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A CONTROL LOOP PERFORMANCE MONITOR by SAMUEL ODEI OWUSU Bachelor of Science in Chemical Engineering University of Science and Te

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A CONTROL LOOP PERFORMANCE MONITOR by SAMUEL ODEI OWUSU Bachelor of Science in Chemical Engineering University of Science and Te A CONTROL LOOP PERFORMANCE MONITOR By SAMUEL ODEI OWUSU Bachelor of Science in Chemical Engineering University of Science and technology Kumasi, Ghana 1994 Master of Science in Chemical Engineering North Carolina Agriculture and Technical State University Greensboro, North Carolina 2001 Submitted to the Faculty of the Graduate College of the Oklahoma State University in partial fulfillment of the requirements for the Degree of DOCTOR OF PHILOSOPHY May, 2006 A CONTROL LOOP PERFORMANCE MONITOR Thesis Approved: Dr. R. R. Rhinehart Thesis Advisor Dr. J. R. Whiteley Dr. R. G. Ingalls Dr. E. Misawa Dr. G. X. Chen Dr. A. Gordon Emslie Dean of Graduate College ii ACKNOWLEDGMENTS It is with great pleasure that I write to acknowledge my gratitude to those that have made an impact on my educational life. First, my unqualified gratitude goes to Dr. R. R. Rhinehart, my research advisor whose in-depth knowledge, ideas, guidance and support has helped steered this project to this conclusion. I am also grateful for his continuous financial assistance. I found in him an advisor for his constant guidance and support, a father for always standing towards me in loco parentis, and a true friend for always being available to meet with me for discussions. I would like to extend a special appreciation and gratitude to my advisory committee members; Dr. J. R. Whiteley of the School of Chemical Engineering, Dr. E. Misawa of the Department of Mechanical and Aerospace Engineering, Dr. R. G. Ingalls of the School of Industrial Engineering and Management and Dr. G. X. Chen of the Fractionation Research Incorporated (FRI). I am truly grateful to you all for taking time of your busy schedules to review my work and to guide me in completing this research. I would also like to gratefully acknowledge the Measurement Control and Engineering Center (MCEC) for providing financial support and industrial guidance for this work. Thanks also to the Oklahoma State University (OSU) and also to the College of Engineering and Architecture (CEAT) for providing me with a conducive academic environment for my research work. To the school of Chemical Engineering, I say thanks for the awesome academic programs and the knowledge you have instilled. I am proud to iii have been a student in this august department and for a fruitful academic period here at OSU. For camaraderie, I shall always be grateful to my colleagues, Ming Su and Preetica Kumar for the useful discussions and humorous times we shared together in the laboratory. My special gratitude goes my true love and better half Millicent for her love, encouragement, and precious support in all my academic study. Thanks for being there for me always. Indeed, it takes but two to make a pair. I would also like to acknowledge my parents back home in Ghana, David and Elizabeth Owusu, for their constant prayers and spiritual support and for seeing me through a wonderful education right from my childhood. My pastor Leroy Hawkins and his better half Leta of Stillwater Hosanna Assembly of God for the fellowship we shared together and their prayers. My parents in the United States Don and Alvetta McCabe for making us feel at home and adding us to their family. To all in Hosanna, thank you for your prayers. Lastly, I would also like to extend my love to my daughter Kimberley whose presence around me always glows like a candle and brightens my life. Thanks for being in our life Kimberley. iv TABLE OF CONTENTS Chapter Page List of Tables……………………………………………………………………….....ix List of Figures………………………………………………………………………….x I. INTRODUCTION………………………………………………………………….1 2. CONTROL LOOP PERFORMANCE MONITORING……………………………7 2.1 Literature Review……………………………………………………………….7 2.2 Objective……………………………………………………………………….12 2.3 The Concept of Markov Chains………………………………………………..13 2.3.1 Classification of states and their behavior……………………………….18 2.4 The Binomial Distribution……………………………………………………..20 2.4.1 Moments of the Binomial Distribution…………………………………..22 2.5 The Normal Distribution……………………………………………………….25 2.6 Sample Proportions…………………………………………………………….26 2.7 Test of Hypothesis……………………………………………………………..28 2.8 Errors in Hypothesis Testing…………………………………………………..28 2.9 Analysis of Type-I errors Using Binomial Distribution……………………….33 2.10 Analysis of Type-II errors Using Binomial Distribution…………………….34 2.11 Normal Approximation to the Binomial Distribution………………………..35 3. Development of the Health Monitor ………………………………………………39 3.1 Model States as a Markov Chain………………………………………………39 v Chapter Page 3.2 Overall Structure of the Health Monitor………………………………………46 3.2.1 Estimate the Sampling Ratio..............................................................…...46 3.2.2 Estimate the Number of States………………………………………...48 3.2.3 Identify States Containing the Least Number of Reference Samples....54 3.2.4 Estimate the Window Length………………………………………….65 3.2.5 Estimate the Control Limits for Each State……………………………73 3.2.6 Estimate Type-II Error Rate and Power for all States and the Entire Monitor…………………………………………………………75 3.3 Moving Window Statistics…………………..…………………………………….82 3.4 Grace Period……………………………………..………………………………...87 3.5 Conducting Test Analysis………………………….……………………………...88 4.0 Evaluation of the Health Monitor…………………………………………………90 4.1 Implementation Procedure………..………………...…………………………90 4.2 Computer Simulation Evaluation…..…………………..……………………..91 4.2.1 First-Order Plus Time Delay Process…..……..………………………...91 4.2.2 Performance Monitor Demonstration……………………………….......97 4.2.3 A Second-Order Plus Time Delay Process…………………..………...101 4.2.4 Performance Monitor Demonstration……………………………..……107 4.3 Application on Unit Operations Experimental Data…………………………110 4.3.1 Description of Experimental Unit……………..……………………..110 4.3.2 Performance Monitoring for Pressure Drop Control by Manipulating Signal to Water Flow Control Valve………………….112 vi Chapter Page 4.3.3 Effect of Varying the Overall Type-I Error Rate on Window Length and Performance Monitoring..……………………………….115 4.3.4 Effect of Varying the Type-II Error Rate on Window Length and Performance Monitoring……………………………………………..119 4.3.5 Performance Monitoring for Pressure Drop Control by Manipulating Signal to Air Flow Control Valve……………………..121 4.3.6 Performance Monitoring for Water Flow Control by Manipulating Signal to Water Flow Control Valve………………………….……..125 4.3.7 Application of the Health Monitor on Qing Li’s Data (Monitoring the Performance of Water Flow Control Loop by Manipulating Signal to Water Flow Control Valve)…………………127 4.3.8 Application on Industrial Data………………………………………..131 4.4 Model Based Control……………………….…………..…………………...137 4.4.1 Simulation Using Internal Model Control………………………........137 4.4.2 Performance Evaluation of Health Monitor on the IMC Process…….142 4.4.3 Simulation Using Model Predictive Control………………………….146 4.4.4 Performance Evaluation of Health Monitor on the MPC Process……151 4.4.5 Summary……………………………………………………………...154 5. Conclusion and Recommendations……………………………………………….156 5.1 Conclusions…………………………………………………………………...156 5.2 Recommendation……………………………………………………………...158 REFERENCES……………………………………………………………………......160 APPENDICES………………………………………………………………………...160 APPENDIX A-Controller Tuning for First-Order Plus Time Delay (FOPTD) Process……………………………………….....164 vii APPENDIX B-Controller Tuning for Second-Order Plus Time Delay (SOPTD) Process….………..………………………………………………166 APPENDIX C-Internal Model Control (IMC) Structure………………………...168 APPENDIX D-Auto-Correlation ad Partial Auto-Correlation Analysis…........…171 APPENDIX E-Model Predictive Control (MPC) DETAILS………………….…188 APPENDIX F-Comparison between Exact Binomial Analysis and the Normal Approximation to the Binomial Distribution…….......…194 APPENDIX G-Why Ignoring Amplitude Does not Limit the General Performance of the Health Monitor ………...…………………...198 APPENDIX H-Distinguishing Between State Space Modeling in Time Series and State Modeling in a Markov chain ………………….…....…203 APPENDIX I-Glossary of Some Terminologies Used in this Work………...…...205 viii LIST OF TABLES Table Page 2.1 Decisions in Hypothesis Testing………………………………………………29 3.1 Markov Transition Probability Matrix (Shown Only for 8 Total States)……...45 3.2 Values of the Estimated Type-I Error Rate compared with Bonferroni Approximation…………………………………………………….62 3.4 List of Type-II Error Rates……………..…………………………………..….78 3.3 Array of State Measurements and Their Indexes……………………………...82 3.5 Array of Cumulative State Measurements…………………………………….84 D1 Behavior of the ACF and PACF for Causal an Invertible ARMA Series (P is the lag for an AR process and q is the lag for an MA process)………………………………………………………………….180 ix LIST OF FIGURES Figure Page 2.1 Probability Distribution of X successes in n trials (n = 50, Po = 0.5)………….30 2.2 Probability Distribution of X successes in n trials (n = 50, Po = 0.5, Pa1 = 0.35, Pa2 = 0.65)…………………………………………………………..31 2.3 Probability Distribution Showing a Type-I Error Occurrence…………………33 2.4 Probability Distribution Showing a Type-II Error Occurrence………………...35 3.1 Actuating Error Signals in a Time series of Controlled Data…………………..39 3.2 Controller Run Length, Zero Crossing, State and Transition State (O Represents an Actuating Error Value (The Adjacent Number is the State)…………………………………………………………………………...41 3.3 Illustration of Modeling of States Using Markov Chains to Determine the Transition Probabilities………………………………………………………...43 3.4 Distribution of States for Historical Good Data……………………………….49 3.5 Stages in the Analysis of the Reference Data…………………………………53 3.6 Analysis of Type-I Error Rate
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