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Model Predictive Control (Mpc) Algorithm for Tip- Jet Reaction Drive

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Model Predictive Control (Mpc) Algorithm for Tip- Jet Reaction Drive MODEL PREDICTIVE CONTROL (MPC) ALGORITHM FOR TIP- JET REACTION DRIVE SYSTEMS A Thesis Presented to The Academic Faculty by Brian Kestner In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Aerospace Engineering Georgia Institute of Technology December 2009 MODEL PREDICTIVE CONTROL (MPC) ALGORITHM FOR TIP- JET REACTION DRIVE SYSTEMS Approved by: Prof. Dimitri N. Mavris, Advisor Dr. Jimmy Tai School of Aerospace Engineering School of Aerospace Engineering Georgia Institute of Technology Georgia Institute of Technology Dr. Tim Healy Mr. Randy Rosson Gas Turbine Combustion Engineering Gas Turbine Performance Methods General Electric Energy General Electric Energy Prof. Brian German School of Aerospace Engineering Georgia Institute of Technology Date Approved: November 13, 2009 ACKNOWLEDGEMENTS I would like to thank my advisor, Professor Dimitri Mavris, for giving me the opportunity to join the ASDL and pursue my PhD. In addition to providing me with this opportunity, his philosophy towards research was most inspiring. I would like to especially thank Dr. Jimmy Tai for all the support, advice, and help over the last five years. The formulation of this dissertation came out of our weekly meetings. I could not have completed this dissertation without his help. I would like to thank Dr. Tim Healy and Mr. Randy Rosson. The feedback and help provided was always most enlightening, even though it usually took me awhile to realize it. I would to thank Professor Brian German for always keeping an eye on me. To the love of my life, Gina Martell, thank you for being there through all the good and the bad. I know it has not always been easy over the last year but I am forever grateful for the love and support. Coming home to your smile always cheered me up when I was stressed out. Thanks to my mom, dad, sister, and brother whose words of encouragement and patience allowed me keep my focus when the going got tough. Also I would like to say thanks to all my friends both here in Atlanta or back home in Milwaukee for providing encouragement and the necessary distractions to keep me sane over this five year odyssey. iii TABLE OF CONTENTS Page ACKNOWLEDGEMENTS iii LIST OF TABLES vii LIST OF FIGURES x LIST OF SYMBOLS AND ABBREVIATIONS xvii SUMMARY xix CHAPTER 1 INTRODUCTION 1 2 PROBLEM STATEMENT 3 Tip-Jet Reaction Drive System 3 Multivariable Control Methods 7 Tip-Jet Multivariable Control Feasibility Analysis 16 3 MODEL PREDICTIVE CONTROL 18 MPC Basics 18 Literature Review 20 4 TECHNICAL CHALLENGES, RESEARCH QUESTIONS, AND HYPOTHESIS 26 MPC Design Constraints 26 Centralized MPC 30 Multiplexed MPC 31 Feasible Cooperative MPC 33 Feasible Cooperative Multiplexed MPC 36 5 COMPUTATIONAL BURDEN 39 iv Centralized MPC 39 Multiplexed MPC 46 Feasible Cooperative MPC 49 Feasible Cooperative Multiplexed MPC 56 Tip-Jet Reaction Drive MPC Computational Burden Reduction 59 6 BASELINE PI CONTROLLER 61 Baseline PI Controller Design Process 61 Baseline PI Control Architecture 63 Control Sizing and Analysis 74 Baseline PI Control Simulations 80 Baseline PI Control Summary 102 7 CENTRALIZED MODEL PREDICTIVE CONTROL 104 Centralized MPC Design Process 104 Centralized Model Predictive Control Development 107 Centralized Model Predictive Control Design 132 Centralized MPC Simulations 152 Centralized MPC Summary 173 8 DISTRIBUTED MODEL PREDICTIVE CONTROL 175 Distributed MPC Design Process 175 Distributed Model Predictive Control Development 178 Distributed Model Predictive Control Design 187 Distributed MPC Simulations 215 Distributed MPC Summary 237 9 CONTROL ARCHITECTURE COMPARISON 239 Controller Design Comparison 239 v Controller Simulation Comparison 247 Multivariable Control Feasibility Study 257 10 SUMMARY, CONCLUSIONS, AND FUTURE WORK 260 Summary 260 Conclusions 261 Future Work 264 APPENDIX A: TIP-JET REACTION DRIVE SYSTEM NPSS .MDL SOURCE CODE 266 APPENDIX B: NON-MODEL BASED RELATIVE GAIN ARRAY 293 APPENDIX C: MODEL BASED RELATIVE GAIN ARRAY 295 APPENDIX D: EXTENDED KALMAN FILTER S-FUNCTION SOURCE CODE 297 APPENDIX E: DISTRIBUTED MPC S-FUNCTION SOURCE CODE 300 REFERENCES 307 vi LIST OF TABLES Table 1: Tip-Jet Reaction Drive Control Feasibility Metrics .......................................... 17 Table 2: Centralized MPC Dimensions ........................................................................... 45 Table 3: Multiplexed MPC Dimension ............................................................................ 49 Table 4: Feasible Cooperative MPC Dimension ............................................................. 52 Table 5: Feasible Cooperative Dimension with no Interactions ...................................... 56 Table 6: Feasible Cooperative Multiplexed MPC Dimensions ....................................... 59 Table 7: Tip-Jet Eigenvalues and Associated Dynamics ................................................. 67 Table 8: Shaft, Heat Soak, Gas Path Eigenvalues with Duct Dimension Relative to Engine Dimension ............................................................................................................. 68 Table 9: Relative Gain Array of Tip-Jet Reaction Drive System at 0 rad/s .................... 72 Table 10: Steady State Performance Variation for Different Input/Output Pairings ....... 73 Table 11: PI Controller Bode Plot Descriptions .............................................................. 76 Table 12: Baseline PI Control Performance Metrics ....................................................... 79 Table 13: Stall Margin Sensitivity to Control Inputs ....................................................... 98 Table 14: Relative Gain Array of Tip-Jet Reaction Drive System Model Based Control at 0 rad/s .............................................................................................................................. 109 Table 15: Model Based and Non-model Based Control Performance Variance Comparison over Useful Life of System ........................................................................ 111 Table 16: Available States for Use in State Estimator ................................................... 115 Table 17: Available Sensors for Tip-Jet Reaction Drive System .................................. 117 Table 18: States and Sensors Used in Tip-Jet Reaction Drive State Estimator ............. 122 vii Table 19: Model Based Control Inputs, Outputs, References, States, and Disturbances ......................................................................................................................................... 127 Table 20: Centralized MPC Bode Plot Descriptions ..................................................... 133 Table 21: Centralized MPC Candidates ......................................................................... 147 Table 22: Centralized MPC Performance Metrics ......................................................... 147 Table 23: Centralized MPC Sensitivity to Modeling Error ........................................... 149 Table 24: Model Based Control Inputs, Outputs, References, States, and Disturbances for Left Engine MPC ............................................................................................................ 181 Table 25: Model Based Control Inputs, Outputs, References, States, and Disturbances for Right Engine MPC .......................................................................................................... 181 Table 26: Model Based Control Inputs, Outputs, References, States, and Disturbances for Tip-Jet MPC .................................................................................................................... 182 Table 27: Distributed MPC Bode Plot Descriptions ...................................................... 188 Table 28: Distributed MPC Final Design Variable Choices .......................................... 208 Table 29: Final Distributed MPC Design Control Performance Metrics ...................... 211 Table 30: Distributed MPC Sensitivity to Modeling Error ............................................ 213 Table 31: Stall Margin Sensitivity to Control Inputs ..................................................... 230 Table 32: Turbine Inlet Temperature Sensitivity to Control Inputs .............................. 230 Table 33: Non-Model Based and Model Based Steady-State Performance Variation .. 240 Table 34: Model Based Control Sensitivity to Modeling Error ..................................... 242 Table 35: Control Architecture Bandwidth Comparison ............................................... 244 Table 36: Updated Tip-Jet Reaction Drive Control Feasibility Metrics ........................ 259 Table 37: Relative Gain Array of Tip-Jet Reaction Drive System at 0.1 rad/s ............. 293 viii Table 38: Relative Gain Array of Tip-Jet Reaction Drive System at 1 rad/s ................ 293 Table 39: Relative Gain Array of Tip-Jet Reaction Drive System at 10 rad/s .............. 294 Table 40: Relative Gain Array of Tip-Jet Reaction Drive System Model Based Control at 0.1 rad/s ........................................................................................................................... 295 Table 41: Relative Gain Array of Tip-Jet Reaction Drive System Model Based Control at 1 rad/s .............................................................................................................................. 295 Table 42: Relative Gain Array of Tip-Jet Reaction Drive System Model Based Control at 10 rad/s ...........................................................................................................................
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