium), in conjunction with a feed having nearly stoichiometric amounts of carbon and nitrogen. When grown upon these media C5 appears to be able to achieve a maximum density of 5 to 6 g dry biomass/1; however, to do so consistently 178 seems to require in excess of 300 hours. Limited quantities of Proflo has demonstrated an ability to consistently reduce the time required for growth by approximately half, but does not appear to contribute to increase in the final biomass concentration. Lastly, since growth of C5 on a defined medium seems to be affected by levels and rates of change of nutrient, and since it exhibits a lag phase having variable duration, and since its growth curve varies unpredictably, possessing a shape intermediate between an exponential and a linear curve, open loop feeding schemes cannot provide consistent performance. In short, since it appears that salts must be fed to avoid promoting anthracycline production, but the growth of the organism is unpredictable and is affected by the feed rate, a feed strategy possessing feedback character is required to achieve maximum biomass. CHAPTER VIII SIMULATION RESULTS AND DISCUSSION Chapter VI stated that the purpose of the simulation studies accomplished for this research was (i) to develop and validate the process model, (ii) to develop and test estimator and control schemes, and, (iii) in conjunction with results from on-line experiments, to refine the estimator and controller. Since the behavior of the microorganism is poorly understood, detailed validation is not possible. Therefore, instead, validation consisted of merely ensuring that the process model exhibited correct, general characteristics: exponential growth early in the fermentation; substrate uptake proportional to growth; decreasing dissolved oxygen; and so on. Inspection of the simulation studies results in Appendix C, reveals that the process model does exhibit the correct characteristics. Chapter IX describes the results of simulation studies that used data from on-line experiments to refine the estimator and controller. This chapter describes the second topic: development and testing of the estimator and control scheme. Appendix C gives the results of these studies . The simulations described in this chapter are not those upon which the estimator and optimal controller for the first on-line fermentation were based. The original simulations, stored onto magnetic tape, were lost due 179 180 to mechanical problems with the tape drive. As a result, the simulation studies discussed herein are approximate recreations of the earlier studies. They are approximate recreations because the original studies were based upon data from high-density fermentations using complex media (J. V. Blackwell and P. L. Lorensen-Kretz, personal communication), and not upon data later acquired from defined-medium fermentations, as the simulation studies described below have been. The earlier studies, explained exactly how the estimator for the first on-line fermentation was tuned and precisely how the tuning parameters were obtained; some of which eventually were carried over to the third on-line fermentation. This chapter will only describe the performance of the estimator and give a broad description of the tuning procedure. Simulation Study Strategy The simulation studies assisted in the definition of an effective, practicable estimator model and aided in determining satisfactory values for the tuning parameters of the Kalman filter which included the process noise covariance matrix, or "Q" matrix, the measurement noise covariance matrix, or "R" matrix, and the initial error covariance matrix, or "P(0)" matrix. By definition, the noise covariance matrices are not design parameters, but are, in fact, noise statistics used in deriving the optimal estimator. Since noise statistics are seldom known in practice, it is common for the elements of the matrices to be treated as design parameters. Hamilton et al (1973) recognized this when they suggested increasing the magnitude of elements in the process noise covariance matrix relative to the measurement noise covariance matrix to shift the weighting from the process model to 181 process measurements in situations where unmeasured process disturbance may exist and where modeling error may be great. Two characteristics of effective estimator performance are the rapid detection of process changes and the convergence of estimated values within a reasonable time frame. Comparing the values obtained from the estimator with the uncorrupted output from the process model over time, provides a means of quantitatively evaluating the estimator performance. Process simulator, fo adequately represent the process, the model chosen to simulate the process not only had to exhibit behavior described by the dynamic biomass, substrate, oxygen and volume balances, equations (5.25) to (5.28), but, on occassion, had to exhibit behavior characteristic of growth conforming to a cube root growth law (Marshall and Alexander, 1960), jçl/3 = + kt (8.1) of Contois (1959) kinetics, = kj^^ s (8.2) KgX + 8 of double substrate limitation, one of which is a gas (Finn and Wilson, 1954) K = s o (8.3) (Kg + s)(Kg + o) and of sudden drops in the oxygen mass transfer coefficient due to antifoam addition. Additionally, process and measurement noise levels approximating those inherent to the process were incorporated into the process simulator. 182 The strategy adopted for the simulator was to utilize the exponential growth model of equation (5.25) with constant process parameters as the standard process model, while altering growth law, kinetic parameters and other factors individually—oir^in^pairs^to observe the effect of these factors upon the performance of the estimator. To simulate measurement noise, the process model outputs, dissolved oxygen concentration, and oxygen uptake and carbon dioxide evolution rates, were corrupted by white noise having a mean equal to the zero and a standard deviation equal to ten percent of the uncorrupted output, and the substrate concentration output was distorted by zero-mean, white noise having a standard deviation of 0.5 grams/liter. With the exception of a few simulations, no process noise was included in the process simulator because no satisfactory basis existed for estimating the process noise level. Specific factors studied. The effect of the following factors upon estimator performance were examined during these simulation studies: 1. Measurement noise level. 2. Growth law. 3. Kinetic parameters. 4. Biomass composition. 5. Error in initial state and parameter estimates. 6. Initial error covariance matrix estimates. 7. Noise covariance matrix estimates. Before study of those factors could proceed, however, a preliminary simulation was performed to verify the consistency of the process and estimator models. The process model was run in the absense of process and measurement noise, while the estimator was provided correct initial state estimates and its P, R, and Q matrices were set to zero. As was expected. 183 no difference between the process and estimator output was observed indicating that Gear's method of variable step integration of the estimator and the Runge-Kutta method of the process model were consistent. Bench-mark Simulation To assist in the evaluation of controller performance during these simulations studies, one particular simulation was selected to serve as a reference against which other simulations would be compared. The simulation that was chosen was one that applied the "standard" process simulator, that is, exponential growth in a batch process with constant parameters, in conjunction with the estimator that had performed the best under a range of anticipated conditions and which eventually was adopted for the on-line experiments. The results of that simulation are depicted in the first set of figures appearing in Appendix C, Figures 5 through 12. In addition to employing the "standard" process simulator, which superimposed 10 percent white noise on the measurements, but provided no process noise, the reference simulation imposed the "standard" initial estimate errors upon the estimator and set the estimator's P, Q, and R matrices to the "standard" values. Specifically, the initial biomass, substrate, dissolved oxygen and saturated dissolved oxygen concentrations were 0.15, 20.0, 0.0078 and 0.0080 g/1, while the process simulator's specific growth rate, oxygen mass transfer coefficient, and overall substrate and oxygen yields were fixed at 0.0577 h~^, 120 h“^, 4.056, and 0.5, respectively. However, the initial estimates of the same factors that were provided to the estimator were 0.12 g/1 (20 percent in error), 20.5 g/1 (3 percent in error), 0.0075 g/1 (4 percent in error), 0.0079 (2 percent in 184 error), 0.063 h“^ (13 percent In error), 132 h~^ (10 percent in error), 0.45 (10 percent in error), and 4.45 (10 percent in error), respectively. The values of the elements of the P and R matrices appear in the program listing of subroutine KNLAST in Appendix B. The Q matrix in this simulation was set at zero. One, final, "standard" aspect of this reference estimator is that it incorporated three new state variables, described in equations (5.32) to (5.39), to improve the performance of the specific growth rate, overall substrate yield, and oxygen mass transfer estimates. The estimates depicted in Figures 5 through 12 of Appendix C, exhibit an initial deviation from the actual state, but show general convergence later towards the end of the simulation. For example, biomass, specific growth rate and the oxygen mass transfer coefficient each exhibit ca. 150 percent deviation early in the simulation, but converge to within 4, 6 and 16 percent, respectively within 60 hours. Although characteristic of the particular values set into the estimator design parameters, the P, R and Q matrices, the early deviation appears partially attributable to overshoot exhibited by the specific growth rate and oxygen mass transfer coefficients; deviations that have been reported by Stephanopoulos and San (1984) and Shioya et al. (1985). The values of the P, Q, and R matrices were arrived at through substantial, but not exhaustive, simulation experience. The values of the P(0) matrix are listed in the PROJP matrix of program KNF028 of Appendix B (lines 82 through 94). Off-diagonal elements were set equal to zero. The Q matrix was set equal to zero, while the diagonal elements of the R matrix, R(1,1) through R(6,6), were 0.00823, 0.0251, 5.63 x 10 185 0.0189. 33.5, 0.25, respectively. Elements off the diagonal of the R matrix were zero. They were selected to provide satisfactory estimator performance, not only under "standard" conditions, but under a variety of conditions, and were designed to perform best during the later stages of fermentation, specifically, during the Interval In which the biomass concentration Is between 2 and 5 g/1. Reduction of the divergence of the filter during these simulation studies was accomplished by reference to explanations for the appearance of divergence offerred by Blerman, Melsa and Sage, and others. Blerman (1971) gave three explanations for the appearance of Kalman filter divergence: Incorrect a priori statistics and unmodeled parameters; the presence of nonllnearltles; and computer roundoff. Although he presented no substantial solutions to the first cause, and merely commenting that, while the second situation Is generally unsolvable, effective ad hoc approaches to Its resolution do exist, Blerman detailed several techniques for addressing the third problem: roundoff. His suggestions Included : (1) computation of upper triangular matrices, and then forcing symmetry; (11) computing the entire matrix, and then averaging off-dlagonal elements ; (111) periodic testing and resetting of the diagonal elements (maintaining nonegatlvlty) and other elements (maintaining correlations that are less than unity); (Iv) using the stabilized Kalman expression In place of (I-KM)P (discussed In Chapter V); (v) using larger values or minimum constraints on the values of elements In the error covariance matrices; and (vl) application of square root covariance filtering to preserve the positive semldeflnlte character of the error covariance matrix. At the time of the publication of his book. 186 Blerman considered the last alternative to be the superior approach, but, in 1976 he introduced a U-D factorization technique that demonstrated advantages in terms of rduced computation time. Melsa and Sage (1971) also discussed Kalman filter divergence, and concluded that the basic reason divergence occurs is that the (Kalman) gain matrix approaches zero too quickly. In such a situation prior data is weighted more heavily than recent input which reduces the effect of the increasing observation error on the filter, thereby decoupling the filter from the observation sequence. Such a situation frequently comes about when the process noise is small compared to the measurement noise, resulting in a small process noise covariance matrix and relatively larger measurement noise covariance matrix which combine to reduce the gain matrix. The methods recommended by Melsa and Sage were essentially the ad hoc methods alluded to by Bierman, and included direct increase of the gain matrix, establishing minimum constraints on the error covariance matrices and artificially increasing the plant-noise variance. As an aside, Melsa and Sage also mentioned the use of adaptive filtering algorithms, such as adaptive noise estimation as described by Jazwinski in 1970 and Brown in 1983. Use of these techniques and previously mentioned methods to reduce overshoot recommended by Stephanopoulos and San (1984) and Shioya et al (1985) were considered to reduce filter divergence, but were felt to require time in excess of that available for this research. In addition to serving as a basis of comparison with other simulations. Figure 5 through 12 in Appendix C will also be used to depict results from other simulations when the difference between the two 187 simulations are insignificant. Performance Improvement through Additional State Variables The first simulation studies concentrated upon tuning the measurement noise covariance matrix. Using the knowledge that the process model output was corrupted with ten percent measurement noise as a starting point, laborious trial-and error fine-tuning produced a set of ratios between the diagonal elements of the measurement noise covariance (R) matrix that exhibited acceptable estimator performance. Additional investigation improved the estimator performance by maintaining the ratios, but reduced the magnitude of the individual elements. Although similar to the results displayed in Figures 5 through 12 in Appendix C, the performance of the improved estimator suffered from limited responsiveness. Figures 13 and 14 depict the sluggish response of the specific growth rate and oxygen mass transfer coefficient under "standard" conditions. The slow convergence exhibited by the specific growth rate, oxygen mass transfer coefficient and substrate yield parameters was undesirable. This condition was exacerbated by the experimental observation that these parameters were not constant, as the "standard" process model simulated, but varied with time; slowly for the specific growth rate and substrate yield, but often rapidly for the mass transfer coefficient when antifoam was added. Although adequate to demonstrate that the parameters changed with time, the experimental observations lacked the consistency necessary to modify the estimator model reliably. As a first step in addressing this problem, the estimator model was redesigned to provide the parameters with Increased dynamics by altering their rate of change. Prior to the modification their 188 rate of change with respect to time was zero; afterward it was set equal to an estimated variable that had a zero time rate of change. Expressed mathematically for specific growth rate, then, = 0 (8.4) dt was replaced by the system, ^ = cd (8.5) dt d(d) = 0 (8.6) dt where c is a constant and d is an additional estimated variable. When incorporated into an estimator that was applied to the standard process simulator, the immediate effect of this inclusion appeared to be counterproductive; the filter exhibited no obvious improvement in its estimates of most values, and demonstrated significantly decreased accuracy during the early portions of the simulation for parameters that were changed, as can be observed by comparing Figures 8 and 13, and Figures 10 and 14 of Appendix C. However, when the process simulator was altered by introduction of a time-varying specific growth rate through Contois kinetics, exhibited in Figures 15 through 18, and time varying oxygen mass transfer coefficient through simulation of antifoam addition, depicted in Figures 19 through 24, the estimator incorporating the additional state variables exhibited superior performance. In the case of Contois kinetics, while estimates of several variables were roughly comparable, significant errors arose in estimated biomass and substrate concentrations for the 189 estimator lacking the additional state variables. In the instance of antifoam addition, estimates of several variables were, again, nearly identical, but dissolved oxygen concentration, the oxygen mass transfer coefficient and saturated dissolved oxygen concentration exhibited significant error without the additional dynamics. In addition, in both instances the speed of response of the estimated parameter was improved with the additional dynamics: from 20 hours to 10 hours for the specific growth rate under Contois kinetics; and from 27 hours to 5 hours for the oxygen mass transfer coefficient under antifoam addition. Effects of Changes in the R Matrix and of Measurement Noise Level Tuning of individual elements of the measurement noise covariance matrix appeared to produce somewhat localized effects. For example, a ten-fold increase in the element related to overall substrate yield primarily affected biomass, specific growth rate, overall substrate yield and substrate estimates, having much less effect upon oxygen-related estimates as is shown in Figures 25 through 28. While a decrease of nine-tenths in the oxygen yield-related element principally affected biomass, saturated dissolved oxygen and dissolved oxygen concentrations, oxygen mass transfer coefficient, and oxygen yield, had substantially less effect upon substrate-related estimates, as evidenced in Figures 30 through 34. A decrease in the substrate concentration-related element of the measurement noise covariance matrix followed this pattern by exhibiting its greatest effects in biomass, substrate concentration, and specific growth rate estimates. The biomass estimate, depicted in Figure 35, decreased the 190 Initial error substantially, but exhibited a greater error later in the simulation. However, it should be noted that, while, as a general rule, effects are localized, exceptions are not uncommon. Figure 29 depicts an improved oxygen mass transfer coefficient due to the change in the overall substrate yield element described above. Increasing all elements of the measurement noise covariance matrix ten-fold, as expected, resulted in significantly improved performance for a simulation employing the "standard" process model, as evidenced by Figures 36 through 43. However, the increases slowed the response of the parameters that possessed additional dynamics, that is, specific growth rate, overall substrate yield and the oxygen mass transfer coefficient, and would not be expected to perform as well with a "nonstandard" process model. Instead of varying the R matrix under constant noise levels, two simulations were performed in which the R matrix was the same, but the noise levels varied. Aplying the "standard" estimator, it was observed that the noisier the measurement, the less accurate the estimate. In a noise-free environment, the estimator generally converged within 36 hours, except for the overall oxygen yield which required 70 hours and for biomass concentration which slowly diverged. Biomass, overall substrate and oxygen yields and the oxygen mass transfer coefficient exhibited off-sets of less than twenty percent. Significant errors resulted when noise levels were three times the stanrard levels. These are depicted in Figures 44 through 51 of Appendix C. The most deleterious effects were exhibited by the oxygen mass transfer coeffcient which did not converge and biomass and dissolved oxygen concentrations and overall substrate and oxygen yields which appeared 191 to converge, but experienced off-set. Effects of Changes in the P Matrix and of Error in Initial Estimates Estimating initial values for the error covariance, P, matrix is easier than obtaining values for the noise covariance matrices, Q and R, since it is easier to estimate the inherent error of the initial state estimate than it is to estimate process and measurement noise statistics. Estimates of the errors of the three state variables introduced to improve the performance of the specific growth rate, overall substrate yield and oxygen mass transfer coefficient parameters required some simulation experience. Ultimately, however elements of the P matrix are arrived at, their effect is short term as the influence of new measurements dilutes that of old measurments. To demonstrate this, two simulations were accomplished which increased the magnitude of elements of the initial error covariance matrix. In one simulation all estimates were increased ten fold, in the other only the element related to the biomass concentration was increased ten times. The result, as represented by the profile of biomaca concentration over time in Figure 52, was a larger initial deviation than occurred with the standard values for P matrix elements; ca. 470 percent error for the larger elements versus 150 percent error for the standard elements. The effect diminished with time, though, as after forty hours most of the estimates had returned to levels approximating those having a standard initial P matrix. 192 Two simulations were also performed to observe the effect of the different levels of initial error upon estimator performance, once the P matrix was established. In these runs the "standard" estimator was applied. When the initial estimates were correct there was a significant improvement in all estimates throughout the duration of the simulation. The improvement in the biomass estimate,depicted in Figure 53, is representative of that improvement, as the overall error was smaller and convergence occurred approximately seven hours sooner than in simulations under standard conditions. On the other hand, when the initial error was twice that under standard conditions, overall error was larger and convergence occurred much later than under standard conditions. Again, biomass concentration is used to represent this situation in Figure 54. Effect of Cube Root Growth Law Designed to not only follow quickly changing parameters, such as those exihibited by Contois kinetics, the standard estimator was also intended to follow different growth laws, such as the cube root growth law. Figures 55 through 58 exhibit the performance of the estimator when the process simulator is based upon such a growth law. Expectedly, estimates of some variables are not as accurate as those provided for an exponential growth law: biomass concentration requires 60 hours for convergence, and the specific growth rate exhibits a 40 percent error at the end of the simulation. In defense of the estimator's performance, however, the specific growth rate of the process model and that of the estimator do not really represent the same quantity, and four of the estimates, substrate concentration, dissolved oxygen concentration, saturated dissolved oxygen 193 concentration, and overall substrate yield perform almost as well under these conditions as under standard conditions. Effect of e-Rhodomycinone Production Potentially important factors Influencing estimator performance are the formation of products other than biomass and error in biomass composition. Since the major product of C5 on a GNPS medium is the secondary metabolite e-rhodomycinone, one simulation was accomplished in which the process simulator modeled a situation in which 25 percent of the biomass produced is anthracycline. A yield similar to that of biomass, 0.5, was assumed for its production so that this was equivalent to a situation in which the estimate of the biomass composition was in error; the composition of the process simulator being CHi,67%.48%.14" After applying the standard estimator, the only significant differences observed between the two simulations are in the overall substrate and oxygen yields, and the oxygen mass transfer coefficient, exhibited in Figures 59 through 61. If all of the anthracycline is excreted, the substrate yield would be 0.38, if none is, the yield would be 0.50, but the estimator is Incapable of distinguishing between the two situations. Similarly, the new oxygen yield is 3.61 if the product is held in bulk and 2.71 if excreted. Lastly, in this situation, the oxygen mass transfer coefficient exhibits an initial rise and slow decline. Effect of Double Substrate Limitation, Glucose and Oxygen To oberve the potential effect of low dissolved oxygen levels upon growth, the process model was modified so that the specific growth rate 194 followed kinetics described by Finn and Wilson (1954), expressed in equation (8.3). Kq was assumed to be 0.7, Kg was assumed to be unity and the maximum specific growth rate was set equal to 0.577. The resulting simulation indicated that at cell concentrations less than 10 g/1, the dissolved oxygen concentration would decrease by ca. 12 percent and the specific growth rate would decline by ca. 11 percent, which would not significantly affect estimator performance. The oxygen mass transfer coefficient and overall oxygen yield estimate profiles, however, were altered and appeared very similar to Figures 57 and 58, respectively. Effects of Changes in the Q Matrix and of Measurement Noise Level With the exception of a brief remark at the beginning of this chapter describing the value of the Q matrix in improving filter performance in situations where process noise is important or where significant modeling errors or unmeasured process disturbances are expected, little attention has been given to tuning the process noise covariance (Q) matrix. A difficulty encountered in this research with tuning the Q matrix is that there is no information available describing the amount of process noise existent in a fed-batch C5 fermentation. In order to observe the effect of process noise upon the standard estimator and of the Q matrix upon the behavior of the estimator, a series of simulations were performed in which an attempt was made to tune the matrix under varying levels of process and measurement noise. Results from simulations in which the process model was subject to measurement and process noise consisting of zero-mean white noise having 195 standard deviations of ten and one-hundred twenty percent, respectively, indicated that a non-zero Q matrix provided more accurate estimates when the additional dynamics of the specific growth rate, overall substrate yield and oxj’gen mass transfer coefficient parameters were eliminated, and that the performance of the standard estimator was not significantly affected by process noise at this level. Figures 62 through 68 exhibit the performance of an estimator having a relatively small Q matrix and no additional dynamics in estimating the state of a process which exhibits the process and measurement noise described above plus Contois kinetics and a rapid drop in the oxygen mass transfer coefficient at one point. Figures 69 through 76 depict the performance of the standard estimator to such conditions. When compared, the former estimator exhibits a slower response and greater overall error than the latter, standard, estimator. Simulation studies indicate that the performance of the former estimator appears to improve as the magnitude of the elements of the Q matrix are reduced. Estimator Performance with a Constraint on Specific Growth Rate Since much of the early error in the estimator appears to be due to unreasonably high estimates for the specific growth rate, a simple approach to reducing the error is to place a constraint upon the specific growth rate. Such a constraint was imposed of 0.1 h”^, a 7 h generation time. Although most estimates changed insignificantly when this limit was imposed in a standard estimator in conjunction with a standard process model, biomass and specific growth rate estimates were clearly improved, as depicted in Figures 77 and 78, respectively. 196 Combined Estimator and Optimal Controller Performance The ultimate test for any estimator In this research Is how well It performs In conjunction with the optimal controller. Since the optimal controller essentially functions to maintain optimal conditions, which In this case would be a constant substrate concentration, the performance of the estimator may be evaluated by how well It maintains a constant substrate concentration. Figures 79 through 82 depict two estimators working under the standard process model and a process model exhibiting Contois kinetics and a sharp decrease In the oxygen mass transfer coeffcient. Under the standard process model the substrate concentration deviation between the initial and final times was 2.6 g/1 for the standard estimator without additional dynamics, In Figure 79, and 6.15 g/1 for the standard estimator, In Figure 81. Estimations based on a process simulator exhibiting Contois kinetics and a sudden decrease In the oxygen transfer coefficient resulted In differences between the Initial and final substrate concentrations of 9.4 g/1 for the standard estimator without additional dynamics. In Figure 80, and 9.1 g/1 for the standard estimator. In Figure 82. Summary of Results Laboratory experiments have demontrated that growth of C5 on a GNPS defined medium can be unpredictable, based upon our present level of understanding of the microorganism. Possible behavior Include growth consistent with a cube root growth law, substantial, rapid decreases In the oxygen mass transfer coefficient due to antifoam addition, exhibition of process and measurement noise, a variable specific growth rate conforming to 197 Contois kinetics or some other kinetic model, and changes in growth rate due to large, rapid changes in nutrient concentration. In addressing the problem of developing an estimation scheme that would perform under such conditions, simulation experiments were performed to obtain a satisfactory estimator model and to tune the noise covariance matrices. These were followed by simulations in which the process model and other conditions were varied to determine their effect upon the performance of the estimator. During this evaluation a reference process model, which was based upon exponential growth and constant process parameters, a set of reference conditions, and a reference estimator were chosen to serve as a basis for comparison. The approach ultimately adopted for developing the estimator involved empirically tuning the R matrix, modifying the eight-equation estimator model to include three additional state variables that would provide the specific growth rate, overall substrate yield and oxygen mass transfer coefficient parameters with a faster response (frequently described herein as, "additional dynamics"), setting the Q matrix equal to zero, and imposing a maximum constraint upon the estimated specific growth rate. In implementing this approach trade-offs appeared between (i) fast response or overshoot for variables with the additional dynamics, (il) greatest accuracy occurring earlier or later in the simulation, (ill) greater model or measurement dependence, and (iv) tuning for one set of conditions or tuning for a range of conditions, and so on. In the end, it was observed (i) that errors in the estimated biomass composition have little effect upon estimator performance, (il) that the estimator without additional dynamics performs signficantly better than that with such capability when modeling 198 error is small and.parameters are constant or slowly change with time, but the reverse was true when modeling error was large, (iii) that large values for elements of the R matrix and small values for elements of the Q matrix provide better performance when modeling error is small, that the reverse is true when modeling error is large, but some intermediate state is better for potential conditions in C5 fermentation, (iv) that process noise levels exhibiting standard deviations of one-hundred twenty percent (ca. 0.2 for biomass) do not significantly affect the accuracy of most estimates of the "standard" estimator, (v) that dissolved oxygen levels for cell concentrations under 10 g/1 will have little expected influence upon growth or estimator performance, (vi) that most effects of error in the initial P matrix estimate will disappear before 40 hours has elapsed, under anticipated conditions, (vii) that a maximum constraint on the estimated specific growth rate improves the peformance of the standard estimator, and (vii) expectedly deleterious effects result from large process and measurement noise, large error in initial estimates and so on. The ultimate test of the performance of the estimator is when it operates in conjunction with the optimal controller, since the controller calculates its action based upon a combination of several variables, and since optimal control is the objective of this research. A characteristic of the optimal controller derived for this research was that it acts to maintain conditions existent when it is activated. It would appear that, since the controller operating in conjunction with the standard estimator exhibits substantially poorer performance (three times more error) during standard conditions and only marginally better performance, 3 percent less 199 error, during conditions exhibiting Contois kinetics and rapid changes in the oxygen mass transfer coefficient, the controller without the additional dynamics would have been adopted for on-line application. However, such was not the case. The estimator with the additional dynamics was chosen because its response was faster and its performance was more consistent with respect to unexpected process changes than the estimator without additional dynamics, and because the potential exists for unexpected process changes to occur on-line that are greater than those simulated. Its greater consistency is demonstrated by the observation that when the process simulator changed from the "standard" process model to one exhibiting Contois kinetics and a rapid decrease in the oxygen mass transfer coefficent, the estimator without the additional dynamics had a 400 percent Increase in error, while the estimator with the additional dynamics had only a 50 percent Increase. Simulation studies also Indicated that controller peformance improved when a constraint was placed upon the maximum specific growth rate. As a result, such a constraint was included in the on-line estimator. Simulation studies indicate that estimator performance may be Improved further in four ways: obtaining improved process knowledge through laboratory experimentation; obtaining improved tuning through more simulation studies; adoption of an adaptive Q matrix; and modification of the additional dynamics to reduce overshoot through methods described by Stephanopoulos and San (1984) and Shioya et al. (1985). CHAPTER IX EXPERIMENTAL RESULTS AND DISCUSSION The experimental application of the estimator and optimal controller consisted of three supervised fermentations. Although designed to perform identically, their behavior differed markedly. Fermentation One The first fermentation differed from the two that followed in several important respects. First, after collecting more than 70 hours of data during an 85 hour fermentation, all but a few hours of data stored in the minicomputer were lost during a daily purge of higher versions of files by the system management. Second, this fermentation served to test experimental procedures and the system as whole. The fermentation highlighted the need for a better filter for the glucose analyzer, it brought out the importance of starting with a larger initial liquid volume to compensate for drawdown due to sampling, it emphasized the need for improved dissolved oxygen probe calibration, and demonstrated the need to store Apple-VAX communications to facilitate post-run simulation. Finally, unlike other fermentation runs, this run exhibited no significant sensor failure. 200 201 Although the system functioned remarkably well mechanically, the results that were recovered indicated substantial estimator error. Given initial state estimates of 0.07 g/1 dry biomass, 20.7 g/1 glucose, 0.0076 g/1 dissolved oxygen, and 0.0080 g/1 saturated dissolved oxygen concentrations, within three hours the estimator was providing estimates of 6.67 g/1 dry biomass (probably more than 6 g/1 in error), 20.81 g/1 glucose, 0.00423 g/1 dissolved oxygen (probably more than 40 percent in error), and 0.0101 g/1 saturated dissolved oxygen (probably more than 25 percent in error) concentrations. Estimates at the end of the fermentation, then, were 13.8 g/1 dry biomass (more than 11 g/1 in error), 26.0 g/1 glucose, 0.0069 g/1 dissolved oxygen (more than 10 percent in error) and 0.00638 g/1 saturated dissolved oxygen (probably more than 20 precent in error) concentrations. Estimated parameters followed an equally convulsive pattern as the initial specific growth rate, substrate and oxygen yields, and oxygen mass transfer coefficient were 0.046 h~^, 0.45, 4.06 and 120 h~^, respectively, which became 0.21 h“^, 0.62, 17.3 and 13.7 h~^ within three hours, and which finished at 0.0075 h”^, 0.62, 19.3 and 3.7 h“^. When these results were reviewed after the fermentation, two principal sources of error were believed to have accounted for a substantial portion of the error in the estimates. First, error in calibrating the dissolved oxygen probe appeared to have resulted in inordinately high oxygen transfer estimates, indicative of more biomass than was actually present. Second, the tuning of the R matrix still, inappropriately reflected some of the assumptions made during early simulation studies which were based upon growth in a complex medium. These errors were corrected by additional 202 simulation studies prior to the next on-line fermentation and by more careful calibration of the dissolved oxygen probe during preparation for the next fermentation. The additional simulations assumed values for parameters such as specific growth rate and the oxygen mass transfer coefficient that were more representative of growth in the defined medium, and retuned the R matrix based upon these new values. Fermentation Two In contrast to the first fermentation which exhibited satisfactory mechanical performance, the second fermentation was marred by instrumentation failure (principally by the glucose sensor and associated filter). Designed to proceed over 90 hours, nine hours after inoculation a glucose sensor pump failed. Thirty hours later, a new pump was installed, but the fermentation had progressed too far to obtain useful data. Lacking a suitable seed culture, it was decided to withdraw all but approximately one liter of broth, to serve as a seed, then aseptically refill the vessel with fresh medium in the manner of a repeated fed-batch fermentation. The technique succeeded, and computer monitoring commenced eleven hours later. However, seven hours into the monitored portion of the fermentation, the glucose sensor valve failed, which resulted in a transient glucose concentration measurement of 350 g/1 that affected all state and parameter estimates throughout the remaining 47 hours of the fermentation. The results of the second fermentation are depicted in Figures 83 through 94 of Appendix D. Shortly after the glucose concentration transient, estimates of all variables moved to unreasonable levels; the biomass concentration estimate 203 rose to approximately 135 g/1; the substrate concentration estimate Increased to 350 g/1; the dissolved oxygen concentration fell by 0.006 g/1; the specific growth rate rose by 0.8 h~^; the overall substrate yield jumped to 17; the oxygen mass transfer coefficient rose by 350; the overall oxygen yield Increased by 31; and the saturated dissolved oxygen concentration dropped by 0.005 g/1. In addition, substrate and oxygen maintenance energy requirements rose to 0.34 h“^ and 0.1 h~^, respectively. Maintenance energy requirements were calculated off-line after the completion of the fermentation by applying the relation, m = kj^(l/Y' - 1/Y) (9.1) where the true substrate and oxygen yields, Y, were assumed to be 0.5 and 4.06, respectively. Although the glucose sensor produced Inaccurate measurements for only five hours, only five measurements, specifically, glucose concentration, dissolved oxygen concentration, substrate yield, saturated dissolved oxygen concentration and the oxygen mass transfer coefficient, appeared to recover and converge to reasonable values. Excluding the first seven hours. It would be difficult to extract much useful Information from the results exhibited In the first twelve figures of Appendix D. However, since all Apple-VAX communications were stored. It was possible to alter the erroneous glucose concentration measurements to more reasonable values and repeat the fermentation through simulation. Of course, the controller could not be tested through simulation because flow rates observed during the actual fermentation had to be retained In the simulation studies. In addition to correcting the 204 erroneous glucose concentration measurements, however, a modification also was made to the estimator: this and all succeeding fermentations and simulations had a 0.1 h“^ maximum specific growth rate estimate constraint Imposed upon the estimator. The results of this process are displayed In Figures 95 through 104 of Appendix D. The essential character of the results, by estimate. Is as follows: for biomass concentration, an Initial 3 g/1 transient at the 12 - 27 hour point, which was about ten times greater than that measured off-line, and a general tendency to overestimate; for glucose concentration, a fast recognition, but somewhat sluggish response to rapid changes, otherwise good tracking characteristics; for dissolved oxygen concentration, generally good tracking character, but a slight (less than 4 percent), unrepresentative movement at the 14 hour point In time; for specific growth rate, sharp Initial oscillation during the first 25 hours, after which the estimate appears to converge with overshoot to a reasonable estimate; for substrate yield, after an Initial overshoot at the 14 hour point, apparent convergence; for the oxygen mass transfer coefficient, an Initial rise at 12 hours was followed by slow apparent convergence; for oxygen yield, continuous oscillation; for saturated dissolved oxygen concentration, after an Initial oscillation, a slow decline; for substrate maintenance energy requirements, apparent convergence only after 40 hours of rapid changes; and for oxygen maintenance requirements, rapid transitions during the first thirty hours, followed by possible convergence. A description of "possible convergence” Is attached to the oxygen maintenance energy requirements estimate because negative maintenance energy requirements were equated to 205 zero in these figures. The estimates and apparent deviations at the conclusion of the simulation were as follows: biomass concentration, 3.0 g/1 (180 percent error, based upon off-line dry weight measurements); glucose concentration, 29.3 g/1 (2.8 percent error, compared to on-line measurements); dissolved oxygen concentration, 0.0074 g/1 (2.5 percent error, compared to on-line measurements); specific growth rate, 0.024 h”^ (40 percent error, based upon a rate of 0.017 h“^ derived from the last two dry weight measurements); glucose yield 0.33 (probably 10 percent high, based upon experimentation described previously); the oxygen mass transfer coefficient, 530 h”^ (probably more than 300 percent in error based upon values obtained from the literature (Tuffile and Pinho, 1970) and experiments described previously); oxygen yield, 4.1; saturated dissolved oxygen concentration, 0.0076 g/1; glucose maintenance requirements, 0.023 h“^, based upon a true glucose yield of 0.5; oxygen maintenance requirements, 0.000 h“^, based upon a true oxygen yield of 4.06. In analyzing the difference between the estimated and the observed values that existed at the end of the simulation, four sources of error were identified: error in initial estimates; actuator error; premature fermentation termination; and sensor error, excluding the glucocse sensor failure. The error in the initial estimates were as follows; biomass concentration, 0.34 g dry biomass/1 (210 percent); substrate concentration, less than 0.2 g/1 (less than 1 percent); dissolved oxygen concentration, less than .0008 g/1 (less than 1.2 percent); specific growth rate, 0.0074 (24 percent); and overall substrate yield, less than 0.2 (less than 70 per 206 cent). The error in the initial estimate for the remaining variables could not be estimated due to lack of means to determine the actual initial values. As was observed in simulations, the effect of error in initial estimates is diluted as new measurements are received by the estimator. However, error of the magnitude of that of the biomass concentration and the overall substrate yield had not been created In simulation, so it is difficult to determine how far into the fermentation it influenced the estimator. Additionally, since the run ended prematurely, there was less time for its influence to diminish. The second error source, actuator error, may have affected the performance of the estimator in estimating the substrate concentration, since the greatest deviation of the substrate estimates from on-line measurements occurred during feeding intervals. The third source of error, premature termination of the fermentation, had an effect in addition to that just mentioned. Since the estimator, as a trade-off, was designed to perform better during later portions of the fermentation, in biomass concentrations above 3 g dry biomass/1, termination of the fermentation prior to this concentration characteristically resulted in error in certain estimates, especially estimates of biomass concentration. Differences between the actual and estimated biomass concentration in simulations in this range of concentrations was 100 to 150 percent, even when the error in the initial biomass concentration estimate was half of that observed in this fermentation. The fourth error source consisted of sensor error. The three process outputs included the glucose concentration, dissolved oxygen concentration, and carbon dioxide evolution rate. The failure of the glucose sensor was an obvious source of error, but 207 even after some of its output were modified with more reasonable data, the remaining data contained error. For example, a transient ocurred at ca. 45 hours. Output from the dissolved oxygen probe appear to contain no obvious erroneous deviations, but the carbon dioxide evolution rate exhibits an unexpect decline after 14 hours. The decline may be due to pH effects of the feed which had a slightly different pH than the broth at that time, and which reached its maximum flow rate just prior to the decline. The effect may have been responsible for the decrease in the estimated biomass concentration after 14 hours and the dramatic drop in the specific growth rate. Disturbances such as these interfered with the accuracy of estimates and impeded convergence. The original fermentation and subsequent simulation both assumed an initial biomass concentration of 0.5 g/1, which was, in reality, 0.34 g/1 in excess of the dry weight measurement obtained off-line after completion of the fermentation. To investigate the effects of this error upon the estimator, a second simulation was accomplished based upon the observed dry weight, that measured off-line, and a smaller growth rate-related element in the measurement noise covariance matrix. In comparing these results with those from the previous simulation, it was observed that, although the biomass peak at 14 to 30 hours was shorter and broader than the previous simulation, that Is, exhibited smaller error early in the simulation, its error at the conclusion of the simulatéd fermentation was 2.9 g/1 (173 percent error). Compared to the 180 percent error in the biomass concentration at the end of the previous simulation, this would seem to indicate 54 hours, the ultimate duration of the fermentation, was sufficient 208 to almost completely dilute the influence of errors in the initial estimate. The modifications made to the second simulation had other effects also as some estimates exhibited increased deviation when compared to the previous simulation, specifically, substrate concentration, specific growth rate, overall substrate yield and the oxygen mass transfer coefficient. This seemed to be due to the smaller R-matrix element. Fermentation Three The third and final fermentation was designed to run for approximately 88 hours with computer monitoring and control commencing 10 hours after inoculation. This is essentially what transpired with the exception that the fermentation was extended for an additional eight hours to observe the anticipated conclusion of an apparent growth spurt that began near the 57 hour point in the fermentation. With the exception of a glucose concentration transient at 20 hours, and an unexplained decline in the dissolved oxygen concentration 36 hours after computer monitoring began, the system's mechanical performance seemed to be satisfactory. The results of the third fermentation are presented in Figures 105 through 116 of Appendix D. The biomass concentration estimate displayed two periods of growth from 7-20 hours and from 44 - 75 hours followed by periods of small declines in biomass. The decline in the growth rate is supported by dry weight measurements made off-line, by changes in the carbon dioxide evolution rate, and by operator observation; although unexpected, it appeared to be genuine and not instrument error. The estimate of 1.72 g/1 for the final dry weight differed from dry weight measurements accomplished off-line, after completion of the fermentation by 0.94 grams (120 percent). 209 Substrate concentration estimates followed the on-line measurements very closely, responding within 1.5 hours to the drop at 20 hours and recovering within 5 hours. The estimate at the end of the fermentation was within 0.3 g/1 (1.3 percent) of the on-line measurement which was within 0.3 g/1 of its value at the beginning of the run. Overall, excluding the transients at 6 and 20 hours, the substrate varied within a range of jp.9 g/1 (4.5 percent) over the course of the fermentation. The dissolved oxygen estimator did not track the on-line measurements of dissolved oxygen as closely, however, as an unexpected, gradual decline in the dissolved oxygen concentration from 0.0078 g/1 at 35 hours to 0.0074 g/1 at 50 hours was responded to by a decrease in the estimate from 0.0078 g/1 at 35 hours to 0.0076 g/1 at 87 hours. The difference at the conclusion of the run amounted to 0.0002 g/1 (or 3 percent error). When compared to the specific growth rate measurements that were based upon dry weight measurements, the estimated specific growth rates exhibited two periods of oscillation and overshoot. The first occurred within the first thirty hours of computer monitoring and was marked by large, rapid changes. The second followed subsequently and exhibited a smaller range and more gradual changes with possible convergence near the end of the fermentation. At the conclusion, the estimate of the specific growth rate was ca. 0.0087 h~^ (compared to 0.014 h~l, a 45 percent error, based on the final three dry weight measurements or 0.0096 h"l, a 9 percent error, based upon the last two measurements). The overall substrate yield displayed three periods of activity. The first occurred within the first thirty hours of computer monitoring and was characterized by large changes, punctuated by a series of 210 smaller peaks. The second period followed thereupon and continued exhibiting the smaller fluctuations but not the larger movements. The third Interval began at the conclusion of the second (at ca. 60 hours) and was characterized by a smoother profile and gradual decline. Although the Initial range of values was between 0.14 and 0.49, the estimates fell from ca. 0.31 to 0.19 at the end of the fermentation. This observation Is consistent with experimentation reported In Chapter VII, where, for a slightly faster growing culture, the overall substrate yield fell from 0.27 during the first forty hours to 0.25 over the next thirty hours to 0.21 over the final fifty hours. The oxygen mass transfer estimate displayed no convergence, however, as It maintained ca. 80 - 150 h”^ for the first 40 hours of computer monitoring, then began an uninterrupted rise to 2000 h~^ by the conclusion of the fermentation. This rise coincided with the unexplained decrease In the dissolved oxygen measurement. Conversely, the overall oxygen yield fell from 5.8 to 1.4 during the entire course of the fermentation with the only break occurring as a 0.75 rise at 26 hours. Neither the oxygen mass transfer coefficient, nor the overall oxygen yield exhibited any apparent tendency to converge over the second half of the fermentation. The estimated saturated dissolved oxygen concentration displayed an Initial decrease from 0.008 g/1 to 0.0078 g/1, followed by nearly forty hours of slow movement about 0.0079 g/1, which subsequently transitioned to a very gradual decline from 0.0079 g/1 at 40 hours to 0.0076 g/1 at the end of the fermentation. This was an expected condition as biomass and metabolic products began to accumulate. Both the substrate and oxygen maintenance energy requirements exhibited three periods of change. 211 The Initial period, lasting 27 hours, consisted of large, rapid changes, which was followed by a brief ten hour Interval of near constancy, which. In turn, was followed by a transition to a second period of possible convergence. The Initial period for the substrate maintenance energy requirements displayed a range of 0.01 h”^ to 0.13 h“^ with a mean of approximately 0.035 over the first twenty-five hours. At 37 hours a rise occurred from 0.01 h~^ to 0.028 h“^. From 60 to the end no general movement occurred, and the final substrate maintenance requirement was approximately 0.29 h”^. These values are consistent with those related by Plrt (1975) for Aerobacter cloacae grown aerobically under glucose limitation, 0.094 g glucose/g dry blomass/hour, and for Pénicillium chrysogenum grown aerobically on an unidentified carbon source, 0.022 h~l. Oxygen maintenance energy requirements displayed an Initial range of 0.000 to 0.0053 h“l which resolved to a period of small changes In the vicinity of 0.0004 h"^, which led to a 22 hour rise to 0.0037 h"l. The final twenty hours of the fermentation were characterized by a very gradual Increase over 15 hours to 0.0039 h“^ which was followed by a jump to 0.0044 h”^. As was the situation for the previous fermentation, there appeared to be four primary sources of error: sensor error; actuator error; termination of the fermentation prior to reaching later portions of the fermentation for which the estimator was tuned; and error in the Initial estimates. Unexplained sensor deviations occurred at the following times : 0 to 5 hours when the carbon dioxide evolution rate rose, then returned to Its Initial value; 6 and 20 hours when the glucose sensor exhibited short, rapid excursions of more than 1 g/1 glucose concentration; and 34 to 44 hours when 212 the dissolved oxygen probe reported a decline in the dissolved oxygen concentration. To investigate the effect of the more than 3 g/1 decrease in glucose concentration at 20 hours, a simulation was performed that replaced that transient with more reasonable values. While some estimates show little effect, such as biomass concentration, overall substrate and oxygen yields, and substrate concentration outside of the neighborhood of the transient, other estimates are clearly influenced by the change. For example, a peak appears in the specific growth rate, and substrate and oxygen maintenance energy requirements at 22 hours with the transient, but disappears when the transient is excised. Interestingly, the oxygen mass transfer coefficient, saturated dissolved oxygen concentration, and dissolved oxygen concentration are affected by the removal of the transient as the oxygen mass transfer coefficient changes from an ever divergent curve to one that converges at approximately 25 h“^, as the saturated dissolved oxygen concentration changes from a curve that gradually declines to 0.0076 g/1 to one that only declines to 0.0079 g/1, and as the estimator changes from requiring more than 50 hours to converge to the on-line measurement to requiring only 4 hours after the unexpected decline in the on-line measurement at 34 hours. The second error, actuator error, again seems to influence the substrate concentration estimate as the estimator's poorest performance in estimating this variable occurs during the first 27 hours of the fermentation and during the final 22 hours which are the periods having the highest feed rates. Actuator error affects the other estimates also through its dilution effect, but affects the substrate estimate the most because its influence is more than merely dilution; it's 213 adding substrate. For technical reasons, the fermentation could not progress past 90 hours. Because of this and the low specific growth rate exhibited by the organism, the fermentation never progressed into the region for which the estimator was designed which resulted in less than optimal estimator performance. This fermentation, as did the previous, exhibited a deviation in the biomass concentration estimate of more than 100 percent which is consistent with the original simulation studies that were performed to develop the estimator. Also consistent with the simulation studies is the small change in the biomass estimate, relative to the observed growth of the microorganism, after the culture has passed 0.7 to 0.8 g/1. In simulation, the culture continues to grow faster than the estimate until at 2 to 3 g/1 they converge. Two additional simulations were accomplished to observe the effect of error in initial estimates upon the estimator performance. While both incorporated the substrate concentration "correction" of the first simulation, the second simulation, exhibited in Figures 117 through 126, corrected the initial biomass estimate from 0.5 to 0.23 and decreased the biomass-related element in the R matrix from 0.019 to 0.004, and the third simulation additionally changed the specific growth rate from 0.023 to 0.03 h~^, and altered the overall substrate and oxygen yields from 0.45 and 4.41 to what appeared to be more reasonable values of 0.35 and 3.0, respectively. The modification had the following effects: for the biomass concentration, the second simulation exhibited little change from the original fermentation, however, the third simulation showed a downward shift in the profile of the estimate such that the final biomass concentration was 214 only 90 percent In error; for the substrate concentration, the third simulation exhibited a faster response to the change in the substrate concentration at 20 hours, deviating from the on-line measurement by at most 0.5 g/1 and converging within 3.5 hours after the increase stopped, as opposed to a deviation of at most 1 g/1 and convergence within 5.5 hours for the second simulation; for the dissolved oxygen concentration, both simulations follow the unexpected decrease in the on-line dissolved oxygen measurement at 34 hours, but the third appeared to diverge towards the end of the fermentation, producing a deviation error of ca. 9.5 percent in contrast to essentially no deviation for the second simulation; for the specific growth rate, both simulations exhibited significantly larger peaks at 11 hours than did the on-line estimate, but all three finished within 10 percent of the specific growth rate obtained from off-line dry weight measurements; for overall substrate yield, the on-line estimates and both simulations were essentially the same with the exception of the first few hours and hours 11 to 40, but even then the differences were less than 10 percent; for the oxygen mass transfer coefficient, the simulations did not diverge to 1950 h~^ as the on-line estimate did, instead, the second simulation followed the path of the first simulation with a final value of ca. 24 h~^, while the third followed a similar path, but continued to rise over the final twenty hours and finished at ca. 65 h""^; for overall oxygen yield, again estimates of the the second simulation were similar to those of the first, but the third simulation's estimates began a steeper decline after 65 hours and finished at 0.2; for saturated dissolved oxygen concentration, the two simulations gave nearly identical, almost constant 215 estimates that varied less than 3 percent from 0.008 g/1; for substrate maintenance energy requirements, the second simulation was, again, similar to the first simulation, but the third simulation did not exhibit the gentle rise between 22 and 50 hours observed by the other two, instead, it exhibited noisy estimates in the neigborhood of 0.014 h“^, after which, at 65 hours, a rise to another plateau of ca. 0.023 h~l occurred; for oxygen maintenance energy requirements, the second simulation was nearly identical to the first, but the third simulation differed substantially by exhibiting a low initial peak followed by a constant period from 22 to 44 hours during which the estimated value was ca. 0.001 h”^ which was followed by a rise to 0.048 h~^ during the last half of the simulation. As was observed for Fermentation Two, the effect of errors in the initial state estimate appears to be short-lived. Even the 60 percent improvement in biomass concentration estimates by the third simulation (as compared to the on-line estimates) at 23 hours decreases to 30 percent at 87 hours. Two further simulations were performed to observe the effect of removal of the additional dynamics and the effect of a ten-fold increase in the measurement noise covariance matrix upon the estimator's performance. In the former instance, a simulation identical to the second simulation described in the previous paragraph was accomplished without inclusion of the additional dynamics. In general, the response of the estimator was very sluggish relative to the second simulation, as may be observed when the specific growth rate profile of the simulation with additional dynamics, Figure 120, is compared to that without the additional dynamics. Figure 127. For the most part, differences between the third simulation and the 216 simulation that repeated It with a ten-fold increase in the R matrix are insignificant and not worthy of comment. Three differences worth noting, however, include; a downward shift in the biomass concentation curve in which the initial peak and subsequent curve of the estimator possessing the greater R matrix is 0.1 g/1 less than that of the third simulation which resulted in a final estimate less than 80 percent in error (compared to less than 90 percent error for the third simulation); a 20 percent larger initial peak in the specific growth rate at approximately 11 hours for the estimator with the larger R matrix, but roughly equivalent performance beyond 44 hours ; and a slight upward shift after 63 hours in the substrate maintenance energy requirements curve of the simulation possessing the greater R matrix such that its final estimate was 0.026 h“^, as compared to 0.023 h"^ of the third simulation. The ultimate evaluation of the estimator does not occur by considering the performance of one or two variables it estimates. The best evaluation occurs in conjunction with the optimal controller, since the optimal controller bases its action upon the combination of several estimates. Further simulations, based upon on-line experiments, to observe controller performance could have been accomplished, but were not because the best evaluation also occurs on-line where the effects of equipment error, such as variable dead time in the glucose concentration measurement and actuator error, are experienced, and not in simulation. Since the process starts at the substrate concentration constraint which is the optimal growth state of permitted states, the optimal controller essentially acts to maintain constant substrate concentration. 217 An obvious follow-on experiment which was not accomplished would be to control substrate concentration through application of a PID controller. Summary of On-Line Experimentation On-line application of the estimator and optimal controller suffered from four principal problems; sensor error; actuator error; error in initial estimates; and inadequately long run time. Sensor error crippled the second fermentation when the glucose sensor failed and seriously affected the third fermentation. Actuator error had little effect upon most variables, in most instances only being related to dilution effects, except for substrate concentration which was the central variable for evaluating the combined estimator and optimal controller performance. Error in initial estimates were observed to be time dependent; significant, for these fermentations, only during the first forty hours or so. The effect of the inadequate run time was significant because the simulations were based upon the assumptions that cell density would exceed 2 g dry weight/1, which was reasonable in light of the preliminary fermentation experiments. Since the estimator had to confront several situations its design was a compromise. As one of the trade-offs the estimator was tuned to tolerate early error while providing better performance during later portions of fermentation when conditions were changing more rapidly and when effects of reduced oxygen concentrations might appear. When fermentations failed to run long enough to reach the required densities the estimator was performing consistent with its design, but inaccurately. The inadequately long run time is a complex problem. There were only two people that understood and 218 were capable of repairing the apparatus. To extend the fermentations would require more time and an additional personnel; resources not available to this research. Instead of more operators, faster growth would have had the same desired effect. The third fermentation ran 96 hours from inoculation to termination and produced less than 1 g dry weight/1 of cells; whereas, a batch fermentation produced almost 3 g dry weight/1 of cells in the same period of time and with essentially the same medium. It was the inconsistency in the growth of the organism that appeared to prevent the system from reaching the region in which the estimator would have exhibited better performance. Addition of small amounts of Proflo appeared to have the ability to consistently improve the growth rate, but it was felt that a semi-defined medium complicated the situation and may have introduced the possibility of other factors affecting the results. Ultimately, for the third fermentation, the on-line estimator and optimal controller acted to maintain the substrate concentration within 40.9 g/1 (+4.5 percent) of the optimal concentration. This performance was remarkably better than that possible by an open-loop feed schedule given the inconsistent growth of the organism during this fermentation. CHAPTER X CONCLUSIONS Traditional techniques of growing microorganisms in submerged culture have depended upon reproducing previously successful fermentations by following pre-established, empirically-determined paths. However, inadequate instrumentation and such open loop control schemes have provided little ability to adapt to process changes. This research has addressed these problems through the application of an on-line, adaptive, optimal control technique that is based upon process information obtained from an extended Kalman filter. More specifically, the goal of this research has been to develop a fermentation control system capable of producing a stated concentration of biomass in minimal time where the final biomass concentration is one that could be considered high-density for the given organism and growth conditions. The experimental system consisted of an anthracycline-producing bacterium. Streptomyces C5, grown in a defined medium, in a 14-liter automated fermenter constructed as a part of this research. The computer-controlled apparatus was capable of on-line monitoring of eleven variables while manipulating six, and possessed a telephonic link to a VAX 8500 minicomputer. 219 220 Preliminary experimentation, consisting principally of medium optimization, indicated that growth of S^. C5 on a defined, glucose-nitrate- phosphate-trace metals medium was capable of producing more than 5 g dry biomass/1 over a period of more than 200 hours. Additionally, preliminary experimentation (i) in shake flasks, indicated that Streptomyces C5 lag phase and specific growth rate increase with glucose concentration to maxima between 80 g/1 and 150 g/1, (ii) in 10-liter fermentations, indicated that growth rate is increased, but final biomass concentration does not change with the introduction of small quantities of cottonseed flour (Proflo), (iii) in 10-liter batch fermentations, indicated that elevated concentrations of nitrate and phosphate promote anthracycline production, and (iv) in shake flasks, demonstrated that the addition of significant amounts of yeast extract elevated final biomass concentrations. Preliminary experimentation also revealed that, for the anticipated biomass concentrations, the oxygen uptake rates could not be measured with adequate accuracy for inclusion in the Kalman filter due to instrument limitations. An optimal control algorithm was derived through application of Pontryagin"s maximum principle. It assumed a time-optimal performance criterion, and incorporated a three material-balance model over biomass and substrate concentrations and volume with control variable constraints and a physical constraint on the maximum allowable substrate concentration. The maximum substrate concentration constraint was due to the filter's requirement for a substrate concentration measurement and a limited measurement range by the glucose sensor. The resulting feeding policy was 221 H2 > 0 t < tj 0, Hg < 0 F = Fg > F^"' ti< t F = X V (10.2) ^s (^feed " An extended Kalman filter was adopted to provide the controller with required state and parameter estimates. The filter received carbon dioxide evolution rate, and dissolved oxygen and substrate concentration measurements every ten minutes, then produced estimates of eight state variables and parameters based upon an exponential growth model in which the specific growth rate, oxygen mass transfer coefficient, and overall substrate yield were changing with time. The specific variables and parameters that were estimated included : biomass concentration; substrate concentration; dissolved oxygen concentration; specific growth rate; overall substrate yield ; oxygen mass transfer coefficient; overall oxygen yield ; and saturated dissolved oxygen concentration. The possible conditions and kinetics of growth anticipated early in the research included : exponential or cube root growth; Monod, Contois or double substrate limitation kinetics; increasing maintenance energy requirements; secondary metabolite production; rapid changes in oxygen mass transfer coefficient due to antifoam addition; and unmeasured disturbances. To create a filter that was capable of operating under such conditions required design compromise between opposing 222 factors, such as speed of response and overshoot in some estimates, or superior performance earlier versus later in the fermentation. Simulation studies were employed to tune the filter through adjustment of diagonal elements of the noise covariance matrices. Ultimately, the process noise covariance matrix was set equal to zero and only measurement noise covariance matrix parameters were manipulated. The filter was tuned to exhibit fast convergence with moderate overshoot and to be most accurate later in the fermentation, that is, above 2.3 g dry biomass/1 when conditions are changing most quickly. Based upon this tuning, under exponential growth conditions with constant process parameters, simulation results exhibited characteristically high biomass concentration estimates and low substrate concentration estimates early in the simulations with convergence occurring when biomass concentrations exceeded 2.3 g/1, overshoot in specific growth rate and oxygen mass transfer coefficient measurements, and slow oscillation around the actual overall oxygen yield by the estimated overall oxygen yield. The remaining estimates tracked the variables they estimated within five percent. All estimates converged to within five percent of the actual values prior to the biomass concentration reaching 6 g/1, except the overall oxygen yield and oxygen mass transfer coefficient which were within 15 percent. On-line experimentation with the estimator and optimal controller suffered from four deficiencies: sensor error; actuator error; error in the initial estimates; and error inherent in the estimator during early portions of the fermentation. Despite these errors and unexpected, large, rapid changes in growth rate, the optimal controller maintained the substrate 223 concentration to within +0.9 g/1 (+4.5 percent) of the optimal concentration. Also, in spite of these errors, the estimator tracked the on-line substrate and dissolved oxygen concentrations within 5 percent, the rapidly varying, off-line specific growth rate measurement within 50 percent, and the off-line biomass concentration measurement within 180 percent overall and within 120 percent at the end of the fermentation. Additionally, the overall substrate yield estimates of ca. 0.30 declining to 0.19, and substrate maintenance energy requirements estimates of ca. 0.023 h“^ agree with literature and experimental values obtained during preliminary experimentation. Significant estimator improvement was observed during simulation studies which were based upon the results from the fermentation, but contained data modified to remove some sensor error and error in initial estimates. APPENDIX A HARDWARE SCHEMATICS 224 VAX 0500 DAC EXPANSION SLOTS p H ADC Figure 1. Experimental Apparatus. ÎO to LA 226 - > > 10 kohm 1N4002 7HR1 JT o 4011 J IN* r 0.1 uF our* I OUT3 IN3 OND r /tF" Figure 2. Interrupt Generator. 4-5 V A D 5 9 2 O 4- A D C k o h ADC Figure 3. Temperature Sensor. 10 kohm 10 kohm GND 1 GO ko h m 6800 pF Figure 4. Agitation Tachometer. N>ro APPENDIX B COMPUTER PROGRAM LISTINGS 228 229 BASIC-LANGÜAGE PROGRAM FEDBATCHO Initialization program. Variables: I Loop counter J Loop counter K Loop counter X Miscellaneous storage X$ Miscellaneous string storage 230 3LIST 70 m o 100 80 IN# 0: PR# 2: C%1 1%2: mU W I 90 PR# 0: INS 2: CMl 1002: (OUIW 100 TEXT : HOŒ : INVERSE : FDR I = 2 TO 39: VTIffl 1: HTflB (I): PRINT ' VTfiB 17: HTRB (I ): PRINT ■ lEXT 110 FOR I » 2 TO 16: HTfffl 39: VTflB (I): PRINT ’ HTAB 2: VTRB (I): PRINT * ÆXT : WJRNflL : VTRB 21 120 HTflB 7: VTIffl 4: PRINT ’THE WIO STATE DIVERSITY" 130 HTflB 5: VTfiB 6: PRINT 'flDWTIVE, O P T m KWTRtL PROGRAM" 140 HTflB 11: VTfffl B: PRINT "STEVEN M. SCHLflSNER" 150 HTflB 7: VTf® 10: PRINT "VERSIKl 1.0 (XTTOKR, 1986" 160 HTflB 12: VT/ffi 12: PRINT "CWYRIBTT(C) 1986" 170 VTflB 14: HTflB 12: PRINT "Kl RIGHTS REKRVED" 160 VTflB 21: HTflB 1: DLL - 958: VTflB 21: HTflB 9: PRINT "PROGRAM LOAD IN PROGRESS" 253 REM 256 KM ======a s REM 262 REM U aSWT mSTER DISK V2.0.3 265 K M 268 REM COPYRIGHT 1C) CYBORG CORP, 1983 271 K M 274 K M PAGE THKE IWORMATICM 277 K M 313 POKE 768,0: POKE 769,173: POKE 770,0: PWE 771,224: PWE 772,72: POKE 773,173: POKE 774 ,129: POKE 775,192: POKE 776,104: 316 KKE 777,72: PIKE 778,205: POKE 779,6: POKE 780,224: POKE 781,208: POKE 782,35: POKE 78 3,173: PŒE 784,131: PCKE 785,192: 319 PIKE 786,173: POKE 787,131: POKE 788,192: POKE 789,169: POKE 790,165: PIKE 791,141: POKE 792,0: PIKE 793,208: PIKE 794,205: 322 PIKE 795,6: PIKE 796,208: PIKE 797,208: PIKE 798,19: POKE 799,74: POKE 800,141: POKE 80 1,0: POKE 802,208: PIKE 803,205: 325 PIKE 804,0: PIKE 8M,208: PIKE 806,208: POKE 807,10: PIKE 808,173: POKE 609,129: POKE 8 10,192: PIKE 811,173: PIKE 812,129: 328 PIKE 813,1%: PIKE 814,169: POKE 815,1: PIKE 816,208: POKE 817,2: POKE 818,169: POKE 81 9,0: PIKE 820,141: PIKE 821,0: 331 POKE 822,3: PIKE 823,104: PIKE 824,205: POKE 825,0: POKE 826,224: POKE 827,240: PIKE 82 8,3: PIKE 829,173: PIKE 830,128: 334 PIKE 831,192: POKE 832,%: 231 337 CALL 769 340 IF PEEK (766) ( ) 1 T)0l 520 343 REM ======346 REM 349 (EM LABStFT (P(££ $DM0 - ) 352 REM 412 X = (EEK ( - 16247) 415 X » PEEK ( - 16247) 416 PRINT CHR$ {4)"BL0AD LABStFT. RAM. OBJ, (»D000* 421 PRINT CHR$ (4)'BRUNLABSTART.OBJ,A$300" 424 X « PEEK ( - 16247) 427 X = PEEK ( - 162471 430 PRINT CHR$ (4)'BL0AD LAKL.SET.A" PEEK (970) + PEEK (971) t 256 433 (EM 436 (EM ======439 (EH 442 REM FEDBATCH PREPARATIW 445 E M 300 FOR K = 0 TD 3: I ROUT, (DV) = 2046, (DO) = 12, (CD = K: NEXT 510 & BOJT, (DV)= 8 520 HIEM: 366% 540 PRINT CHR0 (4);"BL0AD GRAWEEDWAIT,A$92FF" R 0 PRINT CHR$ (4);"BL(m GRADFEEDIRQ,A$9406" 555 PRINT CHR$ (4);'BL[»0 BRADFEED IRQ ON/OFF,A$93D0’ 557 PRINT CHR$ (4)i'BLOAD FEDBATCH GLU AN,A48FD0- K 0 FOR I = 63448 TO 65535; POKE I, PEEK (I): NEXT 570 VTTffl 21; HT(ffi 3; INVERSE ; PRINT 'TO BEGIN SETUPOF GRADIENT FEED RUN"; HTAB 3; PRINT KPRESS ( W KEY "; NORMAL 560 FOR I = 1 TO 15: PRINT CHRf (7);; IF PEEK ( - 16384) ) 127 GOTO 640 590 FOR J = 1 TO 400; (EXT J,I 600 Ftm I = 1 TO 500; IF PEEK ( - 16364) > 127 GOTO 640 610 (EXT 620 VTAB 21; HT(ffl 3; FLASH ; PRINT ' POWER FAILURE '; HTAB 3: PRINT ' DETECTED '; NORMAL 630 GOSUB 40000; PRINT CHR$ (4);'RLM FEDBATCH2 V1.0* 640 VT(ffi 21; HTAB 1; CALL - 956; VTAB 21; HTAB 9; PRINT "PROGRW LOAD IN PROGIESS' 650 PRINT CHR8 (4);'RUN FEDBATCHl V1.0,D1' 660 EM) 232 40000 X = PEEK ( - 16218): IF (< INT (X / 4) « 4) - ( IHT (( IMT (X / 4) * 4) / 8) « 8) = 0 ) TIEN lETUm 40910 CALL 37840: GOSUB 80: POKE - 16221,% 40020 PRINT CHR$ (1); CHR$ (17);‘21111‘: GOSUB 9# 40030 IWUT X$: IWUT X$: INPUT X$,X$,X$,X*,X*,X$ 4%40 K T X$: IF X8 < ) "E" GOTO 4W40 40060 GOSUB 80: FDR I = 1 TO 1000: l€XT : PRINT ’KCGL": KSLB 90: INPUT X$: INPUT X$: IWUT X$: IWUT X$ 40060 GOSUB 80: FOR I = 1 TO 8: PRINT : FOR J = 1 TO 400: NEXT J,I: GOSUB 90:X = . 40070 GET X$: IF X$ ( ) "E" GOTO 4%70 40080 X = X + 1: IF X = 1 GOTO 40070 40090 GOSUB 80: PRINT ■SOLAS’: G^UB 90 40100 m X$: IF X« < } GOTO 40100 40110 GOSUB 80: PRINT ’KATHL’: PRINT CHR$ (15); CHR* (13): POKE - 16221,0: FOR I = 1 TO 5 000: NEXT 40120 PRINT : PRINT : PRINT : K)SUB 90 40150 K T X«: IF X$ ( ) GOTO 40150 40160 GOSUB 80; PRINT "SET TERM/NOBROADCAST’: PRINT "RUN SUPERV"; FOR I = 1 TO 600: NEXT : PRINT CHR4 (19): PR# 0: CALL 1002 40170 RETURN 233 BASIC-LAN3UAGE PROGRAM FEDBATCHl Preparatory program. Variables : A$ Storage of CHR$(4) C%(20) Channel numbers: CX(1) " pH monitor; C%(2) = pH control; C%(3) = turbidity monitor; C%(4) = turbidity control; . . . D%(20) Device numbers: D%(1) - pH monitor; D%(2) ■ pH control; D%(3) = turbidity monitor; D%(4) = turbidity control; . . . D0$ String storage, "OPEN" m$ String storage, "CLOSE" D2$ String storage. "WRITE" D3$ String storage. "READ" E$ String storage, "..... " F$ Miscellaneous string FI Sampling rate F2 Frequency of data storage to disk F3 Frequency of data output to printer F4 Bit number for binary output that Is associated to Interrupt (feed pump) F5 Frequency of communication with VAX supervisor computer G$ Miscellaneous string G1 Maximum glucose feed rate In ml/mln G2 Acid addition rate In ml/mln G3 Base addition rate In ml/mln G4 Ratio of feed rate of all streams to feed rate of glucose stream G5 Initial volume G6 Glucose concentration In all streams G8 Carbon dioxide range/meter: 1 = low range of low meter; 2 = high range of low meter; 3 = low range of high meter; 4 = high range of high meter G9 Vessel pressure H$ Miscellaneous string I Loop counter IX Loop counter ID$ Run Identification J Loop counter K Loop counter P(10,9) Parameter storage; P(*,l) “ calibration slope; P(*,2) = calibration y-lntercept; P(*,3) = minimum acceptable value; P(*,4) = maximum acceptable value; P(*,5) = set point; P(*,6) ■= proportional gain; P(*,7) = Integral time constant; P(*,8) = derivative time constant; P(*,9) “ frequency of control action P$(10) String storage of variables' names: P$(l) = "pH"; P$(2) « "turbidity"; and so on S Storage of number of supervisor variable: 7 “ solution oxygen ; 8 •» solution carbon dioxide; and so on 234 S$ Status string for monitor and control: characters 1,3, . . . monitor pH, turbidity, . . . characters 2, 4, . . . control pH, turbidity, . . . "Z" " no; "Y“ “ yes; other = local supervisor control S$(2) String storage: S$(l) - "MONITOR"; S$(2)="00NTR0L" TH Engineering units high TL Engineering units low V Miscellaneous storage, frequently represents the number of a variable (pH 1; turbidity - 2; and so on) X Miscellaneous storage X$ Miscellaneous string storage, sometimes appearing in data formating routines XH Measurement high in ADC counts XL Measurement low in ADC counts Y Flag in data formatting routines Y$ String storage used in data formatting routines Z$ String storage used in data formatting routines * Numbering of variables follows the order in data statements 62000 - 62190: pH “ 1; turbidity - 2; substrate concentration = 3; . . . 235 JLIST 100 ft WRKV, (DV) = 3, (W) = 1, (W@) = 2 170 A* = CHR$ (4) 160 HIM : POKE - 16368,0 1 % VTfiB 12: PRINT "ENTER IDENTIFlCftTIDN FOR RON ()%X IF 30": IM^UT " OfflRflCTERS) ";ID$ 2 ^ HCM : VTfS 3: HT(æ 7: PRINT "PUCE lATfi DISK INTO DRIVE 2": PRINT : HTAB 17: PRINT "TH E N " 210 VTfiB 9: PRINT " -DEPRESS THE ’R’ KEY IF YOU WISH TO": HTflB 6: PRINT "REVIEW YOJR CfiTM. œ TO VERIFY THflT:" 220 HTflB 4: PRINT "-YOU WWE SIFFICIENT FREE SPJCE": HTflB 6: PRINT "FOR THIS RIR( (DISK Cfl WCITY IS": HTAB 6: PRINT "WROXMTELY 496 KCTORS)' 238 PRINT : HTIffi 4: PRINT "-(M) TWIT THE DISK ClMfllNS fffl FILES";: HTflB 6: PRINT "WITH THI S RIM'S IIENTIFIER" 240 PRINT : PRINT : PRINT : PRINT " -OTTERWISE, DEPRESS TÆ ’RETURN' KEY": K T G$: PRINT 250 IF œ C (G$) = 13 GOTO 1000 260 IF fiæ (G$) ( ) 62 T)£N KBUB 60000: K)TO 200 270 HO* : PRINT fi$;"D)T(K%,D2" 280 PRINT : TOINT : PRINT : PRINT "-KPRESS THE ’R’ KEY IF YOU WISH TO": HTflB 4: PRINT "REP UCE TIE DATA DISK' 290 PRINT : PRINT "-OTÆRHISE, KPESS THE ’RETURN’ KEY": K T G$ 3 # IF fisc (G$) = 82 KITO 2 # 310 IF (60) ( ) 13 TIEN GOSUB 60000: PRINT : H)TO 270 % 0 GOTO 1000 400 Hira 24: IF NID$ (S$,2 * I - 1,1) ( ) "Z" THEN INVERSE 410 PRINT " ";S*(1);" ";: NORMflL : IF NID$ (S$,2 » 1,1) ( ) "Z" TIEN INVERSE 420 PRINT " ";S$(2);" ": NORMAL : HTflB 4: lETURN 500 VTfffl 19: HTJffl 1: CflU. - 958: HTflB 7:: PRINT "ENTER TIE fFPROPRIftTE VfClE,": HTflB 16: PRINT OR -■ 510 PRINT • DEPRESS TIE ’RETUIfîl’ KEY IF IK) OTOE": HTfffl 15: PRINT "IS EKJIRED";: lETURN 5 % PRINT " TIEN DEPRESS ANY KEY TO CONTIIKE": K T G$: lETUIW 600 % " 0: * ffflUM,(TV) = X, (D#) = D%(2 * I - 1), (Cl) = C%(2 * I - 1),(RT) = 3,(SW) = 333:X = X / 333: IETOI% 610 P(I,1) = (TH - TL) / (XH - XL):P(I,2) = TH - XH » P(I,1): RETURN 1000 H M ; VTflB 11: HTflB 11; PRINT "SETIP IF FERIENTOR": VTflB 14: HTfffl 9: PRINT "MONITOR INB fm) CWMX." 1010 D0$ = "WEN ":D1« = "CLOæ ":D20 = "WRITE ":D3$ = "READ ":E$ = ".... ":S$ = "ZZZZZZZZZ 2ZZZZZZZ2ZZ" 1020 S#(l) = "WIITR":S$(2) = "CWTRL" 1030 DIM C%(20),DK(20),P(10,9),P$(10) 1%0 F M I = 1 TO 10: Œfffl P$(I),D%(2 * I - 1),C%(2 * I - 1),P(I,1),P(I,2) 1070 READ D>(2 « I),C%(2 « I),P(I,3),P(I,4),P(I,5),P(I,6),P(I,7),P(I,8),P(I,9): lEXT 1080 BERR GOTO 63000: f^INT fl$:"DELETE RUN m*.Dl" 236 \ m MKE 216,0: PRINT R$;m;'Rm M%,D1": PRINT A$;D2$;"RUN NME": PRINT ID$: PRINT A$;D l$;'m NAME' 1100 TEXT : lOE 1110 VTAB 3: HTAB 4 1120 FOR 1 = 1 TO 6: PRINT I;’.";P$(I);: H)SUB 400: ÆXT 1130 HTAB 7: PRINT "IN-SdUTm:": HTfS 4 1140 I = 7: PRINT I;". OXYffiN KSJB 400 1150 I = 8: PRINT I;". CARBW DIOXIDE";: GIKUB 400 1168 HTAB 7: PRINT "m -m s-.'t HIPB 4 1170 I = 9: PRINT I;". OXYGEN";: GOSUB 400 i m HTAB 3il = 10: PRINT I;". C A R m DIOXIDE";: HBUB 400 12% VTfffi IB: HTAB 4: PRINT "ENTER 0 19EN YOU DO NOT WISH TO": PRINT " MAKE FURTÆ R SELECTimS": HTAB 3 1240 VTRB 22: INVERŒ : HTAB 2: PRINT "ENTER THE RJMBER CF T Æ ITEM YOU WISH": HTAB 6: PRINT ‘ TO ŒLECT FOR ";: mR m . : IWUT " ';! 1250 IF I ( 1 GOTO 13% 1260 ON I %SUB 20000,23000,26000,29000,32000,35000,38000 41000,44000,47000: GOTO 1100 1270 IF I ) 10 TIEN %SUB 60000: VTAB 1: %T0 1110 1300 K M : VT® 11: PRINT " IF YOJ WISH TO ŒENTER THE PAiffiMETERS": HTAB 9: PRINT "DEPRESS TIE »R« KEY" 1310 PRINT : PRINT " ODERWiæ- TO CtMINUE, DEPfESS THE": HTAB 11: PRINT "'RETURN’ KEY ";: ŒT 6$ 1%0 IF 60 3 "R" %T0 1100 1330 IF A æ (6$) ( ) 13 TIEN 60000: KTTO 1300 1340 K M : VT® 8: PRINT "ENTER TIE SA®tIK3 INTERVAL COE TM,": PRINT : HT®4: PRINT "IN BIKJTES, KTIEEN SfWLES)" 13% VT® 14: MINT "KITE: IF TIE SWLIK3 INTEfiVffl. ENTEIED": HT® 8: PRINT "IS LESS TH® TIE TIE lEOIIED": HT® 8: PRINT "FOR TIE SYSTEM TO CtmETE ITS"; HT® 8: PRINT "®TI ®B, TIE SYSTEM HILL SAMPLE" 1360 HT® 8: PRINT " ® KJICKLY ® POSSiai - TIE": HT® 8: PRINT "STWLING RATE WILL BE": HT® 8: PRINT "ISCXMKUED ® D VARIAKjE." 1370 VT® 10: HT® 34: imiT " ";Fl 13% K M : VT® 5: PRINT "ENTER TIE FREERENCY UN TERMS IF": PRINT : PRINT " S®PLING CY CLES) WITH KIICH THE Ftt.-": PRINT : PRINT " LKJIIE DEVICES WILL S W L E ® D RECO®:" 13% VT® 21: MINT "EXimE: ENTER '5' TO AVERAK FIVE": HT® 11: PRINT "BWLE CYCLES tmiCH WILL K": HT® 11: PRINT "RECORDED ® A SINGE DATIM" 1388 VT® 13: HT® 3: INVERSE : PRINT " COMPUTER ";: NORMAL : PRINT " COWNICATIDN" 13% VT® 15: HT® 3: INVtRæ ; PRINT " DIG! ";: Klim. : PRINT " DRIVE 2"; VT® 17: HT® 3 : IIM®E : MINT " MINTER ";: Klim. : PRINT " IKIMTA 92" 1400 VT® 13: HT® 27: IWUT " ";F5: VT® 15; HT® 27: IKHJT " ";F2:VT® 17: HT® 27; IWUT " “;F3 1410 K M : VT® 11: HT® 7: PRINT "ENTER BIT KJMKR CONTRHLIIE": PRINT : PRINT ; HT® 9: PRINT "KTTRIENT FEED f W 0" 1420 VT® 14: HT® 30: IIPUT " ";G$: IF 6$ = "" TIEN F4 = 0: GOTO 1700 14% F4 = VM. (G$): IF (F4 ( 0) OR (F4 ) 15) TIEN KSUB 60000: K)TO 1420 17% K M : VT® 2: INVEME : PRINT "ADMTIVE, IPTim. CfNTRO. GESTIIM:": NORMAL 1720 VT® 5: PRINT "ENTER PUMP SEEDS (IN ML/MIN) FOR:" 17% PRINT : PRINT " MAX GLlCtSE FEED ";G1: VT® 7: HT® 21: INPUT " ";G$: IF 6$ = "" GOTO 1758 1740 61 » VflL (6$) 237 r m PRINT • BCID FEED *;K: VTBB 8: HTAB 14: 1WHÏÏ ' ";G$: IF Gi = " GOTO 1770 1760 B = m . (G$) 1770 PRINT ■ KIK FEED ";G3: VTf® 9: HTAB 14: IWITT ' ";G$: IF G$ = " GOTO 1790 1788 G3 » VAL (G«) 17% VTAB 11: PRINT "ENTER RATIO IF TOTfl FEED RATE TO": PRINT " GLUCtSE FEED WITE ";G4: VT® 12: HI® 22; lJi>UT " ";G$: IF G$ = "" ®T0 1810 18% G4 = V ® 20110 PRINT : PRINT "-USIIE TIE DELTA KNC® ON TIE PH METER": PRINT ' K T DISPLAY TO A LHI ER VALUE, TIEN": IIWT " ENTER THAT VALUE ";TL 20120 HJSUB 600;XL = X: PRINT : PRINT "-SET DISPLAY TO A GREATER VW.IE, THEN": IWUT ' EN TER TWT VALUE ",TH 20130 HJSUB 6%:XH = X: GOSUB 610: PRINT : PRINT "-RETURN DISPLAY TO ";K: t PAUSE = 4: HJSUB 59900; RETUm 22000 RETURN 23000 HJSUB 1%00: lETUm 23100 : VTIffi 8: PRINT "TURBIDOfETER CALIBRATim:": VTfffl 11: PRINT "-ENSURE VIEWING TUB E IS HEAR fMD CLEAN": PRINT : PRINT "-TURN OFF UW": HJHJB 550: I PAUSE = 50:TL = 0: GOSUB 6%:XL > X 23110 PRINT : PRINT "-TURN ON LA*': GOSUB 550: t PAIBE = 50:TH = 100: HJSUB 6M:XH = X: HJSUB 610: lETUW 25000 RETURN 26000 HISUB 10000: lETUm a i % HJME : VTfffl 8: PRINT "AGITATION RATE CALIBfmTlON": VTfffl 13: PRINT " CALIBRATIW IS NO T lEOUIIED KEN TIE": PRINT ; PRINT " STEPP»® HJTOR WIDULE IS tPERATIDNAL*:PI3,1) = 1 :P(3,2) = 0: « PffflŒ = 7: IETUI9I 28000 lETURN 29000 BOStffl 10000: lETURN 29100 WHE : VTAB 8: PRINT "TC^ERATURE CALIBRATION:": VTfffl 11: PRINT "-fUfflE TIE TEHPERATU RE ®ASURE®IT": PRINT ' KVICE IN A HW. BATH, TIEN,": PRINT " KEN EQUILIBRATED, ENTER TIE KITH" 8118 im n • TE)®ERATWE ";TL: HJSUB 600:XL = X: PRINT : PRINT "-PLACE THE DEVICE IN A WARM KITH, TIEN": PRINT " KEN EHJILIBRATED, ENTER TIE BATH" 8120 INPUT " TEWERATURE "jTH: GOSUB 600:XH = X: HJSUB 610; RETUI% 31000 IF MID* IS*,7,11 = "Z" TIEN GOSUB I I W 31010 WJ^ : VT® 111 MINT " TO CONTROL TEKERATURE, imjALLY SET": PRINT : PRINT : HT® 5: PRINT "TIE BATH OR FERIENTOR TIEfiKJSTAT": POP : « PAUSE = 8: RETURN 32000 HfflUB 10000: lETUm 32100 I Œ : VI® 8: PRINT "OXYGEN FLOW RATE CALIBRATION:": VT® 13: PRINT " OXYGEN FLOW RA TE MWITORII® CA.IBRATION": PRINT : HT® 6: PRINT "IS NOT AVAILAHE AT THIS THE": t PA USE a 7: RETURN 34000 RETURN 35000 HJSUB 10000: RETURN 241 3510» toi : VTd Bi PRINT 'AIR FU^ KtlE CfllBRATWi': VTAB 13: PRINT ' AIR FLUt RATE MO NITORI^ Cm.IBmim": PRINT : HTAB 5: PRINT 'IS tOT MI I i m E AT THIS TIffi': I PfHJæ = 7: RETURN 37000 RETURN 38000 B = I: KtStm 10000:8 « 0: K T l# 38100 IDE : VTRB 8: PRINT "OXYKN PRCE CM.IBmTim:': VTAB 16: HTfffi 3: F L ^ : PRINT 'Mi STANDBY DURING ADJliimNT': NORMAL 38110 K M w**«ROUTINE TO SET KITATim tMTE TO FUl KiS tiRE****** 38120 I miT, (D@) = Dg(12), (C@) = « (1 2 ) , (IW) = 0: & P M ^ » 60: R AtXJT, (DS) = D%(12), (C@) = « (1 2 ), (DV) = 2048 38130 VTO 16: OU. - K 8: VTf© 11: f©IHT '-W)IT FOR A Him DISSOLVED OXYKN LEÆL": 550 38140 PRINT : PRINT '-K T ’KASURIfffi fffl® ’ ON DXYKN ŒTER': PRINT ' TO ZERO': KfiUB 559 :TL » 0: Sm m 600:XL = X a m PRINT : (%INT '-S T 'KASIRIK RANGE: TO 100%': PRINT : PRINT '-S T DISIAY TO 99 USI NO T S S C i KNOB': PRINT ' ON T ti OXYSM tETER': G(KUB 5%:TH = 99: HKUB 600:XH = X : S a m 619 a i6 0 PRINT : f%INT '- S T 'MEABURINB RASE: TO 100": S S B 550 a i7 0 SM WHWROUTIS TO S C S A S (©ITATm SES SRE****** a i æ S miT,(D#) = «(12),(C@) = «(12),(DV) = 4095: & PfR^ = 69: g fOlT, (D#) = D%(12),(C 0) = «(12), (m = 2048 a i9 0 RETIRN 40000 S » I: IF MID# (St, 13,1) = 'Z°TtEN m © 11000 40010 150N:I > 7 48020 8 0 SOJ3 59900: STURN 41000 HOME : VTAB 11: f^INT "SMTKBI CARBON DIOXIS S m R T IS WT':PRINT :PRINT :HTf© 10: PRINT "AVAIimE AT THIS TIS': I PAUS = 5: S T M 44000 S ° I: GOSUB 10000:8 « 0: STUmt 44100 tOi : VT@ 11: HTf© 3i PRINT "OXYSN SF-S© (m_YZER CM.IBF»TI(M': PRINT ;HTAB 6: PRINT •IS NOT mium. AT THIS TIffi': I P M ^ » 5: S TUm 46000 S = I: IF m m (St, 17,1) = 'Z' TSN 11000 46010 BOGUB 15000:1 » 9 46020 8 0 SOB 59900: RETURN 47000 S = I: SOB 10000:8 = 0: STUm 47100 S K : VTf© 4: HTAB 5: PRINT 'Cf©m DIOXIS OFF-SE ANfLYZER': PRINT : HTAB 15: PRINT 'CKIB^Tim': VTAB 10 47110 PRINT 'mTE: -(3a.IBI»Tim MAY ®T PRKEED': HTAB 9: PRINT 'IMIL A THIRTY Œ) MINUT E': HTf® 9: PRINT 'WARM4P SRIOD CP(MR' AND': HTfffl 9: PRINT " f W * SWITCtiS 00 H ffi': HTfffl 9: PRINT 'TfgWIRED.' 47120 PRINT : HTfffl 8: PRINT '-IF Tt€ (MITE LIS S TS ’FL(RJ*; HTfffl 9: PRINT 'tOIITOR» AP PEffflS IN TS SD': HTAB 9: PRINT 'SGim S TIE DIS^Y, INSPECT* 47ia HTAB 9: MINT "AND, IF SSSSRY, SMJtS Tti": HTfffl 9: PRINT "fWlYZER'S THRS (3) F ILTERS.': PRINT : PRINT : S O B 550 47140 HOME : INVE^ : PRINT "CARm DIOXIS (FF-Sffl Cf».lBRATim*: NORMAL : fO(E 34,2 4 7 m VTfffl 3: PRINT "-POSITIfflY 'RANS SECT* SWITCH ON": PRINT ' tmVZER TO’L0>'; I f«EE = 8: PRINT : PRINT '-ADJIST TtE ’ZERO* Vm UNTIL Tti': PRINT ' METER INDICATE S ZEfffl f#': I PAUS = 8 47160 PRINT : ffflINT '-POSITItH ’PUMP’ SWITCH ON fm.YZER": PRINT ' TO IFF': I fWlBE = 8: PRINT : fffllNT '-INTIfflDIEE STfYfflARD Sffl INTO Tti': PRINT ' fm.YZER THRtXEH Tti ’STD. Bffl" 242 47171 PRINT " IMET’ (TRWfâlSSICW (F 7 - 8": PRINT ' œCWlDS IF S S IS SIFFICIENT)*: & P W æ = 12: PRINT : PRINT '-ADJUST 'SPAN' WfflB (W TIE ffl^YZER* 4718® PRINT * UNTIL TIE ClMENTRATim EXHIBITED BY": PRINT * TIE «TER AGREES WITH THAT 0 F TIE*I PRINT * STIWARD MS*: & PAU% = 8: PRINT : PRINT '-PIfilTION ’PifiP’ SWITCH TO m, m * 471% PRINT * [©SERVE «TER. IF METER NO LHœi*: PRINT * EADS ZEM3, «PEAT TIE ABOVE* : PRINT * PMCEDUIE WITHXJT ADDI« ADDITKML*: PRINT * MS*: PRINT : GOSUB 550: TEXT I «r u m 49800 S = I: IF MID$ (S$,19,l) = *Z* THEN MSt© 11000 49010 æ a © 15000:1 - 10 49020 S - 6%UB 59900: RETUFDI 55000 Y# = * ": IF X < 0 TIEN Y* = *-*:X = ABS (X) 55010 X# = S7R$ (X): IF (X < 1) M) (X ) = 0.01) MTO 55400 55020 IF LEN (X$) < 4 MTO 5%40 55030 IF MID$ IX«, LEN IX«) - 3,1) = *E GOTO 55600 55040 Z» = Y0 + LEFT# (X#,l) + *.*:Y = 0: IF LEN (X$) = 1 THEN X = 0; MTO 55080 55045 FOR II = 2 TO LEN (X#): IF MID$ (X$,II,1) = *.* THEN X = II - 2:Y= 1:GOTO S % 0 55059 Z# = Z# + MID# (X*,II,1) 55060 «XT : IF Y = 0 THEN X = II - 2 55070 IF LEN (Z$) = 11 H)TO 5%90 55080 FORII = LEN (X$) - (V » 1) TO 8:Z$ = Z$ * *0": «XT 55090 Z# = Z$ + *E+*: IF X < 10 TIEN Z# = Z# + *0* 55100 Z# = Z# + STR# (X): RETUIM 55400 X = - (X < 1) - (X ( .1):Z# = V# ♦ HID# (X$,l - X,l) + *.*: IF LEN (X$) ( 2 - X H)TO 55410 55405 FOR II » 2 - X TO LEN (X#):Z$ = Z# + MID# (X$,II,1): «XT 55410 Fffil II » LEN (X#) ♦ X TO 8:Z# = Z# ♦ *0*: «XT 55428 Z# = Z# + ‘E-0* + STR# » ® S (X)): lETURN 55600 IF MID# 1X8,2,1) = E* TIEN Z# = Y# + LEFT# (X#,l) + 00000000 + RIBÏÏ# (X#,4): RETU« 55618 I - 0:Z# « Y# ♦ LEFT# (X$,3) 55620 FOR II = 4 TO 10: IF MID# (X«,II,1) = *E* TIEN X = 1 55630 IF X = 1 TIEN Z# = Z# + *0* 5%40 IF X «. 0 TIEN Z# » Z# + MID# (X#,II,1) 55650 «XT :Z$ = Z# ♦ RIBff# IX#, 4): RETUm 55900 Z# = STR# IX): RETURN 55950 Z# = ": IF X 1 10 THEN Z# = *0’ 5596® Z# = Z# + STR# (X): RETUIDl 59000 VTAB 5: HTf© 11: PRINT '«VICE «MBER*;: HTAB 26: PRINT D%(2 * I - 1);: HTAB 33: PRINT DX12 « I): «T U M 59010 VTAB 6: HTAB 10: PRINT "CimEL NUMBER';: HTAB 26: PRINT C%(2 < I - 1);: HTAB 33: PRINT 0(2 » I): RETURN 5%20 VTAB 7: HTAB 7: PRINT 'CALIBRATE a.KE";: HTfffl 26: PRINT INT IP(I,1) « 100 + .5) / 100: « T U m 59830 VTfffl 8: PRINT "DLIBRATIM Y-INTERCEPT*;: HTAB 26: PRINT IMT (P(I,2) * 1% + .5) / 1 • 00: « r u m - 59040 VTAB 9 ; PRINT "MINIMUM ffflCEPTABLE VfllE*;: HTAB ffi: PRINT ES;: HTAB 33: PRINT P(I,3): «Tuim 59850 VTfffl 10: PRINT 'MAXIMUM fKCEPTARÆ VfWiJE";: HTAB 26: PRINT E#;: HTAB 33: PRINT P(I,4) : «TUmi 243 59060 VTflB 11:PRINT 'SET POINT';: HTflB 26: PRINT E$;' ';P(I,5): RETURN 5%70 VTflB 12:PRINT 'PROPORTIONAL GAIN';: HTflB 26: PRINT E$;' ';P(I,6); f£TUfW 59%0 VTIffl 13: PRINT 'INTEGRM. TIME COBTflNT';: HTfffl 26: PRINT E$;' ';P(I,7): KTURN 590% VTflB 14:PRINT 'KRIVflTIVE TIf£ CONSTfWT';: HTflB 26: PRINT E$;' ";P(I,8): KTUIffl 591% VTflB 15:PRINT 'FREQUEIO';: HTflB 26: PRINT E$;' ';PU,9): lETURN 599% HCSS : INVERŒ : PRINT P$(I) 59910 VTflB 3: HTfffl 26: IF MID$ (S$,2« 1 - 1,1) = 'Z' TIEN KJRMflL 59920 PRINT S$(l);: INVERT : HTflB 33: IF MID$ (S$,2 * 1,1) = 'Z' TÆN NORMAL 59930 PRINT S$(2): NORMAL 59940 GCfflUB 59000: %SUB 5%10: GOSUB 5%20: GOSUB 59038: KISUB 59040 59950 %SUB 590: GIBJB 5%60: GOaiB 59070: GOSUB 59080: KStffl 59090: GOSUB 591%: RETURN INVERK : VTfffl 21: HTfffl 1: CflL - 958: VTflB 22: HTfffl 1: PRINT ' ERROR ENTRY IS UmEPTffflLE ■; 6%10 HTfffl 9: PRINT ' PLEASE REENTER ': i m S S . = 3: IfflRMflL : VTfffl 22: HTflB 1: CfU - O : RETURN 62000 DATfl ' PH', 12,0,.,. 62010 DATfl 8,9,2,12,7,10,16+36,0,1 62020 DATfl ■ TUiffiIDITY',12,4,.,. 62030 MTfl 13,8,0,1%,%,1,1E+36,0,1 62040 DATfl ' aiKTRATE CONC',1,3,1,0 62050 DATfl 13,1,0,%,20,1,1E+36,0,1 62%0 DATfl ' TEMPERATURE', 12,5,1,. 62070 DATA 0,0,10,40,37,1,1E+36,0,1 62%0 KtTfl ' AIR FLOW RATE OUT", 12,7,0.00486710,0.04730417 620% MT A 12,2,0,20,8,0.%25,1E+36,0,1 62100 mfl ' AIR FLKI RATE IN',12,2,0.%486710,0.04730417 62110 DATfl 12,1,0,20,8,5,16+36,0,1 62120 MTTfl ' SOLN OXYKN CONC',12,3,.,. 62130 DATA 0,0,0,l%,50,l,lE+%,0,3 62140 DATA ' 9XN CflRB DIDX CONC',12,6,.,. 62150 m m 0,0,0,100,20,1, lE+36,0,3 62160 WTfl ' OFF-KS DXVffiN COIC', 1,1,0.03136388,-76.74570233 62170 DATA 0,0,0,25,20,1,16+36,0,3 62180 MTA ' OFF-GAS CARB DIOX COM:", 1,0,1,0 621% DATA 0,0,0,6 0 0 0 ,1,1, lE+36,0,3 63%0 1 = PEEK (222): IF 1 = 6 %TD 10% 63010 PRINT : PRINT : PRINT '’ERROR ";I;" ENCOUNTERED IN L M 1080": PRINT : PRINT : END 244 BASIC-UNGUAGE PROGRAM FEDBATCH2 Direct digital control program. Variables: A$ Storage of CHR$(A) AD Amount of acid and base added during this cycle. In milliliters AH(10,1) High level alarm for each variable monitored AL(10,1) low level alarm for each varable monitored C(10) Output from FID controller CL Carrier signal lost status flag CO Carbon dioxide meter status variable: 0 = low range, low meter; 1 = high range, low meter; 2 ” low range, high meter; 3 = high range, high meter CR Communication (with VAX) request status flag D0$ String storage, "OPEN" Dl$ String storage, "CU)SE" D2$ String storage, "WRITE" D3$ String storage, "READ" E(2,10) Error (deviation of actual measurement from set point): E(0,*) = error of twlce-prevlous measurement; E(l,*) = error of previous measurement; E(2,*) « error of present measurement F Feed rate obtained from supervisor In liters/hour F(A) Frequency of communications: F(l) = duration of sampling Interval In minutes; F(2) = frequency of communication with supervisor In sampling cycles; F(3) = frequency of data storage to disk In sampling cycles; F(A) = frequency of data output to printer GC Glucose concentration In fermentor (taken manually) In grams/liter GD Volume of glucose added this cycle: line 1800, milliliters of glucose feed stream added ; line 1810, liters of total feed added GT Minutes passed since last manual measurement of glucose concentration In fermentor was sent to VAX I Miscellaneous storage, primarily loop counter J Miscellaneous storage, primarily loop counter K$ String variable storage for CHR$(17): resume transmission for XON/OFF protocol L$ String variable storage for CHR$(19): stop transmission for XON/OFF protocol H(10,A) Values of variables monitored: M(*,l) = present measurement; H(*,2) = average of measurements to be transmitted to VAX; M(*,3) = average of measurements to be stored onto disk; M(*,A) = average measurements to be output to the printer; M(0,2) = number of samples In average to be transmitted to the VAX; M(0,3) ■= number of samples In average to be stored onto disk; H(0,A) = number of samples In average to be output to printer 245 0(16) Status variables; 0(0) “ bit of binary output to be set; 0(1) ” duration of binary output in seconds; 0(7) = total volume of acid added in milliliters; 0(8) = acid pump rate in ml/min; 0(9) « total volume of base added in milliliters; 0(10) ■= base pump rate in ml/min; 0(11) = volume of glucose stream added in milliliters; 0(12) » glucose pump speed at 100% rate in ml/min; 0(13) = total volume in fermentor in liters; 0(14) » ratio of total feed rate to feed rate of glucose stream; 0(15) = glucose concentration in total feed streams in g/1; ; 0(16) •= bit number for binary output of feed pump P(10,17) Parameter storage for each variable: P(*,l) ■= device number (Off) to monitor variable; P(*,2) » channel number (Off) to monitor variable; P(*,3) “ calibration slope; P(*,4) = calibration y-intercept; P(*,5) ° device number (Of) to manipulate variable; (P*,6) = channel number (Cf) to manipulate variable P(*,7) “ minimum acceptable value; P(*,8) = maximum acceptable value; P(*,9) « set point; P(*,10) = proportional gain; P(*,ll) = integral time constant; P(*,12) = derivative time constant; P(*,13) “ frequency of control action; P(*,14) =■ flag to enable (1) or disenable (0) monitoring of variables; P(*,15) = alarm low values; P(*,16) ” alarm high values; P(*,17) “ flag to enable (1) or disenable (0) contoller P$(10) String storage of variables' names: P$(l) = "pH"; P$(2) = "temperature"; and so on Q(12) Estimates of variables from VAX T(20) Time in format of year/month/date/hours/minutes: T(0) - 1(4) «• start time of fermentation; T(5) - T(9) = start time of next sampling cycle; T(10) - T(14) = present time; 1(18), T(19), T(20) = agitation rate timing in hours/minutes/seconds format U Miscellaneous variable storage for input routine U$ Miscellaneous string storage for input routine V Number of variable presently being monitored/manipulated VA Volume adjustment of VAX estimated volume in liters VP Vessel pressure X Miscellaneous storage X$ Miscellaneous string storage, sometimes appearing in data formating routine XI$ String storage for "00" string XX Variable storage to correct estimates in VAX Y Miscellaneous storage and flag in data formatting routines Y$ Miscellaneous string storage primarily used in data formatting routines Z Miscellaneous storage Z$ Miscellaneous string storage, primarily used in data formatting routine * Numbering of variables follows the order: pH = 1; temperature = 2; dissolved oxygen concentration = 3; dissolved carbon dioxide concentration = 4; off-gas oxygen concentration =5; off-gas carbon dioxide concentration = 6; air flow rate in “ 7; air flow rate out = 8; turbidity ” 9; glucose concentration = 10 246 3LIST 10 GOTO 6000# 80 IN# 0: PR» 2: CALL 1002: Œ T U ^ % PR# 0 : IN@ 2 : CAJ. 1002: RETUim 93 GOSUB M: PRINT K$: GOSUB 90: I W T U$: KRIB PRINT L$: IF LEN (U$)(2 GOTO 93 94 IF LEFT* (l»,2) <> 'XX' GOTO 93 95 PR# #: cm. 1#2:U - V d ( RIQÏÏ* (U*,U)): RETUm 100 FOR I = 5 TO 9: IF T(I) < 10 TUN PIKE 37856 ♦ 2 * (I - 3), ftSC C0'): POKE 37856 ♦ 1 ♦ 2 « (I - S), nsc ( RIBTT* ( STR* (T 13500 HOE : VTAB 7: IMER% : PRINT "CARKK DIOXIDE RANGE/METER 0 8 ^ ' : NTAB 4: PRINT "RA ) W ^ R IS PiE^NTLY ";C0: NORMAL 1%10 VTRB 10: PRINT "1 CHANGE TO LO) RAIEE IF LOW mE R " 13520 VTffi 12: PRINT "2 CHANBETO HIGH RANGE (F m mE R" 1 ^ VTffî 14: PRINT "3 CHANGE TO RANGE (F HlOi METER" 1%40 VT® 16: PRINT "4 CHANGE TO HIS( RANGE CF HIB( !€TER" 13550 VT® 19: PRINT "ENTER # TO KD(E m OmSE" 13560 VT® 22: CdL - %B: IIWT "ENTER DESIIO RfD^/tOER VfLlE ";X: IF X = 0 T)€N RETURN 13570 IF (X < 0) OR (X ) 4) T)0l K)TO 13%0 13580 CO = X: ^BJB 55900: MINT ®;I^;ID$;*.PAR,D2": PRINT A$;"POSITI(BI ";ID$;".PAR,R196": PRINT ®;D2$;ID$i".PAR": PRINT Z$ 135% PRINT ®;D1$;ID$;".PAR": ffiTUfW 14000 CR > 100: RETUm 15000 HOME : PRINT : INVERT : FOR I = 1 TO 10; IF (1(1,1) = 1 DEN PRINT P$(I);" ALARM L mi": NEXT 15010 PRINT : PRINT : FOR I = 1 TO 10: IF ®(I,1) = 1 DEN PRINT P$(I);' dARM HIBC: lEXT 15020 VT® 22: MINT "DEPffiSS S TO TURN IFF M l d A M " : PRINT "DEPiESS C TO COfTIWE A LL dARMS": K T G$: IF G$ = "C" DEN fETURN 15030 IF G$ ( ) "S" a)TO 15020 15040 FOR I = 1 TO 10:d(I,l) = .:AH(I,1) = .: fEXT ; lETUffil 15500 CL - 0: KTUI^ 16000 HOME : VT® 11: MINT "ENTER VOLIM TOJUSDCNT (IN LITERS)" 16010 VT® 15: D M T " ";VA 16%0 CR = 2: ® T i m 16500 CR = 0: RETUM 250 17000 W M : VTffi 11: PRINT "VESŒL PRESSURE IS -;VP 17010 VTflB 14: PRINT "ENTER lESSEL PRESSUfE (IN MM (€)": PRINT : HT(B 7: I(WT "";VP 17020 VTAB 19: IN\Oæ : PRINT "USE COMPUTER COMM TO IlfOI^ SWERVISOR":NORMAL 17030 X = VP: BOSUB 55000 17040 PRINT A$;m;ID$;'.W)R,D2": PRINT ftIj’PKITim ";lW;*.PflR,R197*: PRINT A$;D2$;ID$;'. PAR": PRINT Z« 17050 PRINT A$;Dl$;m;".PAR": FOR II = 1 TO 5W: (EXT : RETUm 17500 M m : VTAB 8: PRINT "UGT MJEOSE C m %NT MS ";GC 17510 VTAB 12: imiT "ENTER OUHISE CQKENTRATim ";K 17520 VT® 14: MINT "ENTER NWBER OF BIMITES SIICE UST ": imiT " H.IE(KE DM:ENTRY ";GT 17530 CR = 4: (ETUm 20000 cm. 37840 20010 U » 10: BRIB 93:F = U 20020 KffilB ®:X = « (3 ,2 ) / 100 « «(5,2) / 100 * VP # 5.074E - 5: PRINT K$: PRINT X 20030 X = 01 PRINT X: REM mmCCWVERT DCO TO B/L TIEN PRINT X 20040 X = «(5,2) / 100: PRINT X 20050 X = «(6,2) / 100: PRINT X 20060 X = «(7,2) * 60: PRINT X:X = «(8,2) « 60: PRINT X 20070 X « (0(7) + 0(9)) / 1000: PRINT X:X = «(10,2): PRINT X: PRINT L$ 20080 U = 10: BOaiB 93 20200 IF CR = 0 TIEN KBIB 80: PRINT K$: PRINT "9999": PRINT L$: PRINT A$;"PR#0": PRINT A$ ;"IN#0": CALL 378^: lETURN 20300 X$ = CHR$ (7): PRINT X$;X$;X$;X$;X$;X$;X$;X$ 20500 IF CR = 1 # TIEN B®UB 21000: GOTO 20520 20510 ON CR BOaa);BaNN^27000,26000,25000 20520 m 20600 M M : VT® 4: INVERSE : PRINT "REH-TM OPERATIIM MODIFICATION": NORMAL 20610 X$ = CHR$ (7): PRINT X$;X$;XS;X$;X$: VT® 8: PRINT " 1 FIX/FREE B.IXBSE f W RATE" 20620 PRINT " 2 O I S ^ / C M V M ESTmTED VARIAMES" 20650 PRINT ■ 7 MJITCH ESTIMATOR MIIEL" 20660 PRINT "10 VOUM ®DITIB(/®«OVAL (EXCEPT PH)" 20670 MINT "13 IBHWTE ai C O æ C£B«ENTRATICS(" 20690 VT® 16: PRINT "ENTER 0 TO END CCmiTER COM" 20700 VT® 19: HT® 15: INVERT : PRINT " SWPLE";: NORMAL : PRINT " ";:X = 5: GCSUB 51 W : PRINT 20710 VT® 22: IWUT "ENTER NWBER IF DESIRED WDIFICATItW ";X: VT® 23: HT® 1: CALL - 868: VTAB 22: CALL - 868: IF X = 0 TIEN CR - 0: GOTO 20200 20720 IF (X ( ) 1) AND (X ( ) 2) AND (X ( ) 7) AND (X ( ) 10) ® D (X ( ) 13) TIEN VT® 22: INVERSE : PRINT " ERROR — PLEfM lEENTER ": NORMAL : FOR II = 1 TO 2 #00: NEXT : 13003 20710 20730 [%= (X = 1) * 3 + (X = 2) + (X = 7) * 100 + W = 10) * 2 + (X = 13) * 4: GOTO 20500 21000 B O m 80: MINT Kl: PRINT PRINT L$:U = 1: GOSUB 93:X = U 21010 HOME : VT® 11: MINT "PIEffiNT ESTimOR MODEL IS:": HT® 11: IF X = 0 THEN PRINT "S T ® D A ® (FIRST ORDER) mOEL'i ®T0 21040 21020 IF X a 1 TIEN MINT "CUBIC L ® MEL": KTTO 21040 21030 MINT "imECIFIED GRKTTN L®' 21040 VT® 17: PRINT "IIWT 0 FOR FIRST 0®ER L®": HT® 18: PRINT "- OR -": MINT " 1 FOR ciBic m w 21060 IWUT " ";X: IF (X ( ) 0)AND(X ( ) 1) THEN PRINT "ERTOR — MEASE REENTER";: HT® 1: c m - 868: GOTO 21040 21#M GKUB 80: PRINT K$: PRINT X: PRINT L$: PR@ 0: CRUL 1002: RETURN 251 22000 a a m 80: print K$: print "I"; PRINT L$ 22016 FOR I = 1 TO 12:U = 10: æaJB 93:0(1) = U: TEXT 22030 SaiB 33000: KKUB 80: PRINT K$: PRINT X: PRINT Y: PRINT L$ 22040 PRI 01 c m 1002: lETUm 25800 æSlB 175W:GT = GT / 60: 80: PRINT K$: PRINT "4": PRINT K : PRINT GT: PRINT L$ : PR# 0: OKI 1002: RETUIM 28000 a a m 80: print K$: PRINT "3": PRINT U:U = 10: KBUB 93:X = U:U = 10: G C ^ 93:Y - U 26010 HOME : VTAB &TY"Y * HNM/ 80: PRINT "FEED FLIB) RATE IS ";Y;" Ü./BIN‘: PRINT : IF X ( ) 1 DEN PRINT 'FEED FLOW RATE CWTRtL BY aXERViajR'; H)TO 260^ 26020 PRINT "FED FUM KITE IS FIXED MANUALLY" 26030 VTAB 15: PRINT 'ENTER 0 FOR aiERVIKIR EMTRCL -OR-': ITPUT ' 1 FOR MANUAL CONT m . ';X 26040 IF X = 1 THEN VTfffi 20: D W T 'ENTER KSIED FL(M MTE (M./MIN) ';Y 26050 H®JB 80: PRINT K$: PRINT X:IFX=1DENF = Y«6© / 1000: PRINT F:PRINT L$ 26%0 PR3 0: c m 1002: ETUI&I 27800 a)SUB 16000: KBUB 80: PRINT K«: PRINT '2': PRINT VA: PRINT L$: PR# 0: C m 1^:0(13 ) = 0(13) * W: lETim 30008 )KBE :V = 1: KKCB 32800: PRINT 30018 VTIffl 4: PRINT ' KID K D I T m ' { 0 ( 8 ) ML/MIN';:X = 0(7): KSUB 500: PRINT ' )L' 38020 VTAB 5: PRINT ' K)^ ADDITim ';O(10);' ML/MIN';:X = 0(9): K)SUB 500: PRINT ' ML' %030 FORV = 2TO 10: K S B 32000: NEXT 30048 VTiffi 15: HTAB 2: INVERT : PRINT ' a.l£(££ FEED ADDITm';: NORMAL :X = 0(11): KSUB 580: PRINT ' N.' 30858 VTAB 16: HTK 11: INVERSE : PRINT ' TOTK VCX.HC';: NORMAL :X = 0(13): GOajB 500 PRINT ' L* 30068 VTAB 17: PRINT '&U RATE ';:X = PEEK (38255):X = INT (X / 2) * 2: PRINT X;'% ';D( 12);'MVM';:X = X « 0(12) / 180: GOaJB 500: PRINT ' H/M" 30100 VTRB 19: INVERT : PRINT ' TIME ': NORMAL 30110 VTAB 20: NT® 3: PRINT 'START ';:X = 0: G ( ^ 51800: PRINT ' %120 PRINT SAMPLE ';:X « 5: ^HJB 51000: PRINT 30130 VTAB 21: IF Cl « 1 DEN FUBH : PRINT '(%RRIER LOST'; ^135 IF CR { ) © DEN FLAS( : NT® 28: PRINT 'COWI lEQUEST'; 30137 NORMAL : PRINT 30148 VT® 22:X = (F(2) - «(6,2)) » F(l): PRINT ' ';: IF X ( 5 DEN INVERT %145 PRINT X;' «IfâJTES TO lOT CtmHER CM ' ; NORMAL 30158 X = IF(3) - M(#,3)) * F(l): HTAB 7: IF X ( 5 DEN INVERSE 38iæ PRINT X;' MUtlTES TO lEXT DIS< SAE': NORMAL 30160 lETUmi 32000 VTAB (V + 2 + 2 * W ) D): HT® (23 - LEN (P$(V))): INVERSE : PRINT ' ';P$(V);: W R M K :X = H(V,1): KRIB 508 £010 CM V BKUB ££0,32048,32^, 32%0,3 S m , 32050,32070, £070,32080, £0 % 32£0 ® T U ® £040 PRINT ' C': RETURN 32058 PRINT ' <': (ETUIM £060 PRINT ' ®R': KTURN 32878 PRINT ' L/M': RETURN 32080 PRINT ' ffiS': RETURN 32090 PRINT ' G/L': lETURK 252 33900 « M : VTfffl 3; INÆRŒ : P R M "ESTlffiTED VARIAIS': NORMAL : PRINT 3:^10 PRINT " 1"?: HTAB 10: INVEI^ : PRINT " BIOMASS CXM';: NORMAL :X = 0(1): KKUB 500: PRINT ■ G/L" 33029 PRINT " 2";: HTfB B: IIMflSE ; PRINT ' KJBSTRATE CONC";: NDR®L ;X = 012): æSJB 500: raiMT • B/L" 33030 PRINT • 3';: HTfffl 6: IN\ER% : PRINT ' SIN OXYKN CM:";: NORMAL :X = 0(3): fflSJB 50 0: PRINT " G/L" 33040 PRINT ' 4";: HTAB B: INÆŒE : MINT ' SP BRtMH RATE";: NORMAL :X = 0(4); SKUB 500: PRINT " 1/H" 33050 PRINT " 5";: HTIffl 7i INVERT ; PRINT " SJKTRATE YIELD";: NORMAL :X = 0(5); H)SUB 500 : PRINT " B/B" 33060 PRINT " 6";: HTAB 4: INVEf^ : PRINT ’ OX mSS TRANS CtEF*;: NORMAL :X = 0(6): S)SUB 500: PRINT " 1/H" 33070 PRINT " 7";: HTfB 10: INVEISE : PRINT " OXYKN YIELD";: NORMAL :X = 0(7): H)SUB 500: PRINT ’ G/G" 33080 PRINT " B’;i HTAB 7: IN\ÆRSE : PRINT " S)T OXYKN CSC";: NORMAL :X = 0(B): SaiB 500 I PRINT " B/L" 33090 PRINT " 9";; HT® 9: IN\ÆRSE ; MINT ' LKRJID VOU0E";: NORMAL :X = 0(9): KSJB 500: PRINT " L" 33100 PRINT "10";: HTAB 4: IWERK : PRINT " FEED CSCENTRATIW";:: NORMAL :X = 0(10): SIS» 500: PRINT ' B/L" 33110 PRINT "11";: HTAB 9: INVERSE : PRINT " MAX FEED SITE";: NORMAL :X = 0(11): H)SiB 500: PRINT " L/H" 33120 PRINT "12";: HTIffl 7: INlÆf^ : PRINT " ÆSSEL PIESSUIE";: NORMAL :X = 0(12); HISJB % 0: PRINT " M M " 33200 VTAB 19: HTAB 15: INVERT : PRINT " SfmE";: NORMAL : PRINT " ";:X = 5: SKUB 51000: PRINT 3%10 VTAB 22: IWUT "ENTER MffiBER (F VARIASE TO K D^ T OD ";X; VTAB 23: HTAB 1: CSJ. - B6B: VTRB 22: c m - 33220 IF (X { 1) OR (X ) 12) Ti€N VTAB 22: INVE(^ ; PRINT " ERROR — PLEASE REE NTER ": NORMS. : FOR II = 1 TO 2000: lEXT : S)TO 33210 3%:% VTAB 22: PRINT "ENTER NEW VffliE FDR VARIASE ";X: IlffUT " ";Y:0(X) = Y 33240 IF (X = 12) inSMVP = V:XX = X:YY = Y: S)SUB 17030:X = XX:Y = YY 33250 lETim 36000 )%BE : VTRB 4:l%mv= 1 TO 9: PRINT " ";V;" ";f^(V): )EXT : PRINT "10 ";P$(10) 36003 VTT® 17: PRINT "ENTER 0 TOINWENO Sm%S": VTRB 19: HTAB 15: INVERSE : PRINT " SA MPLE";: NORMAL : PRINT " ";:X = 5: S3S® 51000: PRINT 36006 VTAB 22: IWUT "ENTER NUMBER (F WRIAHl TO BE ( W Œ ) ";X: VTAB 23: HTAB 1: CS.L - B6B: VTAB 22: CALL - 66B: IF X = 0 THEN fETU^J 36008 IF (X { 1) cm (X ) 10) T)EN VTAB 22: INVERSE : PRINT " ERROR — PLEfŒ REE NTER ": NORMAL : FOR II = 1 TO 2000: TEXT : STTO 36006 36010 V = X: HOME : PRINT " 1" ;: HTAB 24: INVERT : PRINT " D#";: NORffflL : HTAB 27:X = P(V,1 ): SfiUB 500: PRINT 36020 PRINT " 2";: HTAB 24: INVERT : PRINT " C#";: NORMAL : HTAB 27:X = P(V,2): ffiSJB 500: PRINT 36030 PRINT " 3";; HTAB 21: INVEI^ : PRINT " SL(P£";: NORMAL : HTAB 27:X = P(V,3): GOSUB 5 00: PRINT 36040 PRINT " 4";: HTfS 15: INVERT : PRINT " Y-INTERCEPT";: NMMAL : HTAB 27:X = P(V,4): H®JB 500: PRINT 36050 PRINT " 5";: HTAB 24: INÆi^ : PRINT " D@";: IF V = 1 T)OI HTAB 19: PRINT " (CID C@ 253 36*0 NORMAL : HT(@ 27:X = P(V,5)i KHJ6 500: PR M 36070 PRINT " 6";: HTAB 24: Ifraæ : MINT " Ci*;;IF V = 1 TISNHT® 19: PRINT " Ci 36080 NORMAL : HT® 27;X = P(V,6): ®aJB 500: PRINT 36003 PRINT " 7*;: HT® 13: IN\ÆHæ : PRINT * MINIMUM Vffl.l£";;NORMAL :HT® 27:X = P(V,7): æ a m 500: PRINT 36086 PRINT " 8";; HT® 13: IfWEI^ : PRINT * MAXIMUM VK.IE*;: NORMAL : HT® E7:X = P(V,8): 590: PRINT 36090 PRINT " 9*;: HT® 18; INVERT : PRINT * SETMINT";: NORMAL : HT® 27;X = P(V,9): KSIB 500: PRINT 36100 PRINT "10";: HT® 9: INÆR* ; PRINT " PRtMJRTIIM. KlIN";: NORMAL : HT® 27:X = P(V, 10) : æaiB 500: PRINT *110 PRINT *11*;: IWE®E : HT® 7: PRINT * INTEGRAL T M CtXfâT*;: NORMAL : HT® 27:X = P( V,ll): GOam 500: PRINT *120 PRINT "12*;; HT® 5: INÆRœ : PRINT * DERIVATIF T M CmST";: NORMAL : HT® 27:X = P 50030 IF T(X - 2) > Z 7»B1 T(X - 2) = T(X - 2) - 2 + 1;TIX - 3) = T«X - 3) + 1 5%4@ IF T 55610 X a 0:ZI a Yl ♦ LEFTI (XI,3) 55620 FOR II a 4 TO 10: IF MIDI (XI, 11,1) = "E" DEN X = 1 55638 IF X a 1 d e n Zl a Zl + "0* 5640 IF X a 0 DEN Zl a Zl + MIDI (XI, 11,1) 55650 lOT :ZI = ZI+ RIBITI (XI,4): ETUIDI 5 % 0 Zl a STRI (X): RETUfffl 5950 Zl a »•: IF X ( 10 DEN Zl a "0" 55960 Zl a Zl + STRI (X): RETUWI 60000 & AIN,(TV) = I,(C3) a 0 6%10 PRINT CHRI (4){"WEN m )@Æ,D1': PRINT CHRI (4);"READ RUN NA)E': IfMJT IDI; PRINT CHRI (4);"dOSE RUN NAME" 6 ^ PRINT c m (4)j"(B5EN ";IDI;'.PAR,D2': PRINT CHRI (4);*READ ";IDI;".PAR" 60330 DIM T(29): FOR I = 10 TO 14: D W T T(I): lEXT 60040 DIM M(10,4),0.(10,l),m(10,l),P(10,17),0(16),F(4),Q(12),E(10,2) 60050 DIM PI(10) 60%0 FDR V a 1 TO 10: FOR I = 1 TO 17: imJT P(V,I): lEXT I,V: FOR V a l TO 10: INPUT P#(V ): )£XT 60070 FOR I a 1 TO 4: D8UT F(I): )£XT : INPUT 0(B): I)I>UT 0(10): INPUT 0(12): INPUT 0(13): IWUT 0(14): D M T 0(15): IIWT 0(16); D M T CO: D M T VP 6 0 m AI a CHRI (4):KI = CHRI (17):LI = CHRI (19):D0l a "KEN ":D1I = ’CLtSE ":D2# = "WRI TE ":D3I a "READ ' 60600 PQ(E - 16%B,0 256 62000 IF T(l@) < ) 0 GOTO 62030 62010 raiMI PRINT W;D2$;1D$;\MT": PRINT IDt: PRINT W;D1«;IM;MW T" 62020 PRINT A$;'PR@1': PRINT CHR$ PRINT ID*;' ADWTIVE, IPTim. FED BATCH': PRINT : PRINT I PRINT : PRINT "miTOŒD VARIABLES:': PRINT : PRINT A*;'PR@0' 62030 TEXT : M m : INVE^ : PRINT IDt: POKE 34,1 62040 warn 30000 62%0 F(% 1 = 1 TO 10 62070 IF TI10) = 0 DEN PRINT A$;'WPm •;IDt;'.DRT,D2': PRINT (%;Kt;IDt;'.DAT': PRINT P t(I): PRINT At;Dlt;IDt;'.m' 62080 IF TI10) « 0 DEN PRINT A$;'PR@1": PRINT CHRt (9);"8#!': PRINT ' CHR* II ♦ 64); ';Pt(I);' C;P(I,7);' TO ';P(I,B);')': PRINT A*;'PR#0' 62100 (EXT K110 & m TO T(5),T(6),T(7),T(B): i TIME TO T(B),T(9),D 62120 T(9) = T(9) + 3:X = 9: GORE 50000 62140 PRINT A$;'PR@1': PRINT CHRt (9);'B#I": MINT : PRINT : IF T(10) = 0 DEN PRINT 'STA RT THE: ';: GOTO 62160 62150 PRINT : PRINT i PRINT : PRINT : PRINT 'lESTART THE: '; 62160 PRINT T(6);"/';T(7);'/';T(5);' ';T(8);':";: IF T(9) < 10 DEN PRINT'0'; 62165 PRINT T(9); PRINT : MINT : PRINT : PRINT : PRINT : PRINT At;'PR#0' 62170 VTAB 20: HTAB 3: CALL - 868: NORMAL : PRINT 'START '; K1B0 IF T(10) = 0 DEN X = 5: KSUB 51000: PRINT ' ';: KTO 62200 62190 IF T<12) ( 10 DEN MINT ' '; K195 X a 10: aaiB 51000: MINT ' '; • 62200 MINT ' a m E ";:X = 5: G(HJG 51000: MINT 62210 IF T(10) < ) 0 arro K260 62220 MINT A*;IW;ID*;*.MR,D2': MINT A*;D2t;IDt;'.PAR- 62230 FOR 1 a 5 TO 9: IF T(l) ( 10 DEN Gt = '0' + STRt MACHINE-LANGÜAGE ROUTINE FEDBATCH GLU AN Glucose analyzer driver. Program: $8FD0 - $9254 Variables: $9260 - $9270 $9260 ADO channel number, 0// (D// assumed to be 13: low level ADC) $9260 Status register: Obtain maximum converted voltage, $FF; Obtain minimum converted voltage, $00 $926E High byte of minimum converted voltage (obtained from $0007) $926F Low byte of minimum converted voltage (obtained from $0006) $9270 High byte of maximum converted voltage (obtained from $0007) $9271 Low byte of maximum converted voltage (obtained from $0006) $9272 Stroke counter $9273 Byte to be output to binary I/O (stored in $9274, $9275, $9276 or $9277) $9274 Storage of binary output high byte to move sample valve to calibrate position, calibration cylinder in carrier stream (bit 12 set, $10) $9275 Storage of binary output high byte to move sample valve to sample position, sample cylinder in carrier stream (bit 13 set, $20) $9276 Storage of binary output high byte to activate carrier pump solenoid (bit 14 set, $40) $9277 Storage of binary output high byte to activate withdrawal pump solenoid (bit 15 set, $80) $9278 Miscellaneous storage: inversion; 0.9 sec counter $9279 Status register: Sample measurement (0) Calibrate measurement (1) $927A Miscellaneous storage: counter for the number of times through 0.1 sec loop $927B Analog input counter $9270 High byte of maximum converted voltage during calibration (obtained from $9270) $927D Low byte of maximum converted voltage during calibration (obtained from $9271) $9550 to $9558 Refer to MAOHINE-LANGUAGE ROUTINE GRADFEEDIRQ 258 903C- A9 23 LDA #$23 8FD0- 78 æi %3E BD C9 91 STA $91C9 ^ 1 - AD BB C8 IDA IC8ffl 9041- 20 C0 91 JSR $91C0 yD4- (SIBBCa IDA #C0BB 9044- 7B SEI ffiD7- SB CLI 9045- AD B9 C0 LDA $C0B9 ST»- AD 75 92 IDA $9275 9046- AD B9 C0 LDA $C0B9 BFDB- 6D 73 92 STA $9273 904B- 58 CLI BFX- 20 60 % JSR $9060 904C- 60 RTS BFEÏ- A9 C5 LDA #$C5 904D- 00 BRH 20 AB FC JSR #CAB 905F- 00 BRK ms- 20 B0 90 JSR $%B0 % 0 - AD 55 95 LDA $9555 BFE9- A9 FF LDA #$FF 9063- 0D 73 % ORA $9273 0TB- BD 6D 92 STA $925) 9%6- BD 55 95 STA $95% 6FEE- A9 0) LDA #$0A 9069- AD 57 95 LDA $9557 wre- BD C9 91 STA $91C9 9%C- 0D 73 92 ORA $9273 SfF3- 20 B0 91 JSR $9160 906F- BD 57 95 STA $9557 0T6- 20 10 91 JSR $9110 %72- 20 AB 90 JSR $9MB BFF9- AD 74 92 LDA $%74 9075- 60 RTS 8FFC- BD 73 92 STA $9273 3076- 00 BRK BFFF- 20 60 90 JSR $9060 907F- % BRK mz- A9 C5 LM #$C5 90B0- A9 FF LDA #$F *9%4L 9082- 4D 73 92 EOR $9273 90B5- BD 78 æ STA $9278 9004- ^ AB FC JSR $FCAB 9088- AD 55 95 LDA $9555 %07- 20 B0 90 JSR $90B0 908B- 2D 78 92 AND $9278 900A- A9 M LDA «$00 90BE- BD 55 95 STA $95% 9 ^ - BD 6D 92 STA $926D 9091- K) 57 95 LDA $9%7 %«:- ft9 23 LDA #$23 9094- 2D 78 92 AND $9278 9011- BD C9 91 STA $91C9 9097- BD 57 95 STA $9557 9014- 20 C0 91 JSR $91C0 909A- 20 AB 90 JSR $90AB %17- AD 70 92 LDA $9270 909D- 60 RTS 901ft- BD 7C 92 STA $927C 909E- 00 BRK 901D- AD 71 92 LDA $9271 9020 BD 7D 92 STA $927D 9022- 20 10 91 JSR $9118 9026- ftD 75 92 LDA $9275 9029- BD 73 92 STA $9273 902C- 20 60 90 JSR $9060 902F- ft9 C5 LDA #$C5 9031- 20 ftB FC JSR $FCAB 9034- 20 60 90 JSR $90B0 9037- ft9 00 LDA #$M 9039- BD 6D 92 STA $925) 9M7- 00 BRK 9iy- 00 BRK 259 90A8- 78 æi 9160- A5 07 LDA $07 90A9- AD 50 95 m 09550 9162- CD 6£ 92 DP $926E m - C9 02 w #002 9165- 90 06 K 2 $916D 90AE- % 07 BCC %mi 9167- F0 ^ K O $9178 90B0- AD 50 95 LDA 9169- B0 14 K S $917F %B3- C9 60 OP #080 916B- A5 07 LDA $07 30B5- 90 23 KC $%DA 916D- BD 6E 92 STA $%6E %B7- A0 0ft LDY #00ft 9170- AS 06 LDA $06 90B9- B1 FA LDA (0FA),Y 9172- BD 6F 92 STA $926F %BB- C9 02 CMP #002 9175- 4C 7F 91 JIP $917F 90BD- B0 14 KS $%D3 9178- (B 06 LIA $06 90BF- A9 D2 LDA 80D2 917A- CD 6F 92 OP $926F 30C1- 8D BB C0 STA 0C0BB 917D- 90 EC BCC $916B 9K4- AD 55 95 LTO 09555 917F- 58 CLI %C7- BD BB C0 STA 0C0BB 9180- 60 RTS 90CA- AD æ 95 LDA 09556 9181- 00 BRK 90CD- BD BA C0 STA 0C0BA 918F- 00 Bf» %D0- 4C EB 90 M> 0%EB 91!&- A5 07 LIA $07 90D3- AD 51 95 u m 09551 9192- CD 70 92 CM) $9271 90D6- C9 02 CMP §002 9195- 90 16 K C $91AD 90D8- B0 E5 BCS 090BF 9197- F0 0D BEQ $91A6 90Dft- A9 D2 LDA §0D2 9199- (ffi 07 LDA $07 90DC- BD BB C0 STA 0C0BB 919B- BD 70 92 STA $9270 91SE- 90DF- AD 57 95 LM 09557 A5 06 LDA $06 91fffl- BD 71 92 STA $9271 %E2- BD BB C0 STA 0C0BB 91A3- 4C AD 91 J » $91ffi) 9K5- AD 58 95 LDA 09558 91A6- AS 06 LDA 30EB- BD ^ C0 STA 0C0BA $06 91AB- CD 71 92 $9271 90EB- 58 CLI DP 91AB- B0 EC BCS $9199 90EC- 60 RTS 91AD- 58 90ED- 00 BRK CLI 9iœ- 60 RTS 9 W - 00 BRK 9iiy- 00 BRK 9110- A9 05 LDA §005 91B0- A9 FF LDA #$FF 9112- BD 72 92 STA 09272 91B2- BD 6E 92 STA $926E 9115- AD 77 92 LDA 09277 91B5- BD 6F 92 STA $926F 9118- BD 73 92 STA 09273 91BB- 4C CB 91 JMP $91C8 911B- 20 60 90 JSR 09060 91BB- BRK 911E- A9 C5 LDA §0C5 91BF- BRK 9120- 20 AB FC JSR 0FCM 91C0- AS % LIA 9123- 20 80 % JSR 0908# #$00 91(2- BD 70 92 STA 9126- A9 09 u m #009 $9270 9128- BD 78 92 STA 09278 912B- A9 C5 LDA #0C5 912D- 20 AB FC JSR 0FCA8 9130- CE 78 92 KC 09278 9133- D0 F6 m 09128 9135- CE 72 92 1£C 0%72 9138- D0 El BfE 09116 913ft- 60 RTS 913B- 00 BRK 260 91C5- 8D 71 92 STA >9271 91C6- A9 28 LDA #$28 91CA- BD 72 92 STA $9272 91CD- AD 76 92 LDA $9276 91D0- BD 73 92 STA $9273 91D3- 20 60 90 JSR $%60 91D6- A9 02 LDA #$02 91D8- BD 7B 92 STA $9278 91DB- 20 40 92 JSR $9240 91DE- AD 6D 92 LDA $9260 91E1- F0 06 BEQ $91E9 91E3- 20 60 91 JSR $9160 91E6- 4C EC 91 J W $91EC 91E9- 20 90 91 JSR $9190 91EC- CE 7B 92 DEC $927B 91EF- D0 ED BI£ $91K 91F1- 20 80 % JSR $9080 91F4- A9 12 LDA #$12 91F6- BD 7B 92 STA $9278 91F9- 20 40 92 JSR $9240 91FC- AD 60 92 LDA $«6D 91FF- F0 K K O $9207 9201- 20 60 91 JSR $9160 9204- 4C 0A 92 JMP $920A 9207- 20 90 91 JSR $91% 920A- CE 78 92 DEC $9278 920D- D0 EA 8 Æ $91F9 920:- CE 72 92 DEC $«72 9212- D0 89 BfE $91CD 9214- 60 RTS 9215- 00 8RX 923F- 00 8RK 9240- A9 86 LDA #$86 9242- 20 AB FC JSR $FCA8 9245- 78 SEI «46- AD 6C 92 LDA $926C 9249- BD 53 D0 STA $8053 924C- A9 01 LDA #$01 924E- 20 32 E6 JSR $E632 9251- 20 07 EC JSR $EC07 9254- 60 RTS 9255- 00 BW 261 MACHINE-LANGUAGE ROUTINE GRADFEEDWAIT Walt and keyboard check. Program: $92FF - $9388 Variables: $93E0 - $93E9 $93E0 - 93E9 format: YY MM DD HH NN (in ASCII) year/month/date/hour/minute storage of the time the next sample is to be taken they are compared with RAM $EFA2, $EFA3, $EFA5, $EFA6, $EFA8, $EFA9, $EFAD, $EFAE, $EFBO, $EFB1, respectively, which represent the same quantities MACHINE-LANGUAGE ROUTINE GRADFEEDIRQ ON/OFF Interrupt enable/disenable. Program: $93D0 - 93DB Variables : None 262 9347- 98 3C BCC 89385 9349- F0 02 KO 8934D 934B- M Cl BCS 893% 934D- AD E5 93 L M 89%5 9350- CD A9 EF C W 8EFA9 9353- 90 30 BCC 89385 3EFE- FF ??? 9355- F0 02 BEQ 89359 32FF- 08 PW> 9357- B0 B5 % S 893% 93W- De CLD 9359- AD E6 93 U» 89%6 9301- 48 PHD - 935C- CD AD EF DP 8EFAD 9302- BA TXA 32SF- 90 24 BCC 89385 9303- 48 p m 9361- F0 02 KQ 89365 9304- 98 TVA 9363- 60 A9 BCS 893% 9305- 48 m 9365- AD E7 93 LDA 893E7 9386- 78 SEI 9368- CD AE EF D P 8EFffi 9307- AD C0 LDA $ceœ 9366- 90 18 BCC 89385 938A- M) 8B C0 LDA 8C086 936D- F0 02 % Q 89371 930D- 58 CLI 936F- % 9D des 893% 93%- 4C æ 93 JM> 893% 9371- AD E8 93 LDA 893E8 9311- AD E0 93 LDA 89%8 9374- CD 60 EF DP 8EFB0 9314- CD % EF C W 8EFK 9377- 90 0C KC 89385 9317- 90 6C % C 89385 9379- F0 02 BEQ 8937D 9319- F0 02 % 0 8931D 9376- 60 91 BCS 893% 931B- B0 FI KS 893% 937D- AD E9 93 LDA 89%9 931D- AD El 93 U » 893E1 9380- CD 61 EF cg» 8EFB1 9320- CD A3 EF DP 8EFA3 9383- FO 02 BEQ 89387 9323- 90 60 %C 89385 9385- 60 87 KS 893% 9325- F0 02 % 0 89329 9387- A9 7F LDA 887F 9327- B0 ES % s 893% 9389- 8D % 93 STA 893% 9329- AD E2 93 LDA 89%2 938C- 78 SEI 932C- CD A5 EF DP 8EFA5 938D- AD 89 C0 LDA 8C089 932F- 90 54 BCC 89385 9390- AD 89 C0 LDA 8C089 9331- F0 02 %Q 89335 9393- 58 CLI 9333- 60 D9 BCS 893% 9394- 68 PLA 9335- AD E3 93 LDA 89%3 9395- A8 TAY 9338- CD A6 EF DP 8EFA6 9396- 68 PLA 933B- 90 48 %C 89385 9397- AA TAX 933D- F0 02 BEQ 89341 9398- 68 PLA 933F- 60 CD KS 893% 9399- 28 PLP 9341- AD E4 93 LDA 893E4 939A- 60 RTS 9344- CD A8 EF C ® 8EF% 9396- 00 61» 263 93AF- 00 BRK 93B0- AD 00 C0 LDA $C000 93B3- 0A ASL 93B4- 60 06 BCS $938C 93B6- 4C 11 93 JW $9311 93B9- 00 BRK 93CF- FF ??? 9300- 78 SEI 9301- 60 RTS 9302- 00 BRK 93D9- 00 BRK 93DA- 58 CLI 93DB- 60 RTS 93DC- 00 BRK 264 MACHINE-LANGUAGE ROUTINE GRADFEEDIRQ Interrupt handler. Program: $9408 - $9517 Variables: $9550 - $95F3 $00FA Low byte pointer to present pump speed in pump schedule table $OOFB High byte pointer to present pump speed in pump schedule table $9550 Pump on counter (counts down from appropriate percentage of time that pump is to be on: $32 for 100% on down to $00 for 0% on) $9551 Cycle counter (counts down from $32 to $00 then resets) $9552 Temporary storage for accumulator; returned to accumulator at the end of the interrupt $9553 Temporary storage for x-register; returned to x-register at the end of the interrupt $9554 Temporary storage for y-register; returned to y-register at the end of the interrupt $9555 High byte to binary output when pump is to be turned off $9556 Low byte to binary output when pump is to be turned off $9557 High byte to binary output when pump is to be turned on $9558 Low byte to binary output when pump is to be turned on $9559 Status register of bank position at interrupt: ROM bank, $00; RAM bank, $AC $9565 - $956E Storage for $39, ASCII "9" (data to turn pump permanently off) $956F Storage for $00 $9570 - $95F3 Storage pump schedule table format: YY MM DD HH NN % (in ASCII, except %) year/month/date/hour/minute/percent pump on % pump on is valid until YY MM DD HH NN $EFA2 - $EFB1 (RAM bank) ASCII Date-time acquired from ISAAC time-of-day clock format: YY MM DD W HH NN (in ASCII) year/month/date/day/hour/minute 265 945E- C8 INY 943- B1 Fft LDft ($Fft),Y 9461- CD A3 EF C8» $EFft3 9464- 90 62 BCC $94C8 9466- F0 02 KO $946A 9468- B0 6C BCS $94% 946ft- C8 INY 946B- B1 Fft LDft ($Fft),Y 9407- 00 BRK 946D- CD ftS EF OP $EFft5 9408- 78 æi 9470- 90 55 KC $94C8 9409- D8 CU) 9472- F0 02 KQ $9476 940ft- m TM 9474- % 60 SCS $9406 94%- BD 53 æ BTft $9553 94K- 98 TYft 940F- M) 54 95 STfl $9554 9476- C8 INY 9412- ftD % EF LDft $EF% 9477- B1 Fft LDft ($Fft),Y 9415- BD 59 95 STft $9K9 9479- CD ft6 EF OP $EFft6 9418- ftD BB C0 LDft $C@% 947C- 90 4fl KC $94C8 941B- ftD BB C0 u n $C0BB 947E- F0 02 KQ $9482 94 lE- 20 08 EF JSR $EF% 9480- B0 54 BCS $9406 9482- C8 INY 9483- B1 Fft LDft ($Fft),Y 9421- CE 50 95 DEC $9550 9485- CD ftB EF $£Fft8 9424- D0 11 M $9437 9488- 90 3E BCC $94C8 9426- ft902 m #$D2 948ft- F0 % KO $948E 9428- 80 B8 C0 STft $C8B8 948C- % 48 BCS $94D6 942B- ftD 55 95 LDft $æs5 948E- C8 INY 942E- 8D BB C0 STft $C@BB 948F- B1 Fft LDft 4$Fft),Y 9431- ftD56 95 U » $%56 9491- CD ft9 EF OP $EFft9 9434- 8D Bfl C0 STft $C0B) 9494- 90 % KC $94C8 9437- CE SI 95 DEC $9551 9496- F 0 % K O $949ft 943ft- F0 0C m $9448 9498- B0 3C KS $9406 943C- 4C F7 94 J» $94F7 949ft- C8 INY 943F- EA NCP 949B- B1 Fft LDft ($Fft),Y 9440- Eft NOP 9441- Eft 9442- Eft m> 94%- CD m EF C®* $EFftD 9443- Eft NOP 94m- 90 26 BCC $94C8 9444- Eft NOP 94A2- F0 02 BED $94% 9445- 20 08 EF JSR $EF08 94A4- B8 30 BCS $94% 9448- ftS Fft LDft $Fft 94A6- ce INY 944ft- C9 E9 QP #$E9 94A7- B1 Fft U» ($Fft),Y 94A9- CD K EF OP $EFK 94K- 90 Ift KC $94C8 944C- D0 03 BÆ $9451 94AE- F0 02 KD $94B2 944E- 4C D6 94 JIP $9406 94B0- m 24 KS $9406 9451- A0 % LDY #$00 94B2- C8 INY 9453- B1 Fft u m ($Fft),Y 94B3- B1 Fft IM ($Fft),Y 943- CD œ EF CMP $EFft2 94B5- CD B0 EF OP $EFB0 9458- 90 6E KC $94C8 94B8- 90 0E KC $94Ca 945ft- F0 02 BEQ $345E 94BA- F0 02 BEQ $94K 945C- % 0ft BCS $9468 94BC- B0 18 %S $9406 266 94BE- C8 INY 9ABF- 61 Fft LDft ($Fft),Y 94C1- CD 61 EF C » 0EF61 94CA- F0 02 K O $9AC8 3AC6- 60 K 6CS 09AD6 9AC8- 18 CLC 94C9- A5 Fft LDft «Fft 94CB- 69 06 ADC <«06 94CD- 85 Fft STft «Fft ■ 94CF- 90 02 K C «9AD3 94D1- E6 F6 lie «FB 94D3- AC AS 9A «9AA5 94D6- R0 K) LDY #«0ft 94D8- 61 Fft LDft («Fft), Y 94DA- 18 CLC 94DB- 6A ROR 94DC- 8D 50 95 STft «9550 94If- F0 11 K Q «9AF2 94E1- A9 D2 LDft <«D2 9AE3- 8D 68 C0 STft «C068 9AE6- AD 57 95 LDft « ^ 94E9- 8D 66 C0 STft «C06B 94EC- AD 58 95 LDft «9558 94EF- 8D 6ftC0 STft «C06A 9AF2- A9 32 LDft #$% 9AFA- BD 51 95 STft «9551 9AF7- ftD 59 95 Uffi « ^ 9 9AFft- C9 ftC CW #«AC 9AFC- F0 06 BED «950A 9AFE- ftD 89 C0 LDft «C089 9501- AD 89 C0 LDft «C089 950A- AD 5A 95 LDA «955A 9507- A8 TftY 9508- AD 53 95 LDft «9553 9506- Aft TftX 95K- ftS AS LDA «A5 950E- 58 CLI 950F- A0 RTI 9510- % BRK 9511- % BRK 9512- 78 SEI 9513- 20 7F 03 JSR «037F 9516- 58 CLI 9517- 60 RTS 267 ASCL PROGRAM ÏD 0F8 Process simulator program. Associated FORTRAN subroutines: SET, establish common blocks; RDIN, Input Initial state and Initial estimated state; VIROUT, subroutine to communicate with supervisor Variables: ACCN Cycle counter COOT Carbon dioxide production dynamic equation CINT Communication Interval In hours DO Corrputed dissolved oxygen concentration In grams/llter DT Duration of sampling Interval In hours ESTP Estimated error covariance matrix ESTVOL Estimated volume ESTX Estimated state vector F Feed flow rate FLOW Feed flow rate GAINK Kalman gain matrix K Glucose half-rate saturation constant KA Oxygen mass transfer coefficient KC Specific growth rate/overall carbon dioxide "yield" KI Substrate Inhibition constant KM Maximum specific growth rate KN Oxygen half-rate saturation constant KO Specific growth rate/overall oxygen yield KS Specific growth rate/overall glucose yield KX Specific growth rate MC Carbon dioxide maintenance energy coefficient MO Oxygen maintenance energy coefficient MS Glucose maintenance energy coefficient 0 Dissolved oxygen concentration ODOT Dissolved oxygen concentration dynamic equation OF Saturated dissolved oxygen concentration 01 Initial dissolved oxygen concentration OP Dissolved oxygen concentration of previous measurement PROJP Projected error covariance matlrx PROJX Projected state vector Q Process noise covariance matrix R Measurement noise covariance matrix ROO Corrupted carbon dioxide evolution rate RDO Dissolved oxygen concentration RO Corrupted oxygen consumption rate RRCO Carbon dioxide evolution rate RRO Oxygen consumption rate RS Corrupted glucose concentration S Glucose concentration SACCN Initial cycle counter SDOT Glucose concentration dynamic equation 268 SF Glucose concentration in nutrient feed SI Initial glucose concentration In fermentor SP Glucose concentration.of previous measurement SOBF Glucose concentration In nutrient feed T Time since the beginning of the fermentation In hours IF Termination time In hours TIME Time since the beginning of the fermentation In hours V Liquid volume In fermentor VDOT Volume dynamic equation VI Initial liquid volume In fermentor VP Liquid volume In fermentor at previous measurement X Biomass concentration In grams dry blomass/llter XDQT Biomass concentration dynamic equation XI Initial biomass concentration In grams dry blomass/llter XP Biomass concentration of previous measurement YC Carbon dioxide "yield" (grams of biomass produced per gram of carbon dioxide produced) YO Oxygen yield (grams of biomass produced per gram of oxygen consumed) YS Glucose yield (grams of biomass produced per gram of glucose consumed) 269 i TYPE FD_0FB.CSL PROGRAM FERME) INITIAL PROCEDURAL(VI,X1,S1,01,F,SF,KM,K,RI,KN,TF=) cm. miN(VI,XI,SI,OI,F,SF,KM,K,KI,KN,TF) END CINT = 1./120. œ C N = -1.0 PROCEDURAL(=flCCN) CALL SET(KCN) END VP = VI XP = XI SP = SI W = OI DT = CINT HS - 0. MO = 0. MC = 0. END DYNAMIC DERIVATIVE TI« = T WOT = F XDOT = KX«X - F«X/V SDOT = -RStX ♦ F*(SF-S)/V - MS*X ODOT = -KD*X - F*0/V -MD*X ♦ KA»(IF-0) CDOT = KC#X ♦ MC*X KX = KM * (S/(K+S4KI»S*S)) * (0/(WWM) OF = 0.00804 KA = 120. KS = RX/YS KO = KX/YO KC = KX/YC YS = .5 YO = 4.055711802 YC = 0.885630802 V = INTEB(VDOT,VI) X = INTEG(XDOT.XI) 270 S = INTEG(SD0T,S1) 0 = INTEB(ODOT,OI) IF(S.LT.1.8E-30)S=1.8E-3i lF(O.LT.l.eE-30)O=l.ffi-3» TER«T(T.ffi.TF) END RRO = KA#(DF-0.5*IO + K>)) * 0.5*(V+VP) RRCO = CDOT » 0.5*(V+VP) RDO = 0 RO = 6M£S(RR0,e.l*RR0) Rco = »)uss(RRCO,e.i«Rn:o) Dû = GAUSS(RDO,0.1#RDO) RS = GAUSS(S,.5) IF (RO. LT. 1. œ-30) R0=1.0E-30 IF(RCO. LT.1.6E-30)RC0=1.0E-30 IF(RS.LT. 1.0E-30)RS=l.œ-30 IF(DO.LT.1.0E-30)DO=l.eE-3@ PROCEDURAL (=T, X, S, D, V, F, DO, RDO, RO, RRO, RCO, RRCO,... KX, KA, YS, MS, YO, MO, KC, MC, OF, SF, RS) ( m WROUT (T, X, S, 0, V, F, DO, RDO, RO, RRO, RCO, RRCO,... KX, KA, YS, MS, YO, fffl, KC, MC, (F, S', RS) END VP X V XP = X SP = S OP = 0 END TERMINAL PROCEDURAL (=T, X, S, 0, V, F, DD, RDO, RO, RRO, ICO, RRCO,... KX, KA, YS, MS, YO, MO, KC, )C, OF, SF, RS) CALL HR0UT(T,X,S,0,V,F,D0,RD0,R0,RR0,RC0,RRC0,... KX, KA, YS, MS, YO, MO, KC, MC, OF, S', RS) END END END SUBROUTINE SET (SACCN) REAL*4 SACCN ACCN,ESTVOL,FLOW,ESTP(13,13),E5TX(13), 1GAINK(13,6),PR0JP(13,13),PR0JX(13),Q(13,13),R(G,6),SF COMMON/KALMAN/ESTP,GAINK,PROJP,PROJX,Q, R CmON/SCHLAS/ACCN, ESTVOL, FLOW, SF, ESTX ACCN = DBLE (SACCN) RETURN END 271 SUBROUTIÆ RDIN(VI, XI,SI,01,F,StÆF,KH,K, Kl,KN,TF) REAL KK,K,KI,KN R£AL«B R(XN,E5TV0L,FUM,ESTP(13,13),ESTX(13), lGAINK(13,6),PmiP(13,13),PR0JX(13),0(13,13),R(6,6),SF comoN/wurn/ESTP, mm , projp, projx, q, r COmON/SCHAS/A(%N, ESTVOL, FLOW, ESTX . 10 FORMATA INPUT VI,XI,SI,OI,F») 20 FORWK» SF,KB,K,KI,KN>) 60FORW)T('TF F10.A») 30 FORMAT(F10.4) 40 FORMAT(5F10.4) 210 FOIMAT (6F10.4) 220 FORMAT (' IWUT VI, XI,SI, 01, F, ff, F10.4’) 230 FORMAT (» IWUT KX, YS, KLA,YO, 0» F10.4M 240 FORMAT (K^IO.4) WRITE (6,10) WRITE (6,20) WRITE (6,60) READ (5,40) VI,XI,SI,OI,F lEAD (5,40) SlffiF,KM,K,KI,KN READ (5,30) TF WRITE (6,40) VI,XI,SI,OI,F WRITE (6,40) SU6F,KH,K,KI,KN WRITE (6,30) TF WRITE (6,220) WRITE(6,230) READ(5,210) ESTVOL,PROJX(l),PROJX(2),PROJX(3),FLOW,a: READ(5,240) PROJX(4),PROJX(5),PROJX(6), PROJX(7),PROJX(8) WRITE (6,210) ESTVOL, PROJX (1 ), PROJX (2), PROJX (3), FLtW, SF WRITE (6,240) PROJX (4), PROJX (5), PMUX (6), PffiJX (7), PROJX (8) WRITE ( 11,210) ESTVOL, PROJX ( 1 ), PROJX (2), PIfflJX (3), FUW, SF WRITE(11,240) PROJX(4),PROJX(5),PROJX(6),PROJX(7),PROJX(8) RETURN END 272 SUBROUTINE UROÜT (T, X, S, 0, V, F, DO, RDO, RD, RRO, RCO, RRCO, IKX, Kfl, YS, MS, YO, MO, RC, MC, (F, aJBF, RSI IMPLICIT REAL«A (R,M) REAL*8 flCCN,ESTV0L,FL0»,ESTP(13,13),E5TX(13), I S A M ( 13,6), PROJP (13,13), PROJX ( 13), Q (13,13), R (6,6), SF R£flL«B DT cmm/KAum/ESTP, mm , pmijp, projx, q , r CDMW/SCUflS/flCCN, ESTVOL, FLOW, S', ESTX 100 FORMAT (7E14.B) 110 FORMAT(17) 120 FORMAT(Fil.3) 130 F0RWT(6E12.5) 140 FORMAT(3E12.5) C « n n tm m iiniittH i i m m im i n n i i i i i iiiiiiii i n in ii C SAVE C02, 02, SUBSTRATE CONCENTRATION, VOLUE, FLOW RATE, C FEED SUBSTRATE CONCENTRATION, MB) ACCESS FLAG, C TIEN WAIT FOR ACCESS FLAG OF FOR012.DAT TO CHANGE C « i i i n n iiiii n i i i m i n i i m im m m m in i i m m w H H DT = l./6./(l./120.) C CONVERT GRfMS/MINUTE TO MOLES/MINUTE RRCO = RRCO / (2.0*15.9994 + 12.0111) RCO = RCO / (2.0*15.9994 + 12.0111) RM) = RRO / (2.0*15.9994) RO = RO / (2.0*15.9994) ACCN = ACCN * 1.0 IF (im)((CCN,DT).NE.0.0) SÏÏD 998 WRITE(9,130)T,X,S,O,V,F WRITE (9,130) DO, RDO, Œ, RRO, RCO, RRCO WRITE(9,130)KX,KA, YS,NS, YO,MO HRITE(9,140)RC,RS,(F CALL KHAST(RCO,RO,RS,V,F,DO,X,KX) WRITE (5,120) T WRITE(11,120) T 998 RETURN END 273 FORTRAN SUBROUTINE KNF028 and FORTRAN PROGRAM SÜPERV8 Estimator and optimal controller programs applied In simulation studies and on-line experiments, respectively. Associated FORTRAN subroutines: EXPAQ, calculate the state transition matrix In REAL*16 precision INTEGRATION, apply IMSL's subroutine, DC EAR, to perform Integration FCN, required subroutine for DGEAR containing estimator model FCNJ, required subroutine for DGEAR, generates Jacoblan matrix Main program variables: A(13,13) No longer used AACC Time since start of fermentation In hours ABCC Time since start of fermentation In hours ACCN Sampling cycle counter BETW55(6,6) Intermediate calculated quantity BETW88(13,13) Intermediate calculated quantity DELT Conmunlcatlon (update) Interval In hours DKl Q(l,l) coefficient DK2 0(2,2) coefficient DK3 0(3,3) coefficient DK4 0(4,4) coefficient DK5 0(5,5) coefficient DK6 0(6,6) coefficient DK7 0(7,7) coefficient DK8 0(8,8) coefficient ESTP(13,13) Estimated error covariance matrix ESTX03) Estimated state vector ESTVOL Eslmated liquid volume la the fermentor P(13,13) Jacoblan matrix of state equations PF Eight character string In time acquisition routine FL Feed flow rate In liters/hour FLOFLG Status flag for feed pump: 0 «■ supervisor control; 1 “ manual control FLOW Feed flow rate in liters/hour FLOWMAX Maximum feed flow rate G(13,3) No longer used GAIMC(13,6) Klaman gain matrix GG Eight character string In time acquisition routine GLUGOS Present glucose concentration from manual data entry GLUNEW Present glucose concentration measurement GLUOID Previous glucose concentration measurement GLUR Average rate of glucose utilization GLÜRAT Present rate of glucose utilization GLURATl Previous rate of glucose utilization GLÜRAT2 Twice previous rate of glucose utilization GLURAT3 Rate of glucose utilization obtainedthree measurements previous GLURAT4 Rate of glucose utilization obtained four measurements previous GLURAT5 Rate of glucose utilization obtained five measurements previous 274 GLURAT6 Rate of glucose utilization obtained six measurements previous GLUTIM Time of present, manually-entered glucose measurement H(6) Measurement vector I Loop counter IDMTX(13,13) Multiplicative Identity matrix J Loop counter H(6,13) Jacoblan matrix of measurement equations MODFLG Status flag for growth law, not Implemented MWBIOM Molecular weight of biomass MWC02 Molecular weight of carbon dioxide HWGLUC Molecular weight of glucose MW02 Molecular weight of oxygen N Dimension of system of state equations 0 Dissolved oxygen concentration PHI(13,13) State transition matrix PHIP(13,13) No longer used PROJP(13,13) Projected error covariance matrix PR0JXO3) Projected state vector Q(13,13) Process noise covariance matrix R(6,6) Measurement noise covariance matrix RATIO Ratio of average glucose utilization rate to carbon dioxide evolution rate RCO Carbon dioxide evolution rate RO Oxygen consumption rate RTME Present time or time elapsed since start of fermentation RTHEO Time at start of fermentation S Glucose concentration SACCN Single precision sampling cycle counter SACID Single precision acid and base addition during present sampling cycle SACIDP Single precision acid and base addition duringprevious sampling cycle SACK Single precision variable containing 9999 SAIN Single precision air flow rate In In liter/hour SAOUT Single precision air flow rate out In llter/mln SBASE Single precision volume of base added during present sampling cycle SCO Single precision off-gas carbon dioxide fraction SDMOD No longer used SDCO Single precision dissolved carbon dioxide concentration SDO Single precision dissolved oxygen concentration SEQUST Single precision string In communication routine SEST Single precision variable In the communication routine SESTX Single precision variable In the communication routine SF Glucose feed concentration In grams/liter SFL Single precision nutrient feed rate in liters/hour SO Single precision off-gas oxygen fraction SRCO Single precision carbon dioxide evolution rate SRO Single precision oxygen utilization rate SS Single precision glucose concentration SSS Single precision glucose concentration STRING Twenty character string contalng twenty X's SV Single precision liquid volume In fermentor T Communication (update) Interval In hours TERM51(6) Intermediate calculated quantity TERM55(6,5) Intermediate calculated quantity TERH58(6,13) Intermediate calculated quantity TERH81Ù3) Intermediate calculated quantity TERM85U3,6) Intermediate calculated quantity TERM88U3,13) Intermediate calculated quantity V " Liquid volume In fermentor 275 VESPRES Vessel pressure WK(A61) Working space for IMSL routines YCP Grams of carbon dioxide produced pec gram of biomass produced YOP Overall oxygen yield YSP Overall glucose yield Z(6) Measurement vector ZAP Glucose stoichiometric coefficient based upon one mole of biomass produced ZBP Molecular oxygen stoichiometric coefficient based upon one mole of biomass produced ZCP Nitrate stoichiometric coefficient based upon one mole of biomass produced ZDP Water stoichiometric coefficient based upon one mole of biomass produced ZEP Carbon dioxide stoichiometric coefficient based upon one mole of biomass produced ZT Number of carbon atoms per molecule of carbon source ZU Number of hydrogen atoms per molecule of carbon source ZV Number of atoms of oxygen per molecule of carbon source ZU Number of atoms of carbon per molecule of biomass ZX Number of atoms of hydrogen per molecule of biomass ZY Number of atoms of oxygen per molecule of biomass ZZ Number of atoms of nitrogen per molecule of biomass Subroutine variables: A(13,13) E) Input matrix ACCN I) Cycle counter B(I3,13) E) Output (state transition matrix) BB E) Sampling Interval In hours C(13,13) E) REAL*16, Interroedlate-calculatlon matrix D(13,13) E) REAL*16, Intermedlate-calculatlon matrix ESTVOL I) Estimated liquid volume In fermentor ESTX(13) I) Estimate state vector FLOW I) Feed flow rate In liter/hour H I) DGEAR Integration step size 1ER I) IMSL error number storage INDEX I) DGEAR parameter IWK(13) I) DGEAR Integer working space J E) Loop counter METH I) DGEAR parameter MITER I) DGEAR parameter N I) DGEAR parameter, dimension of system of differential equations PD(I3,13) I) Jacoblan matrix of state equations PR0JX(13) I) Projected state vector R E) Ratio of two elements RR E) Multiplication of the ratio of two elements, r, by Itself multiple times SF I) Glucose concentration In feed SUM E) Sum of terms comprising an element of state transition matrix TERM E) Term of sum of series for an element of the state transition matrix TIME E) Duration of sampling Interval In hours. J E) Loop counter TOL I) DGEAR parameter TTERM E) Intermediate calculated quantity comprising TERM 276 WK(312) (I) IMSL working space X (E) Intermediate calculated quantity XEND (I) DGEAR parameter to stop Integration (upper Integration limit) Y(I3) (I) DGEAR State variable counterpart to ESTX vector YPR1ME(13) (I) DGEAR state equations (E) EXPAQ Subroutine (I) INTEGRATION Subroutine All variables are stored In double precision unless otherwise noted NOTE: KNF028 performs as the estimator without the controller. To obtain the controller performance add the lines; FLOW “ ESTX(4) * ESTX(l) * ESTVOL / ESTX(5) / (SF - ESTX(2)) IF (FLOW.GT.FLOMAX) FLOW - FLOHAX IF (FLOW.LT.O.) FLOW ■= 0. In the same location as the controller In SUPERV8 277 * TYPE KNF02B.FDR SUSmUTIfE KNLAST(SKO,m,SS,SV,SFL,SDO) IMPLICIT REflL«8 (A-H.IM) REn.<4 SRCO, ^,ss,sv,SFL, SDO,SACCN, am ) IBL*B IDMTX(13,13),H(6,13) DIIENSION A(13,13),G(13,13) DDENSION BETU55(&,S),GETHSB(13,13),ESTP(13,13),F(13,13), ia)M(13,6),H(6),PHI(13,13), a>HIP(13,13),PR0JX(13),PM)JP(13,13),0(13,13),R(6,6), 3TE»61(S),TEfDI55(S,S),TERN5a(S,13),TER@l(13),TE)8(8S(13,S), 4TERM8B(13,13),K((451),Z(6) coMm/imm/ESTP,BAm,pmp,PRi)jx,o,R COim^/SOiAS/RCCN, ESTVOL, FUKi, SF, ESn ( 13) 38 FDR)»T(6E12.5) 40 F0RWT(3E12.5) 180 FOR)@T (7E14.B) 110 FDimT (7E11.4) 140 FOIMAfT (5F10.4) 150 FDRt«T (2D16.6) 160 FORMAT (13)10.4) 170 FCmAT (5D12.5) 180 FORMAT (IS) 181 F O m T (18X,IS) C «fw C INITIALIZE IDENTITY MATRIX C ggggg*gH g|g| H lgggglgg»lggg|gg» H l g | ggggglggggggggg DO 899 1=1,13 DO 899 J=l,23 IDMTX(I,J) = 0.0 899 CONTINUE DO 898 1= 1,13 IDMTX(I,I) = 1.0 898 CONTINUE C gggggggg«iiigiiiiggggg|gggggggggg|ggggggggggggggggggg c nmnnnniimnwmmimimiimmiin m ii 278 C INITIALIZE: CONTER, LSUBST, AND C C VARIABLES FOR C C C H 0 (GLUCOSE) OJBSTRATE AND C 6 12 6 C C C H 0 N BIOKGS C 1.8677 0.5016 0.177 C DELT = 1./6. ZT = 6.0 ZU = 12.0 ZV = 6.0 ZU = 1.0 ZX = 1.8677 ZV = 0.5018 ZZ = 0.177 KWBIOM - 24.4014 KWGLUC = 180.1589 NKK = 2.0 * 15.99994 MWC02 = n«2 •» 12.0111 DKl = .0 DK2 « .0 DK3 = .0 m = .0 DKS = .0 m = .0 DK7 " .0 DK8 = .0 C ESTABLISH PKUPO C ESTWLISH Q(),R() C K H n n m i n iiiniggHi«m » ggiinminniinngn IF (ACCN. )£. 0.0) KTO 800 PR0JP(1,1) = .80144 PR0JP(2,2) = .25 PROJP (3,3) = M000065 PR0JP(4,4) = .00M028 PROJP(5,5) = .0025 PROJP (6,6) = 150. PROJP(7,7) = .16 PROJP (8.8) = .%%16 279 PROJP (9,9) > 0.0M01 PR0JP(ie,19) = .01 PROJPJll.Jl) = 0.3 PR0JP(12,12) a 0. PROJP(13,13) » 0. R(l,l) = (12. * PROJX(l) * PROJX(4)) « 1 (12. * PROJX(l) « PROJX(4)) R(2,2) a (3. « PROJX(6) * (PM)JX(8) - PM)JX(3))) # 1 (3. • PROJX(6) « (PROJX(B) - PROJX(3))) R(3,3) a (.1 * PROJX(3)) < (.1 • PROJX(3)) R(4,4) a (.25 * PROJX(5)) ♦ (.25 * PROJX(5)) R(5,5) = (1.3 • PROJX(7)) • (1.3 < PROJX(7)) R(6,6) = .25 AACC a 0. WRITE(10,150)AACC,FLOW WRITE(10,160)(PROJX(I),1=1,13) WRITE (10,170) (Z(I),1=1,5) DO 1779 I = 1,13 WRITE(10,160) ((PRDJPd, J)),J=1,13) 1779 (mriNiE DO 1778 1 = 1,13 URITE(10,160)(Q(I,J),J=1,13) 1778 COMTIW£ DO 1777 I a 1,5 WRITE (10,170) (R(I,J),J=1,5) 1777 (mriNlE DO 1794 1=1,13 WRITE ( 10,170) (mm(I,J),J=l,5) 1794 CONTIMJE C EQUATE ESTATES WITH PROJECTIONS C w t w » m » i i m H - i i i m an im n H n » iiH » m i m i i i D O B M I a 1,13 ESTX(I) = PROJX(I) DO 800 J a 1,13 ESTP(I,J) a PROJP(I,J) 800 CONTINUE C READ EXPERIMENTAL DATA C CARBON DIOXIDE BE)£RATION f»TE C OXYKN UTILIZATION RATE C SUBSTRATE CONCENTRATION C VtLUC C FEED FLOW RATE C SUBSTRATE CONCENTRATION IN FEED C KCESS FLAG 280 C «iiiiiii n i n iiiiin i i n n w im iiH in i iH m m tiH * C CONVERT INPUT ¥ m REK.M TO REOL«B ICO = IBLE(SRCO) RO = DBLE(SRO) S = m E ISS) V = DBLE(SV) FL = DBLEISFL) 0 = DKE(SDO) C i m » m m m m i*Hn»«»iiniiiinminimnin C CALCULATE OBSERVED/ÆASURED VARIABLES C im iHu m winHummumnnHim tHiHum H C CALOIATE OVERALL STOICHIOMETRIC COEFFICIENTS IF (RCO.LE.1.0D-10) RCO = l.K)-10 IF (RD.LE.1.00-10) RO = 1.00-10 IF (S.LE. 1.00-10) S = 1.00-10 IF 10.LE.1.00-10) 0 = 1.00-10 IF (ACCN. EQ. 0.0) a.UOLO = S ELIMW = S 6LURAT = ESTVOL* (a.mJ)-QJMW) /miBLUC/DELT 1 + FLOW * SF / m e u x IF (ACCN.lt. 01.0) H.URAT1 = O-URAT IF (ACCN.LT.61.0) &URAT2 = GLURAT IF IACCN.LT.21.0) aURAT3 = aURAT IF (ACCN. EQ. 0.0) aURAT4 - aURAT IF (ACCN. ED. 0.0) aURATS = aURAT IF (ACCN. EQ. 0.0) aURATB = GLURAT auR = lamAT + auuATi ♦ auRATE + a m T s + auRAT» 1 * aURATS * GLURAT6) / 7. RATIO = aUR/RCO IF (RATIO.FE.0.0) TIEN IF (ZT.EQ.(1.0/RAT1O)) THEN ZAP = 100.0 GOTO 1795 ENDIF ENDIF IF (RATI0.lt. 0.16666667) TIEN ZAP = m . e RATIO = 0.16666667 GOTO 1795 ENDIF Z W = ZW / (ZT - 1.0/RATIO) 281 1795 ZBP * 0.5 * (ZAP # (-ZV + ZU/2.0 ♦ 2.0»ZT) - 0.5*ZX 1 - 2.5*ZZ + ZY - 2.0»ZH) ZCP = ZZ ZDP = 0.5*(ZW « ZU - ZX - ZZ) ZEP = ZAP « ZT - ZW YCP = MWBIOM / (ZEP * MWCD2) YS» = MWBIOM / (ZW « RmiC) YOP = MWBKBI / (ZW • MtfflS) GLUOLD = an e w auRAie = auRATs aURATS = aURAT4 aURATA = aURAT3 aURAT3 = aUWTB aURATB = aURATl aURATl = aURAT WRITE (6,110) ZAP, ZBP, ZDP, ZEP, RATIO, aURAT, aUR C CALCULATE PRODUCTHW/UTILIZATION RATES C BliWHHItHU m i H H I i W I H H I i m H m H H IIH W m Z(l) = RCO » MXZ * YCP / ESTVa Z(2) = ZBP/ZEP * RCO * MW02 / ESTVa Z(3) = 0 Z(4) = YSP Z(5) = YOP Z(6) = S DO 557 I = 1,6 IF(Z(I).LT.1.0D-10) Z(I) a 1.0D-10 557 CONTINUE C i n n H » HHi«iii n n i m n iiiiiin»i i n » i w m » H » n C n i i i n n n n * m F (3,7) = ESTX(J)*£STIW/(ESTX<7)*ESTX<7)) F(3,8) = ESTX(6) FIA,9) = 1.% F (5,10) a .1 F(6,ll) = %. F (7,12) = .0 F (8,13) = .0 C CALCIIATE STATE TRANSITION MATRIX C «nntHim tHWHiiinim m im itw nm w w tw N = 13 T = DELT CfU EXPAQ (F, PHI, T) C CALCULATE PROJECTED X AND P K)TRICES CALL INTEGRATIW(PmiX,mT) DO 558 I = 1,8 IF (PROJX (D.LT.l.eD-lO) PWJXd) = 1.0D-10 558 CONTIMÆ C wwwHintw HtiiiiiiiummiummiitH im C PROJPO = PHI()«ESTP()*PHI() + QO CALL VMJLFF(PHI,ESTP, 13,13,13,13,13,TEM88,13,1ER) CALL V»JLFP(TERMB8,PHI, 13,13,13,13,13,BETU88,13,1ER) 0(3,3) = DK3 * ((Z(3)-ESTX(3))«(Z(3)-£STX(3)) - ESTP(3,3)«ESTX(3>* 1ESTX(3) - R(3,3)) 0(4,4) = DK4 * ((Z(1)-ESTX(1)»ESTX(4))*(Z(1)-ESTX(1)«ESTX(4)) - 1(ESTP(4,4)*ESTX(1)«ESTX(1) ♦ 2.0*ESTP(1,4)«ESTX(1)«ESTX(4) + 2ESTP(1,1)«ESTX(4)«ESTX(4)) - R(1,D) 0(5,5) = DK5 * ((Z(4)-ESTX(5))*(Z(4)-ESTX(5)) - ESTP(5,5)«ESTX(5)» 1ESTX(5) - R(4,4)) 0(6,6) = m # ( (Z (2) -ESTX (6) * (ESTX (8)-ESTX (3) ) ) * 1 ( Z (2) -ESTX (6) * (ESTX (8) -ESTX (3) ) ) - (ESTP(6,6)*(ESTX(B)-€STX(3))« 2(ESTX(B)-£STX(3)) + 2.0»ESTP(6,3)«£STX(6)*(ESTX(B)-ESTX(3» + 3ESTP(3,3)«ESTX(6)«ESTX(6)) - R(2,2)) 0(7,7) = DR7 • ((Z(5)-ESTX(7))*(Z(5)-ESTX(7)) - ESTP(7,7)«£STX(7)* 1ESTX(7) - R(5,5)) 283 DO 997 1 = 1,13 DO 997 J* 1,13 IF (D(l,J).LT.e.e> O(I,J)=0.0 997 C0NT1NÆ DO 799 1=1,13 DO 799 J=l,13 PROJP(I,J) > KTU8B C » m iim tH fw iitn » H « iin n *» n » H H tttnHm C CALCULATE H AND R PRICES HID = PROJXIl) « PROJX(4) HIS) = PROJX16) » IPR0JXI8) - PROJX13)) HI3) = PROJX13) HI4) = PROJX15) HIS) = PROJX17) HI6) = PROJXIS) Hll,l) = PROJX14) 1111,4) = PROJXIl) H(S,3) = -PROJX16) MIS,6) = PROJXIB) - PROJX13) MIS, 8) = PH)JXI6) MI3,3) = 1. MI4,5) = 1. MI5,7) = 1. MI6,S) = 1. C «m H «m ii m i n i m i n in im i n m t i n i i i i iiiii* C CALCULATE KALMAN GAIN MATRIX C GAIW = PROJPI) « TRKGIMD) « INVI MI)*PROJPI)*TMNSIMI))+RI) ) C «iii»n m »g» tm » a )mn H tw»tw w w » DO 798 1=1,13 DO 793 J=l,13 IF IPROJPII,J).œ.0) GOTO 791 79S CONTINUE GOTO 786 791 DO 7% 1=1,13 DO 790 J=l,13 IFIHII,J).)£.6) GOTO 789 790 CONTIiaiE 786 DO 787 1=1,13 DO 787 J=l,6 GAMII,J) = 0.0 787 DMIiaJE 284 GtïïD 785 789 CALL V»JLFF(N,PR0JP,6,13,13,6,13,TEI9e6,6,lER) CALL VMULFP (TER^ M, 6,13,6,6,6, TER^, 6,1ER) DO 793 1=1,6 DO 793 J=l,6 KTW55II,J) = 7ERM55(I,J) ♦ R(1,J) 793 CONTINUE CMl L1NV8: (BETia, 6,6, TERM55,6, W, 1ER) CALL \mfP (PKUP, M, 13,13,6,13,6, TERmS, 13,1ER) CMl VNULFF (TERN85, TERM55,13,6,6,13,6, KIW, 13,1ER) C CALCULATE ESTIMATED X «0 P IMTRICES C ESTXO = PROJX0 ♦ G A m O * ( ZO - HO ) C «i m u m ititu m i m u m i i im iw w H K W HHW tf 785 CONTIIAE DO 784 1=1,6 TERM5K1) » Z(I) - HO) 784 CONTIME AACC = ACCN / 120. + 1./6. AKC = AKC - e.S«(lNT(AACC«2.8)) IF(ABCC.LT.1.0D-05) GOTO 1001 WR1TE(13,30)AACC, 0EIN510), 1=1,5) UR1TE(13,30)AACC,IH(1),1=1,5) WRITEO3,30)M(1,1),M(1,4),M(2,3),M(2,6),MI2,8),AACC URlTE(13,40)»CC,mCC,AACC 1001 CWTINUE CAU. VMULFF (GAINK, TERM51,13,6,1,13,6, TERMBl, 13,1ER) DO 7% 1 = 1,13 ESTXO) = PROJXO) * TERMBl0) 796 CONTINUE DO 559 1 » 1,8 IF(ESTX(D.LT. 1.00-10) ESTXO) = 1.0D-10 559 CfNTlNUE 285 C im w m imimmumnHHHnimm i m m » »»»» C ESTPO = C * BAIW()*R()*TRMG(GAm()) (Ml VHJLFF IBflim, M, 13,6,13,13,6, TERMBB, 13,1ER) DO 795 I = 1,13 DO 795 J = 1,13 K7HB8(1,J) = IDHTX(I,J) - TERB88(I,J) 795 (WriNÆ (Ml VHJLFF (BETUB8, PROJP, 13,13,13,13,13,7EIB4BB, 13,1ER) (Ml VHULFP (TERM88, K7W88,13,13,13,13,13, ESTP, 13,1ER) (Ml VaJLFF (BftM, R, 13,5,6,13,6, TEfM85,13,1ER) (Ml VSULFP(TERS85,6flINK, 13,6,13,13,13, TE1M8,13,1ER) 00 775 1 = 1,13 DO 775 J » 1,13 ES7P(1,J) = ESTP(I,J) ♦ 7ERMB8(I,J) 775 (ÆNTINUE C m H H H IIIH i m t H itHH U M U itW l Ilim i H U HI tt c WRITE DATA INTO FOR010.DAT AACC = A(»J / 120. + 1./6. ABCC = AæC - 0.5i(INT((¥£C«2.0)) IF(ABCC.LT.1.0D-05) GOTO 794 776 UR1TE(10,150)AACC,FUW WRITE(11,160)(PROJX(I),1=1,13) WRITE(10,160)(ESTX(I),I=1,13) WRITE(10,170)(Z(I),1=1,5) DO 779 I = 1,13 WRITE (10,160) ( (ESTP (I, J) ), J=l, 13) 779 CONTIAIE DO 778 I = 1,13 WRITE(ie,160)(Q(I,J),J=l,13) 778 CtWTINUE DO 777 I » 1,5 WRITE (10,170) (R(I,J),J=1,5) 777 CONTINÆ DO 794 1=1,13 tmiTE(10,170) (GAIM((I,J), J=l,5) 794 CONTIWE RETURN END 286 ]PRINrrCHWPR#0TYPE SWERVB.FOR PROGRfM SUPERV C wim nHin m w »miimi»«Hmii»Httwim ttnnminnnmt c C HIBH-DENSITY, FEIhBflTCH FERMENTftTlOT SUPERVISOR CtWTROL PROBRfffl C C VESRIQN 1.0 C C C BY C STEVEN M. S C M J a O C C CtPVRIKfT 1986 C ALL RIGHTS RESERVED [ IMPLICIT REAL»B (R-H,0-Z) CHARACTERiB FF,GG CHfiRACTER*20 STRING REAL<4 SACK, SEQUST, SDO, SDCO, SO, SCO, SAIN, KOUT, SACID, SBASE, lSESTX,æST,SSS,SM:iDP REAL'S IDMTX<13,13),H(6,13) DIIENSION A(13,131,6(13,13) DIIENSION BETU55(6,6),BETNBB(13,13),ESTP(13,13),F(13,13), 1GA1NK(13,6),H(6),PHI(13,13), 2PHIP(13,13),PROJX(13),PROJPI13,13),QI13,13),R(6,6), 3TERK51 (6), TEIBCS (6,6), TEKBB (6,13), TERMBl 113), TERMB5 (13,6), 4TERM88(13,13),W((461),Z(6) CIKMON/KAUWN/ESTP, GAINK, PROJP, PROJX, Q, R COWlON/SCHJfi/ACCN, ESTVOL, FLW, SF, ESTX (13) 30 FORMAT(6E12.5) 40 FDRW)T(æi2.5) 100 FORMAT (7E14.B) 110 FORMAT (7E11.4) 287 140 FOttfWT (5F10.4) 150 FORMAT (2D16.6) 160 FORMAT (13D10.4) 170 FORMAT (5D12.5) 160 FOmAT (15) 181 FORMAT (10X,I5) 190 FORMAT (5D10.4,I1) 200 FORMAT (6D10.4) 210 FORMAT (A) 220 FORMAT (A,E10.4) 230 FORMAT (A,II) 240 FORMAT (9D12.6) 290 FOIWAT (E15.9) 291 FORMAT (14) C C ««» » «»« nm i III ii i n i n in»n »m »« H » i » »»« w C INIT1W.1ZE IDENTITY WTRIX C iiiiiiim iiit i m i m m u Him i i i i u m t i i i n n H iW DO B99 1=1,13 DO B99 J=l,13 ID«TX(I,J) =0.0 899 CONTIWE DO B9B 1= 1,13 IDKTX(I,I) = 1.0 B9B CWÎINUE C IIIIIIIIIIH H IIIIIIIIIIIIIIIIim i llMIIIIIIIIIIIII* c INITIALIZE: COUNTER, LSUBST, AND C C VARIABLES FOR C C C H 0 (GLUCOSE) SUBSTRATE MS) C 6 12 6 C C C H 0 N BIOMASS C 1.B677 0.501B 0.177 C C w m m m i n i i n u iitin Hiiim n im u m iiiiiH -HHi DELT = 1./6. ZT = 6.0 ZU = 12.0 ZV = 6.0 ZW = 1.0 ZX = 1.B677 ZY = 0.5018 ZZ = 0.177 288 K4BI0M = 24.4014 MW5LUC = 180.1389 fW02 = 2.0 » 15.99994 MWC02 = M B + 12.0111 SflCK = 9999 STRIIŒ = 'xnmmntmnnv DKl = 0 DK2 = 0 DK3 = 0 DK4 = 0 DK5 = 0 DK6 = 0 DK7 = 0 DKB = 0 C ESTABLISH ESTXO,ESTPO C ESTABLISH DO,R() C OPEN (UNIT=13, F1LE=’ SWER. DAT’, STATUS=’ HD ’ ) READ03,190)(£CN,SF,FLDU,ESTVOL, RD £ 0 , n m G READ (13,160)FLOMAX,FL(yLG, VESPRE, HUCOS, HUTIM, GLUÆW, 1 GLUOLD, GLURATl, GLURAT2, HURAT3, GLUI»T4, GLURAT5, GLURAT6 READ(13,160) (ESTXO),1=1,13) DO 801 1=1,13 READ (13,160) (ESTPO, J),J=1,13) 801 CONTINUE !EAD(13,2%)(R0,1),1=1,6) CLOSE (UNIT=13,STATUS=’KEEP’) IF (ACCN. Æ. 6.0) GOTO 800 AACC = 0. CALL TI)E(FF) CALL DATE(GG) RTŒ0 = 24.»(10.*(ICHAR(GG(l;l))-48) + ICHAR(GG(2:2))-48) 1 + 10.»OCHAR(FF(l;l))-48) + lCHAR(FF(2:2))-48 2 + (10.*OCmR(FF(4:4))-48) + lCHAR(FF(5:5))-48)/60. IF (RTÆ0.LT.450) RTME0 = RTME0 ♦ 24. «31. OPEN (UN1T=10, FILE=’ WT_VAX. DAT’, ACCESS=’ WPEND’, STATUS=’ OLD’ ) WRITE(10,150)AACC,FLOW WRITE (10,160) (ESTXO), 1=1,13) WRITE (10,170) (20), 1=1,5) DO 1779 1 = 1,13 WRITE (10,160) ( (ESTPO, J)),J=1,13) 1779 CONTIffiÆ 289 DO 1778 I « 1,13 WRITE (10,160) (Q(I,J),J=1,13) 1778 (XJNTINÆ DO 1777 I = 1,5 WRITE(10,170)(R(I,J),J*1,5) 1777 CONTINUE DO 1794 1=1,13 WRITE (10,170) (BfllWd, J), J=l,5) 1794 CtWTIME CLOSE (l»IIT=10,STfmJS=’KEEP’) 800 CONTINUE C c coMmiiCATim with ddc C WRITE(6,220) STRING, FLOW OPEN (IWIT=15, FILE=’ OPT.ftPL. DAT', fiCCESS=’ WPEND', STATUS=’ OLD’ ) READ(5,«) SDO WRITE(15,2%) SDO READ (5,*) SKO WRITE(15,298) SDCO READ(5,*) SO WRITE(15,290) K) READ (5,*) SCO WRITE(15,290) SCO READ(5,*) SAIN WRITE(15,290) S)IN R£ffl)(5,*) SAOUT WR1TE(15,290) SAOUT READ(5,*) SACID WRITE(15,290) SACID feD(S,«) SSS WRITE(15,298) SSS S = DBLE(SSS) 0 = DBLE(SDO) WRITE (6,220) STRING, SICK 9998 READ (5,1) SQUST WRITE(15,290) SEQUST IF (SEQIÊT.EQ.9999) CLOSE (UNIT=15,STATUS»’KEEP’) IF (SEQtm.ED.9999) GOTO 9999 IF (SEQUST. EQ.0.) TÆN WRITE(6,230) STRING, MODFLB REM) (5,*) MODFLG WRITE(15,291) WDDFLB ELSE IF (SEQUST. EQ.l.) T)£N DO 9997 I = 1,8 SESTX = ESTX(I) WRITE(6,220) STRIW, SESTX 9997 (3NTIMJE SESTX «= ESTVOL WRITE(6,220) STRING, SESTX SESTX = SF WRITE (6,220) STRiœ, æSTX SESTX = FL m X WRITE(6,220) STRirS, SESTX SESTX = VESPRE WRITE(6,220) STRING, SESTX R£M)(5,«) SESTX WRITE(15,290) SESTX READ (5,*) SEST WRITE(15,2%) SEST IF ( (SESTX.LT.9.).MO). (SESTX.ST.0.)) THEN ESTX (SESTX) = DBLE(KST) ELSE IF (SESTX. EQ. 9.) THEN ESTVOL = DH^(SEST) ELSE IF (SESTX.EQ. 10.)TKEN SF = mE(SEST) ELSE IF (SESTX.EQ.il.) DCN FLOMAX = DBLE(æST) ELSE IF (æSTX.EQ.12.) T)£N VESPRE = DBLE(SEST) ELK (mriwE ENDIF ELSE IF (SEQUST. EQ. 2.) T)tN READ(5,*) SESTX WRITE(15,290) SESTX ESTVOL = ESTVO. + DBLE(SESTX) ELSE IF (SEQUST.EQ. 3.) THEN SESTX = FUffLG WRITE(6,220) STRING, SESTX SESTX = FLOW WRITE(6,220) STRING, SESTX READ (5,*) SESTX WRITE(15,290) SESTX FLOFLG = SESTX IF (FLDFLG.EQ.1.) TÆN 291 R£AD<5,«) SESTX WRITE (15,2%) SESTX FLOW = SESTX ENDIF ELSE IF (SECXBT.EQ.4.) THEN READ(S,«) SESTX WRITE(15,290) SESTX SLUCOS = DM(æSTX) REfiD(5,*) KSTX WRITE (1 5 ,2 % ) SESTX a.UTIB = DKE(æSTX) ELSE CONTIMÆ END IF GOTO 9998 C «H I l W IBiH H U H H H U m i l H m U H H H K IH U HHIt H W C CALCULATE OBSRVED/IEASURED VARIABLES C w iH H H H H H H m n m i m iii n Bn m Bt n m i i n i t 9999 SACIDP = SCID - SACIDP ra = (SlIN * 0.209 - SWÏÏ * SO) / 22.414 RCO = SAIN ♦ (SCO - 0.000450) / 22.414 ESTVOL = ESTVtL + KLT • FLOW + SACIDP SACIDP = SACID IF (FLOFLS.f£.l.) FL(W = ESTX(1)*ESTX(4) IF (RCO.LE.1.0D-10) œ O = 1.0D-10 IF (RO.LE.1.0D-10) RO = 1.0D-10 IF (S.LE.1.0D-10) S = 1.0D-10 IF (O.LE.1.0D-10) 0 = 1.0D-10 IF (ACCN.ED.0.0) GLUOLD = 5 292 GLl»£H = S B .u m = ESTVOL*(GLUOLD-GUJNEW)/ma.UC/DQ.T 1 + FLOH » SF / HUGLUC IF (ACCN.LT.81.0) GLURATl = GLURAT IF I ACCN.LT.61.0) GLURAT2 - GLURAT IF (ACCN. LT. 21.0) GLURAT3 = a.lRAT IF (ACCN.EQ.0.0) GLURAT4 = GLURAT IF (ACCN. EQ. 0.0) GLUIWT5 = GLURAT IF (ACCN. EQ. 0.0) QJJRAT6 = GLURAT GLUR = (H.URAT + GL1BÎAT1 + H.IWAT2 + BLUIWT3 + Q.URAT4 1 + GLURAT5 ♦ GLURAT6) / 7. IF (GLUR.GT.25.) FLOW = 0. RATIO = R.UR/RCO IF (RATIO.Æ.0.0) THEN IF (2T.EQ. (1.0/RATIO)) THEN ZAP = 1K.0 GOTO 1795 ENDIF ENDIF IF (RATIO.LT.0.16666667) THEN ZAP = 1%.0 RATIO - 0.16666667 HITO 17% ENDIF ZAP = ZW / (ZT - 1.0/RATIO) 1795 ZBP = 0.5 » (ZAP * (-ZV + ZU/2.0 + 2.0*ZT) - 0.5»2I 1 - 2.5*ZZ + ZY - 2.0*ZW) ZCP = ZZ ZDP = 0.5* (ZAP « ZU - ZX - ZZ) ZEP = ZAP * ZT - ZW YCP = AIBION / (ZEP * MWC02) Y%» = NWBICm / (ZAP * )%«JJC) YOP = AIBKM / (ZBP * MWÜ2) GLUOLD = GUREW B.URAT6 = a_URAT5 GLURAT5 = GLURAT4 &.URAT4 = R.URAT3 GLURAT3 = GLURAT2 GLURAT2 = GLURATl GLURATl = H.URAT 293 C C CALCllATE PimJCTIQN/UTILIZATION RATES C WWWWtWjHHHHtWWK» w m HIHHt Z(l) = RCO * B C œ« YCP / ESTVOL Z(2) = ZBP/ZEP * RCO * m02 / ESTVOL Z<3) = 0 Z(4) = Z(5) = YOP Z(6) = 5 DO 557 I = 1,6 IF(Z(1).LT.1.M)-10) Ztl) = l.ro-10 557 CONTINUE C C «ii i i m m i i n a im n n n m w im H W H H i n n H H C CM.CULATE F AND PHI MATRICES F(l,l) = ESTX(4) - FLDH/ESTVDL F(l,4) = ESTX(l) F (2,1) = -ESTX (4)/ESTX 15) F (2,2) = -FLOM/ESTVOL F(2,4) = -ESTX(1)/ESTX(5) F(2,5) = ESTX(1)*ESTX(4)/(ESTX(5)*ESTX(5)) F(3,l) = -ESTX(4)/ESTX(7) F(3,3) = -ESTX(6) - FLOW/ESTVOL F (3,4) = -ESTX (1)/ESTX (7) F(3,6) = ESTX(8) - ESTXO) F(3,7) = ESTX(1)«ESTX(4)/(ESTX(7)#ESTX(7)) F (3,8) = ESTX (6) F (4,9) = 1.00 F (5,10) * 1. F(B,11) = 30. F (7,12) = .0 F (8,13) = .0 C « i i n n iiaim in t i m i m ii»tm m m HHn m m iH C CALCULATE STATE TRANSITION MATRIX C N = 13 T = DELT CALL EXPAQ(F,PHI,T) c CALCUATE PROJECTED X m P «ATRICES CALL INTEGRATION (PROJX, m.T) DO 558 I = 1,8 IF (PROJX (1).LT.1.0D-10) PROJX (I) = l.#-10 558 C m i % E C PROJPO = PHI()*ESTP()»PHI() + QO CALL \MJLFF(mi,ESTP, 13,13,13,13,13,TERN88,13,1ER) Cmi VmJLFP (TEI@488, PHI, 13,13,13,13,13, KTW88,13,1ER) Q(3,3) = DK3 * ((Z(3)HESTX(3))»(Z(3)-ESTX(3)) - ESTP(3,3)*ESTX(3)* 1ESTX(3) - R(3,3)) 0(4,4) = DK4 « ((2(1)-ESTX(1)*ESTX(4))«(Z(1)-£STX(1)*£STX(4)) - 1(ESTP(4,4)»ESTX(1)«ESTX(1) ♦ 2.0*ESTP(1,4)«ESTX(1)*ESTX(4) ♦ 2ESTP(1,1)»ESTX(4)*ESTX(4)) - R(1,D) 0(5,5) = DK5 « ((Z(4)-EBTX(5))*(Z(4)-ESTX(5)) - ESTP(5,5)«ESTX(5)» 1ESTX(5) - R(4,4)) 0(6,8) = m * ((Z(2)-ESTX(6)«(ESTX(8)-ESTX(3)))« H Z (2)-ESTX(6)«(ESTX(8)-ESTX(3))) - (ESTP(6,6)«(ESTX(8)-ESTX(3))« 2(ESTX(8)-ESTX(3)) ♦ 2.0«ESTP(6,3)«ESTX(6)*(ESTX(8)-ESTX(3)) ♦ 3ESP (3,3) «ESTX (6) «ESTX (6)) - R(2,2)) 0(7,7) = 0K7 « ((Z(5)-£STX(7))«(Z(5)-ESTX(7)) - ESTP(7,7)«ESTX(7)« 1ESTX(7) - R(5,5)) DO 997 I = 1,13 DO 997 J= 1,13 IF (D(I,J).LT.0.0) Q(I,J)=0.0 997 CONTINÆ DO 799 1=1,13 DO 799 J=l,13 PROJP(I,J) = BETW88(1,J) * 0(1,J) 799 CmfTIMJE C «II#Ili«iiiiii«««*«i«««««****«*«**«iiiiii«««ii«««*«* C CALCULATE H M ) M KITRICES C ««l«»««flWH«*««««««6«««««H »t«t«t«»»WHHHHHHHIt«««« HO) = PROJXO) « PROJX(4) H(2) = PROJX(8) < (PROJX(8) - PROJXO)) H (3) = PROJXO) H(4) = PROJX(5) H(5) = PROJX(7) H(6) = PROJX(2) 295 «(1,1) = PROJX(4) «(1,4) = PROJX(l) «(2,3) = -PROJX(6) «(£,6) = PROJX(8) - PROJXO) «(2,8)= PROJX (6) «(3,3) = 1. «(4,5) = 1. «(5,7) = 1. «(6,2) = 1. C CPLCUUITE KflUfflN GAIN MATRIX C GAINK = PROJPO # TRANS(NO) « INV( M()«PROJP()«TI»NS(H())+R() ) C iimiiinmim»n m n iiiiHii m n m »HinB»» DO 792 1=1,13 DO 792 J=l,13 IF (PROJP(I,J).Æ.0) GOTO 791 792 CONTINUE HTTO 786 791 DO 790 1=1,13 DO 790 J=l,13 IF(M(I,J).fE.0) GOTO 789 790 CONTIfaJE 786 DO 787 1=1,13 DO 787 J=l,6 GAM(1,J) = 0.0 787 CONTINUE GOTO 785 789 CAd VMULFF(M,PmiP,6,13,13,6,13,TERM58,6,IER) CAU VMULFP(TERM58, M, 6,13,6,6,6, TERMS5,6,1ER) DO 793 1=1,6 DO 793 J=l,6 BÊTH®(I,J) = TERS55(I,J) ♦ R(1,J) 793 CONTIfU CAd LINV2F (BETW55,6,6, TERM55,6, W, 1ER) ( m VMULFP(PROJP,M, 13,13,6,13,6,TEI«85,13,1ER) CAd V«UUF(TERM85,TERHæ, 13,6,6,13,6,GAINK, 13,1ER) C CALCOATE ESTDfflTED X AND P MATRICES C ESTXO = PROJXO + GAOKO f ( ZO - HO ) C 785 CONTINS DO 784 1=1,6 TEfMSKI) = Z(I) - H») 784 CONTINUE 296 CALL VmJLFF (GAm, TERM51,13,6,1,13,6, TERMBl, 13,1ER) DO 7% I = 1,13 ESTX(I) = PROJX (I) * TEIMKI) 7 % CONTINl£ DO 559 I = 1,8 1F(ESTX(I).LT.1.0D-18) ESTX(l) = l.CD-10 559 CONTINUE IF (ESTX(4).GT.0.1) ESTX(4) = 0.1 C «m m Hu m i m m i i m m u m n i iiiiH H m iiH » c ESTPO = (i-mmo#MO)#pROJPo*TRws(i-mmo*MO) C * GAmO*RO*TIWIS(GAINKO) CALL \MJIFF (GAINK, M, 13,6,13,13,6, TERN88,13,1ER) DO 795 I = 1,13 DO 795 J = 1,13 BETW88(I,J) = IDHTX(I,J) - TEIM88(I,J) 795 CONTIWE CALL VHLFF(BETH88, PROJP, 13,13,13,13,13,TER4BB, 13,1ER) CALL VMULfP(TEm88,BETW88,13,13,13,13,13, ESTP, 13,1ER) CALL VNdFF (GAIW, R, 13,6,6,13,6, TERMB5,13,1ER) CALL VI%LFP(TERM85,mm, 13,6,13,13,13,TERM88,13,1ER) DO 775 I = 1,13 DO 775 J = 1,13 ESTP(I,J) - ESTP(I,J) + TERM88(I,J) 775 CJmiNl£ C ««wwm inm iHHtinmmiim m i inninin C WRITE DATA INTO F0R018.DAT C nm n n m i m tm t-n m m m HHUHiiinnimum OPEN (IW1T=13, FILE=’ RPER. DAT', STATUS*’ OJ)’ ) CLOSE (UNIT=13,STATIB*’DELETE’) ACCN = ACCN + 20. OPEN (IWIT=13,FILE*’SUPER.DAT’,STATUS*’)®)’) WRITE (13,190) ACCN, SF,FLOW, ESTVOL, RT)C0, MODFLG WRITE ( 13,160) FLOMAX, FLOFLG, VESPRE, aUCOS, GLUTIM, B.UNEU, 1 GLUdD, dURATl, Q.URAT2, GLURAT3, B.URAT4, S.URAT5, GLURAT6 WRITE(13,160)(ESTX(I),I*1,13) DO 810 1=1,13 WRITE (13,160) (ESTPd, J), J=l, 13) 810 CWTINUE WRITE (13,200) (R(1,I),1=1,6) CLOSE (UNIT=13,STATUS*’KEEP’) 297 flflCC * flCCN / 12». ♦ 1./6. ABCC = AACC - e.5t(INT(flflCC*2.»)) CWl TlfE(FF) CALL DATE(66) RIME = 24.«(ie.*(ICHAR(68(lil»-4B) + ICHAR(GG(2:2))-48) 1 ♦ 10.»(ICHAR(FF(l:l))-«) + ICWW(F(2i2))-48 2 ♦ (10.«(ICWffl(FF(A;4))-4a) + ICHAR(FF(5:5))-48)/60. RTœ = RTÆ - RTNE0 IF (RDE.LT.O.) RTffi = RTI€ + 31. *24. 776 OPEN (UNIT=10,FILE=’QPT_VAX.DAT’,ACCESS=’APPEND’,8TATUS='OLD’) WRITE (10,150) RDE, FLOW WRITE(10,160)(ESTX(I),I=1,13) WRITE(10,170)IZII),1=1,5) DO 779 1 = 1,13 WR1T£(10,160)((ESTP(I,J)),J=1,13) 779 CONTINUE 00 778 I = 1,13 WRITE (10,160) (Q(I,J),J=1,13) 778 CONTINUE DO 777 I = 1,5 WRITE(10,170) (R(I,J),J=1,S) 777 CONTINUE DO 794 1=1,13 WRITE ( 10,170) (B)m(I,J), J=l, 5) 794 CONTINS CLOSE (UNIT=10,STATUS»’KEEP’) SFL = (FLOW) GOTO BW END 298 SUBROinirE 1NTEGRATIDN(PRDJX,DELT) IMPLICIT REAL«B ((Hi,0-Z) C ttHH ii m « «iin n n n i i ain iiiH in i» »»H i n m n C INTEGRATION OF F(ESTXO) VECTOR C APPLYING KAR'S METHOD DIMENSION PM)JX(13),Yll3),I«m3),W(312) EXTERNAL FCN,FCNJ COmm/SCHAS/ACCN, ESTVOL, FLOW, SF, ESTX ( 13) N = 13 X = KCN/10.0 H = 0.0%01 DO 100 I = 1,13 Yd) = ESTX (I) 100 CONTIMJE XEND = ACCN/10.0 + DELT TO. = 0.00001 )ETH » 2 MITER = 1 INDEX = 1 1ER « 0 CMl DKAR(N, FCN, FCNJ, X, H, Y, XEND, TO., METH, MITER, 1INDEX,INK,HK,IER) DO 99 1=1,13 PROJXd) = Yd) 99 CONTIME RETURN END SUBROUTINE FCN(N,X,Y,YPRI)C) IWLICIT REALtfl (A-H,0-Z) C «nHigHmttiim m imnnmiminnmnnimt C REQUIRED SlffPORT SUBROUTME FOR DGEAR C immtwiiinmHiimiiiiimimHwmtmw DIMENSION Y(13),YPRIIC(13) CO)WON/SDLAS/ACCN, ESTVOL, FLOW, SF, ESTX d3) YPRIMEd) = Y(4)*Y(1) - FLOHYd)/ESTVOL YPRIME(2) = -Y(4)»Yd)/Y(5) + FLOW* (SF-Y (2))/ESTVOL YPRIMEI3) = -Y(4)*Y(1)/Y(7) ♦ Y(6)*(Y(B)-Y(3)) - lFLflW*Y(3)/ESTVa. YPRI)£(4) = 1.00 * YPRIRE(9) 299 YPRI«E(5) = .1 * YPRIŒ(10) YPRirSCB) = 30. * YPRllC(ll) YPRIffii?) =0.0 YPRIffi(B) = 0.0 YPfilHEO) = 0.0 YPRIIC(10) = 0.0 YPRlHE(ll) = 0.0 YPRIMEU2) = 0.0 YPHIŒ(13) = 0.0 RETURN END SUBROUTIffi FCNJ(N,X,Y,PD) IMPLICIT REflL«B DO 999 1=1,13 DO 999 3=1,13 PD(I,J) = 0.0 999 CtWTINUE PD(1,1) = YU) - FLDM/ESTVOL PD(1,4) = Yd) PD(2,1) = -YU)/Y15) PDI2.2) = -FLOH/ESTVOL PDI2,4) = -Yd)/Y(5) PD(2,5) = Yd)*YU) / (Y(5)*Y(5)) PD13,1) = -YU)/Y(7) M)(3,3) = -aOH/KTVOL - Y(6) M)I3,4) = -Yd)/Y(7) PDI3,6) = Y(fl) - Y(3) roi3,7) = Yd)*YU) / (Y17)«Y(7)) PD(3,6) = Y(6) PDU,9) = 1.00 PDI5.10) = .1 PD(5,11) =30. PD(7,12) = .0 PD(B,13) = .0 RETURN END 300 SUmOTIÆ EXPM) IR,B,B8> m i C I T KM.*16 (C-H,0-Z) REALfe A(13,13),B(13,13),B8 DIMENSION 0(13,13),0(13,13) C i i m m iiii i n ii i n i ii n i ii n iim i i i H U H W n w w tH n i i ii n C QUAD PRECISION SOLUTION TO EXP (A) WERE A IS 13X13 MATRIX OF C SPECIFIED STRUCTUIE C «HW H Wnn8g«HHHm gginn»«winiw 108 FOmAT (* EXP(F) DID NOT CONVERT FOR AN ELESNT') TI)C = (EXTD(BB) DO 709 1=1,13 DO 700 J=l,13 C(I,J) = (EXTD(A(I,J)) C(I,J) = TIIE » C(I,J) 700 CONTIWJE DO 701 1=1,13 DO 701 J=l,13 D(1,J) = 0.0 701 IWriNUE DO 702 1=1,3 D(I,I) = (£XP(C(I,I)) 702 CONTIWE DO 703 1=4,13 D(I,I) > 1.0 703 CONTIWJE DO 730 1=4,B D(I,I+5) = C(I,I*5) 730 CONTIWE DO 784 1=6,8 IF(C(3,3).EQ.0.0) T)£N D(3,I) = C(3,I) GOTO 704 ENDIF D(3,I> = C(3,IX((I£XP(C(3,3))-1.6)/C(3,3)) 704 CONTINUE DO 731 1=11,13 IF(C(3,3).EQ.0.0) T)€N 0(3,1) - C(I-5,I) * C(3,l-5)/2. GOTO 731 ENDIF 301 D(3,l) = C(]-5,l) » C«3,I-5) * 1 «t£XP(C<3,3))-l.e-C(3,3))/(C(3,3)«C(3,3))) 731 CONTINUE DO 705 1=1,2 IF(Ca,l).ElL0.0) TUN D(I,I+3) = C(I,I+3) GOTO 705 ENDIF D(I,I+3) = C(I,I*3)«((IEXP(C(l,l))-1.0)/Cn,I)) 705 CONTir«£ DO 732 1=1,2 IF(C(I,I).EQ.0.0) TTO D(l,l+B) = C(I+3,I+B) * C(l,1+31/2. GOTO 732 ENDIF Dn,I+B) = C(I+3,I+B) * Ctl,l+3) « 1 ((OEXP(C(I,I))-1.0-C(1,I»/(C(I,I)«C(I,I))) 732 CONTUSE DO 706 1=2,3 lF((C(l,l).EO.e.O).AND.(C(I,l).EQ.0.0)) TÆN D(I,1) = C(l,l) D(l,4) = C(l,4) + 0.5*C(I,1)«C«1,4) D(I,9) =C(4,9) * IF(KBS(C(1,1)).E.QABS(C(I,I))1 TIEN X = C(l,l) R = C(1,I)/C(1,1) ELSE X = C(I,I) R = C(1,1)/C(I,I) ENDIF SUM » (ffiXP(X)-l.)/X + R»(QEXP(X)-1.-X)/X TERM = IGEXP(X)-1.-X)/X TTERM » 1.0 RR = R DO 707 3=2, i m TJ = KTJMT(J) TTERM = TTEmX/TJ TERM = TERM - TTEBI RR = RR * R s s g s P X — « P | | s » X =0 X U Il H Il g 2 W 2 Il n N H O Ci Ci Ci Ci Ci Ci R ZZ ri îri r R m A s - -I-* •— ^ M - Il 11 B-L lif! w w « O Ci Ci S» i l o îî! 2 r r- il r t- R ~ O W w I R i H #1 = I IV O !V I CiI A i l o i «nI w N3o 303 DO 733 J=2,1M» TJ = QFLOflT(J) TTERM = TTEtBHX/TJ TERM = TERM - TTERM RR = RR • R SUM = SUM + RR * TERM ]F(WBS(RR*TEIM).LE.OœS(l.M)-04*SUM)) GOTO 734 733 CONTINÆ WRITE (6,100) 734 IF(C(l,l).EQ.0.e> TIEN D(I,9) = C(l,4)/2. ELSE D(I,9) = C(I,4) * IQEXPICI1,I»-1.-CII,1»/IC(1,I)*CI1,1)) ENDIF D(I,9) = C(4,9) • (Dll,9) + C(I,1)*C(1,4)*SUM) 706 CONTINLE DO 711 1=1,13 DO 711 J«l,13 B(I,J) ■ IffiLEQ(D(I,J)) 711 CONTINUE RETURN END APPENDIX C SIMULATION RESULTS 304 305 ACTVAL ESTUATED CO o o 0. 19 38. 57. 76. TIME (H) Figure 5. Standard Simulation Actual and Estimated Biomass Concentration. .j CO § ICJ § 0 N 8 CO 1 ACTUAL — coRsunro o 0. 19. 38. 57. 76. TIME (H) Figure 6. Standard Simulation Actual and Estimated Substrate Concentration. 306 oI ~ ACTUAL \ u CORRUPTED o 0 d g 8 o o 1 d s I s 9 o oI g? I 6 0. 19. 36. 57. 76. TIME (H) Figure 7. Standard Simulation Actual and Estimated Dissolved Oxygen Concentration. ACTUAL ESTIMATED 19 38. 57. 76. TIME (H) Figure 8. Standard Simulation Actual and Estimated Specific Growth Rate. 307 M N Ùi to uj œ -ESnUATED 19. 38. 57. 76. TIME (H) Figure 9. Standard Simulation Actual and Estimated Overall Substrate Yield. N O L f g: o H S >- 6 ACIUAI. GSmUTED M!. o 19. 38. 57. 76. TIME (H) Figure 10. Standard Simulation Actual and Estimated Oxygen Mass Transfer Coefficient. 308 Vî Is M o § I ACTOAL ESnUATED 19. 38. 57. 76. TIME (H) Figure 11. Standard Simulation Actual and Estimated Overall Oxygen Yield. AODAL ESTUIATED 38. TIME (H) Figure 12. Standard Simulation Actual and Estimated Saturated Dissolved Oxygen Conentratlon. 309 ESnUTQ) I ÜI I 18. 36. 54. 72. TIME (H) Figure 13. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator Without Additional Dynamics. ACTUAL ESnUATED M2 (V2 U ri S § o O 6 18. 36. 54. 72. TIME (H) Figure 14. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator Without Additional Dynamics. 310 ACTUAL ESTUATED 1 41 60. 120 . 160. TIME (H) Figure 15. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics While Applying the Estimator Without Additional Dynamics. § I 21 O u N 0 1 ACTUAL CORRUPTED 1 41.60. 120. 160. TIME (H) Figure 16. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics While Applying the Estimator Without Additional Dynamics. 311 ACTUAL S z 0 1 i i i g 0. 40. 80. 120 . 160. TIME (H) Figure 17. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics While Applying the Standard Estimator. § Iz ou N 0 to 1 ACTUAL CORRUPTED o 0. 40. 80. 120. 160. TIME (H) Figure 18. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics While Applying the Standard Estimator. 312 —— ACTUAL Ü CORRUPTED Iz 8 gI I I 6I 0. IB. 36. 54. 72. TIME (H) Figure 19. Actual and Eatlmated Dlaaolved Oxygen Concentration for a Procesa Simulating a Rapid Decrease In k^a While Applying the Estimator Without Additional Dynamics. ACTVAL I 5 0 u § 1 H1 S § I o 0. 18. 36. 54. 72. TIME (H) Figure 20. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating a Rapid Decrease In kj^a While Applying the Estimator Without Additional Dynamics. 313 § ACniAl, ISniUTED ! i I I S IB. 36. 54. 72 TIME (H) Figure 21. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating a Rapid Decrease In kj^a While Applying the Estimator Without Additional Dynamics. ACniAL CORRUPTED ESTIMATED E- 8 S Q o 0. 16 36. 54. 72. TIME (H) Figure 22. Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating a Rapid Decrease In kj^a While Applying the Standard Estimator. 314 ACTUAL esnUATED I i 0È U rcü 8 1 s s ê Ü O o 18. 36. 54. 72. TIME (H) Figure 23. Actual and Eatlmated Oxygen Maas Transfer Coefficient for a Process Simulating a Rapid Decrease In k^a While Applying the Standard Estimator. CJ ACTUAL ESnWATED i e iz 8 § Ü I % 18. 36. 54. 72. TIME (H) Figure 24. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating a Rapid Decrease in k^a While Applying the Standard Estimator. 315 ■ ACTUAL ESTIMATED w zI 8 Ë I I o 0. 1 6 . 3 6 . 5 4 . 7 2 . TIME (H) Figure 25. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase In the Substrate Yield-Related Term of the R Matrix. \ Ü, Ï2 O U u 0CO u 1 ACTUM, C0RRUP1ÎD 0. 3 6 . 5 4 .18. 7 2 . TIME (H) Figure 26. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase In the Substrate Yield-Related Term of the R Matrix. 316 ACTOAL ESHUATH) 1 0I 1 36. TIME (H) Figure 27. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix. ACniAL ESnUATED 18. 36. 54. 72. TIME (H) Figure 28. Actual and Estimated Substrate Yield for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix. 317 ------ACTOAL ...... ESnUATED i t K w i I, J M o Z L ...... 0. 18. 36. 54. 7 TIME (H) Figure 29. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator with a lOx Increase in the Substrate Yield-Related Term of the R Matrix. —— ACTUAL ESTIMATED 2 0 1 g 2CJ S f- z o s 0. 16. 36, 54. 72. TIME (H) Figure 30. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Oxygen Yield-Related Term of the R Matrix. 318 -AOTU, -CORRUPTED -ESniUTED I; g i. r s ' QI o 18. 36. 54. 72 TIME (H) Figure 31. Actuel and Estimated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Oxygen Yield-Related Term of the R Matrix. ------ACTUAL ...... ESTIMATED I I . uo Cx] W I w 2 < - § I. 1 . 0. IS. 36. 64. 7 TIME (H) Figure 32. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Oxygen Yield-Related Term of the R Matrix. 319 I ü s i ACTVAL E?nUATED 18 36. 54. 72. TIME (H) Figure 33. Actual and Estimated Oxygen Yield for a Standard Process Simulation Applying the Estimator with a O.lx Decrease In the Oxygen Yield-Related Term of the R Matrix. ESnWATED 36. TIME (H) Figure 34. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a 0.1 Decrease In the Oxygen Yield-Related Term of the R Matrix. 320 '■ ACTUAL N § iz 8 X Ü Ë O 9 0. 18. 36. 54. 72. TIME (H) Figure 35. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a O.lx Decrease in the Substrate Concentration-Related Term of the R Matrix. ACTVAL i I IZ 8 Xo oi a 0. IB 36. 54 72. TIME (H) Figure 36. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase in All Elements of the R Matrix. 321 c/3 0. 18. 36. 54. 72. TIME (H) Figure 37. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase In All Elements of the R Matrix. -ACTVU. -CORRUPTED § ■ESnUATED I ! I 18. 36. 54. 72. TIME (H) Figure 38. Actual and Estimated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase In All Elements of the R Matrix. 322 ------AOVAL ...... ESnUATED X r I I I 0. 1 8 . 36. 54. 7 TIME (H) Figure 39. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator with a 10% Increase In All Elements of the R Matrix. OI lA rE3 g: >- d ACniAL ES1UUTB) I.W O 18. 36. 54. 72. TIME (H) Figure 40. Actual and Estimated Substrate Yield for a Standard Process Simulation Applying the Estimator with a 10% Increase In All Elements of the R Matrix. 323 ■ ACTUAL ...... tSTTMATED z 2 bü N . b. i \ r W O u ni A r Z j/ .. ^ : g 8 g 3 f § io 1 8 3 6 , 5 4 . 7 2 . TIME (H) Figure 41. Actual and Estimated Oxygen Mass Transfer Coefficient for a Standard Process Simulation Applying the Estimator with a lOx Increase In All Elements of the R Matrix. I Iz o 5 Ü I ACnJAL o E^IUTED d 1 8 . 3 6 . 5 4 . 7 2 . TIME (H) Figure 42. Actual and Estimated Oxygen Yield for a Standard Process Simulation Applying the Estimator with a lOx Increase In All Elements of the R Matrix. 324 ESTIMATED I I 8 IW I i 16. 36. 54. 72. TIME (H) Figure 43. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Standard Process Simulation Applying the Estimator with a lOx Increase In All Elements of the R Matrix. — — ACTUAL 0z 1z 0 u 1 Q o 0. 18. 36. 54. 72. TIME (H) Figure 44. Actual and Estimated Biomass Concentration for a Process Simulating a 3x Increase in Measurement Noise While Applying the Standard Estimator. 325 I I I I — ACTUAL 0. 16. 36, 54. 72. TIME (H) Figure 45. Actual and Estimated Substrate Concentration for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator. a CORRUPTED 2 ESTIMATED 0 12 0O g 1 I § 5 I 0. 18 54.36. 72 TIME (H) Figure 46. Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator. 326 ACTUAL ESnHATED X ? I I u I % 18. 36. 54. 72. TIME (H) Figure 47. Actual and Eatlmated Specific Growth Rate for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator. 3I I I I Ü >• 6. I ACniAL ESnUATED 18. 36. 54. 72. TIME (H) Figure 48. Actual and Estimated Substrate Yield for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator. 327 Ce cvj ACTUAL EgnWATED 16. 36. 54. 72. TIME (H) Figure 49. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator. § I I ESnUATED IB. 36. 54. 72. TIME (H) Figure 50. Actual and Estimated Oxygen Yield for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator. 328 ACTVAL £?nUATED 1 8I I I § 18 36. 54. 72. TIME (H) Figure 51. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating a 3x Increase In Measurement Noise While Applying the Standard Estimator. o 6 "■ ACTUAL ESTIMATED Ü Z CJ zI 8 Ë Ü csi I o 6 0. 36. 54.16. 72. TIME (H) Figure 52. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Standard Estimator with a lOx Greater Error In the Initial Biomass Concentration Estimate. 329 ACTUU. MZ om O 0. 18. 54. 72.36. TIME (H) Figure 53. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Standard Estimator with a No Error In the Initial State Estimate. ACTUAL Iz 8 IÈ I d 0. 18. 36. 54. 72. TIME (H) Figure 54. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Standard Estimator with a lOx Increased Error In the Initial State Estimate. 3 3 0 — ■ ACTUAL Ji z I COV 8 X O cvi s a o 6 0 20. 40. 80.60. TIME (H) Figure 55. Actual and Eatlmated Blomass Concentration for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator. ACIUM, ESniUTED b] X iÜ 8 83 2 0 . 40. 60. 80. TIME (H) Figure 56. Actual and Estimated Specific Growth Rate for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator. 331 — ■- 1 — >■ -t— ••— ... ' ' • z \ II I teI ^ CO 6 1 = g ------ACTUAL i ... ESnUATED 20 40. 60. 80 TIME (H) Figure 57. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator. Ig 1 2 m o I ACnJAl ESnittTED 20. 40. 60. 80 TIME (H) Figure 58. Actual and Estimated Oxygen Yield for a Process Simulating a Cube Root Growth Law While Applying the Standard Estimator. 332 ESinUTIS 18 36. 54. 72. TIME (H) Figure 59. Actual and Estimated Substrate Yield for a Process Simulating Error In Biomass Composition While Applying the Standard Estimator. --- ACtUAL ... ESIUAIH) I 8 Cx3 M I % 2 S g L 18. 36. 54, 72. TIME (H) Figure 60. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating Error In Biomass Composition While Applying the Standard Estimator. 333 47 <6 1 = I LC g I 18. 36. 54. 72. TIME (H) Figure 61. Actual and Estimated Oxygen Yield for a Process Simulating Error In Biomass Composition While Applying the Standard Estimator. — — ACTUAL <6CO I 8I Ë O s q 0. 30. 60. 90. 120. TIME (H) Figure 62. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease In kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics. 334 N CO CORRUPTED o 0. 30. 60. 90. 120. TIME (H) Figure 63. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease In k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics. ACnJAL Ü CORRUPTED I I s : I I I % 0. 30. 60. 90. 120. TIME (H) Figure 64, Actual and Estimated Dissolved Oxygen Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease In kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics. 335 o i b M I o> Ig I 0. 30. 60. 90. 120. TIME (H) Figure 65. Actual and Estimated Specific Growth Rate for a Process Simulating Contois Kinetics, a Rapid Decrease In k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics. I 3 O a t i: is -ACTOAL -ESnUATED I.M O 30. 60. 90. 120. TIME (H) Figure 66. Actual and Estimated Substrate Yield for a Process Simulating Contois Kinetics, a Rapid Decrease In kj_a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics. 336 a: ■-ESmUTED ë I s I S I o 0. 30. 60. 90. 120. TIME (H) Figure 67. Actual and Estimated Oxygen Hasa Transfer Coefficient for a Process Simulating Contois Kinetics, a Rapid Decrease In k^^a and Procesa Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics. AOTAL CSnUATED 60. 120. TIME (H) Figure 68. Actual and Estimated Oxygen Yield for a Process Simulating Contois Kinetics, a Rapid Decrease In k.a and Process Noise having a Standard Deviation of 0.2, While Applying the Estimator with a Small Q Matrix and Without Additional Dynamics. 337 ACTUAL Ü N Iz 8 S Ü O d 0. 30. 60. 90. 120 . TIME (H) Figure 69. Actual and Estimated Biomass Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease In k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. N I I I I ACTVAL o 0. 30. 60. 90. 120. TIME (H) Figure 70. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease In k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. 338 o ACTUAL CORRUPTS) 9 I : I I I 0. 30.60. 90. 120 . TIME (H) Figure 71. Actual and Eatlmated Dlasolved Oxygen Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease In kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. o o g I o S I o S o 0. 30. 60. 90. 120. TIME (H) Figure 72. Actual and Estimated Specific Growth Rate for a Process Simulating Contois Kinetics, a Rapid Decrease In kj^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. 339 I § O o r QSi j'j — % ■/ g -ACTVAL -ESnUATED COi 30. 60. 90. 120. TIME (H) Figure 73. Actual and Estimated Substrate Yield for a Process Simulating Contois Kinetics, a Rapid Decrease In k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. ACTVAL ESnVATED E- I 8 g 1 I § o O o 30. 60. 90. 120. TIME (H) Figure 74. Actual and Estimated Oxygen Mass Transfer Coefficient for a Process Simulating Contois Kinetics, a Rapid Decrease In kj_a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. 340 g I’ 1= S 0: -ACTOAL I -ESniUTCD 30. 60. 90. 120. TIME (H) Figure 75. Actual and Estimated Oxygen Yield for a Process Simulating Contois Kinetics, a Rapid Decrease in k^a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. ACTUAL ESnVATEO Is Ü 30. 60. 90. 120. TIME (H) Figure 76. Actual and Estimated Saturated Dissolved Oxygen Concentration for a Process Simulating Contois Kinetics, a Rapid Decrease in kj_a and Process Noise having a Standard Deviation of 0.2, While Applying the Standard Estimator. 341 ACTUAL u zI 8 X Û 0. 18 36. 54. 72. TIME (H) Figure 77. Actual and Estimated Biomass Concentration for a Standard Process Simulation Applying the Estimator having a Constraint of 0.1 h”^ as the Maximum Estimated Specific Growth Rate. ACTOAl ESmUTED I I Iu 83 18 36. 54. 72. TIME (H) Figure 78. Actual and Estimated Specific Growth Rate for a Standard Process Simulation Applying the Estimator having a Constraint of 0.1 h“ ^ as the Maximum Estimated Specific Growth Rate. 342 a I Is 8 Z s 1 = - § ------ACTUAL ------CORRUPTED ...... ESTIMATED 20. 40. 60. 60. TIME (H) Figure 79. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Estimator Without Additional Dynamics. § % I uI I o 1 41. 120 . 160.60. TIME (H) Figure 80. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics and a Rapid Decrease In k^a While Applying the Estimator Without Additional Dynamics. 343 ë 5 — ACTUAL CORRUPTCD ESTIMATED 0 20. 40. 60. 80. TIME (H) Figure 81. Actual and Estimated Substrate Concentration for a Standard Process Simulation Applying the Standard Estimator. 21 0 U 1 i — ' ■■ ACTUAL CORRUPTED 1 41. 60. 120. 160. TIME (H) Figure 82. Actual and Estimated Substrate Concentration for a Process Simulating Contois Kinetics and a Rapid Decrease In While Applying the Standard Estimator. APPENDIX D ON-LINE EXPERIMENTATION RESULTS 344 345 0 ACTUAL o, S 2 0 1 S Z o0 ë o 1 ë Q o 0. 14. 27. 41. 54. TIME (H) Figure 83. Fermentation Two Actual and Estimated Biomass Concentration. —— ACTVAL s I § zI uo s 3o o 0. 14. 27. 41. 54. TIME (H) Figure 84. Fermentation Two Actual and Estimated Substrate Concentration. 346 o 6 o z 0 i d 1 i 00 § i 0 d g 1 i d I " ACTVAL [g i d 14. 27. 41. 54. TIME (H) Figure 85. Fermentation Two Actual and Estimated Dissolved Oxygen Concentration. 0 ACTOAL — ESIWATED I o:I Ü 0 EC 1 § d 14. 27. 41. 54. TIME (H) Figure 86. Fermentation Two Actual and Estimated Specific Growth Rate. 347 o 0 3 u 1 i o aOi u Cd P S I o w 0. 14. 27. 41. 54. TIME (H) Figure 87. Fermentation Two Estimated Overall Substrate Yield. o M O 14. 27. 41. 54. TIME (H) Figure 88. Fermentation Two Estimated Oxygen Mass Transfer Coefficient. 348 §I a z o CD 5 C3 i 0> I ESTOUTED o 0, 14. 2?. 41. 54 TIME (H) Figure 89. Fermentation Two Estimated Overall Oxygen Yield. o I ESTIMATED og b § I P o Ig § I o I 6I 0, 27. 41. 54.14. TIME (H) Figure 90. Fermentation Two Estimated Saturated Dissolved Oxygen Concentration. N 349 6 G?nUATS) s I I Q g s Pu o s 6 w 14. 27. 41. 54. TIME (H) Figure 91. Fermentation Two Feed Flow Rate. o — ESnMATtD o § 6 0. 14. 41.27. 54. TIME (H) Figure 92. Fermentation Two Estimated Substrate Maintenance Energy Requirements. 350 E S niU T Q ) s 0 a S ° 1 Ü 14. 27. 41. 54. TIME (H) Figure 93. Fermentation Two Estimated Oxygen Maintenance Energy Requirements. O K (D Ü 9o g 9 o oI 0 14. 27. 41. 54. TIME (H) Figure 94. Fermentation IVo Carbon Dioxide Evolution Rate. 351 0 ACTUAL " ESTIMATED Ü CO i Icvi 8 0. 27. 4114. 54. TIME (H) Figure 95. Actual and Estimated Biomass Concentration of Substrate-Corrected Simulation of Fermentation IWo. ACTUAL § I S zo 8 N 8 3u o 0. 41.14. 5427. TIME (H) Figure 96. Actual and Estimated Substrate Concentration of Substrate-Corrected Simulation of Fermentation Two. 352 o z o 0 6 1 i0 i u 6 § 1 oi i i ACTUAL i 6 0. 14. 27. 41. 54. T I M E ( H ) Figure 97. Actual and Estimated Dissolved Oxygen Concentration ot Substrate-Corrected Simulation of Fermentation Two. o 0 ACTUAL — — ESTIMATED g 6 I § d 10 u § 1 d 83 o§ 0. 27. 41.14. 54. T I M E ( H ) Figure 98. Actual and Estimated Specific Growth Rate of Substrate-Corrected Simulation of Fermentation Two. 353 w ——— ESTIMATED g 6 S3 d o o d 0. 14. 41.27. 54. T I M E ( H ) Figure 99. Estimated Substrate Yield of Substrate-Corrected Simulation of Fermentation Two. CnilATED § CO d CO m o 0. 14. 27. 41. 54. T I M E ( H ) Figure 100. Estimated Oxygen Mass Transfer Coefficient of Substrate-Corrected Simulation of Fermentation Two. 354 § I o 1 cvi I o 6 0. 14. 27. 41. 54. T I M E ( H ) Figure 101. Estimated Oxygen Yield of Substrate-Corrected Simulation of Fermentation Two. ESmUTED 27. T I M E ( H ) Figure 102. Estimated Saturated Dissolved Oxygen Concentration of Substrate-Corrected Simulation of Fermentation TWo. 355 o ESnUATCD s o o 0 6 1Ü ü i z 6 0 1 lO o g 6 o o D i 6 0. 14. 41. 54.27. T I M E ( H ) Figure 103. Estimated Substrate Maintenance Energy Requirements of Substrate-Corrected Simulation of Fermentation Two. o ESTIMATH) S 0 ÔS 6I 1 (O i d 0z g 1g d §I oI 6 14. 27. 41. 54. T I M E ( H ) Figure 104. Estimated Oxygen Maintenance Energy Requirements of Substrate-Corrected Simulation of Fermentation Two. 356 0 ACTUAL ESTMATO) (O i g I CM 8 X Ü CD 6 > i O d 0. 22 . 44. 65. 87. T I M E ( H ) Figure 105. Fermentation Three Actual and Estimated Biomass Concentration. § zI o u M CO 8 3 o ACTUAL ESTIMATED o 0 22 . 44. 65. 87. T I M E ( H ) Figure 106. Fermentation Three Actual and Estimated Substrate Concentration. 357 »CIVAl \ o ESnUTED 2 0 1 I I 6s 44 . T I M E ( H ) Figure 107. Fermentation Three Actual and Eatlmated Dissolved Oxygen Concentration. 0 ACIVAI, ESIHttTED s I Mg o8 I 0. 22. 44 65. 87. T I M E ( H ) Figure 108. Fermentation Three Actual and Estimated Specific Growth Rate. 358 i 30 16 N ë 6 Q (0 I 6 I CTUATED I 22. 44. 65. 87. 0. TIME (H) Figure 109. Fermentation Three Estimated Overall Substrate Yield. ISTIIUTED t- zu I i I 1 I I Is 22 . 44. 65. 87 TIME (H) Figure 110. Fermentation Three Estimated Oxygen Mass Transfer Coefficient, 359 gI I O tri m o I d 0. 22. 44. 66 . 87. TIME (H) Figure 111. Fermentation Three Estimated Overall Oxygen Yield. d I ii E— I 0. 22. 44. 65. 87. TIME (H) Figure 112. Fermentation Three Estimated Saturated Dissolved Oxygen Concentration. 360 ESnUATED 44. TIME (H) Figure 113. Fermentation Three Feed Flow Rate. o BnfctATED Z o PQ 0 o 'Ü 1 bo I g b !I 22. 44. 65. 87. TIME (H) Figure 114. Fermentation Three Estimated Substrate Maintenance Energy Requirements. 361 I N i d I 22 . 44. 66 . 87. TIME (H) Figure 115. Fermentation Three Estimated Oxygen Maintenance Energy Requirements. o o d X CO Ü o d g CO o d o o o d 0. 22. 44. 66 . 88 . TIME (H) Figure 116. Fermentation Three Carbon Dioxide Evolution Rate. 362 0 ACTOAL ESnUATED z o CM !z 8 X 6 Q o o 0. 22 . 44. 65. 87. TIME (H) Figure 117. Actual and Estimated Biomass Concentration of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three. -3 Ü Z0 1 § CJ i u oI 3 Ü ACTUAL 0. 22. 44 65. 87. TIME (H) Figure 118. Actual and Estimated Substrate Concentration of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three. 363 »CTO*I, iSniUTED 2 0 1 I 0o 1 I 22. 44 65. 87. TIME (H) Figure 119. Actual and Estimated Dissolved Oxygen Concentration of Substrate and Initial Biomass Corrected Simulation of Fermentation Three. 6 0 ACTVAL o 6 I o o ÜI 5; k. s 6 S3 § d 0. 22. 44. 65. 87 TIME (H) Figure 120. Actual and Estimated Specific Growth Rate of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three. 364 o i ESTIMATED î IÜ u s o Q i o § ico 6 0. 22. 44. 65. 87. T I M E ( H ) Figure 121. Estimated Substrate Yield of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three. i S I 8 I § i S I 0. 22. 44. 65. 87. T I M E ( H ) Figure 122. Estimated Oxygen Mass Transfer Coefficient of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three. 365 ! O iO « m g ! O 6 0. 22. 44. 65. 07. TIME (H) Figure 123. Estimated Oxygen Yield of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three. § CmiATB) 0 N zr 8 I g " 1 u I r OT5 44. TIME (H) Figure 124. Estimated Saturated Dissolved Oxygen Concentration of Substrate and Initial Biomass Estimate Corrected Simulation of Fermentation Three. 366 o ■ E?nMATED S o § § Ü s d !9 I g § d 22. 44. 65. 87. TIME (H) Figure 125. 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