TOWARDS VERIFIABLE ADAPTIVE CONTROL OF GAS TURBINE ENGINES A Dissertation Presented to The Academic Faculty by Mehrdad Pakmehr In Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the School of Aerospace Engineering Georgia Institute of Technology August 2013 Copyright c 2013 by Mehrdad Pakmehr TOWARDS VERIFIABLE ADAPTIVE CONTROL OF GAS TURBINE ENGINES Approved by: Professor Eric Feron, Professor Vigor Yang Committee Chair School of Aerospace Engineering School of Aerospace Engineering Georgia Institute of Technology Georgia Institute of Technology Professor Eric Johnson Professor Marilyn Wolf School of Aerospace Engineering School of Electrical and Computer Georgia Institute of Technology Engineering Georgia Institute of Technology Dr. James Paduano Professor Jeff Shamma Lead Engineer for Autonomy, School of Electrical and Computer Controls, and Estimation Engineering Aurora Flight Sciences Georgia Institute of Technology Date Approved: 17 May 2013 To my parents. iii The knowledge of anything, since all things have causes, is not acquired or complete unless it is known by its causes. Pur Sina (also known as Avicenna or Ibn Sina), 980-1037 A.D. Persian philosopher, mathematician, and physician iv ACKNOWLEDGEMENTS I am eternally grateful for the guidance from my advisor, Dr. Eric Feron. His support, advice, and suggestions over the years have helped me grow as a researcher and an engineer. Without his direction, this dissertation would not have been possible. I would also like to thank the people at Aurora Flight Sciences, whom I worked with on the gas turbine engine control project, including Dr. James Paduano, Nathan Fitzgerald and George Kiwada. Especially, I am thankful to Dr. James Paduano, who provided me with precious comments and pieces of advice during this research, and Nathan Fitzgerald who managed to develop a very good physics-based model of the turboshaft engine and conducted experiments to verify the model. I am also thankful to Dr. Alireza Behbahani of the Air Force Research Lab (AFRL) for his support during the course of this research project. I am also indebted to Dr. Jeff Shamma who helped me to understand and develop gain scheduled sys- tems. I would like also to thank my other committee members including Dr. Yang, Dr. Johnson, and Dr. Wolf for their support. I would like to thank AFOSR and NSF for sponsoring my research. I sincerely thank my parents for everything they have done for me, especially for their support, love, and sacrifices over the years. I am also thankful for all of the enlightening discussions with all of my lab mates and co-workers at Georgia Tech. I would like to thank all of my fellow colleagues in the School of Aerospace Engineering, including Dr. Tansel Yucelen, Dr. Alireza Esna-Ashari, Gi Yun Chung, Romain Jobredeaux, Emmanuel Boidot, Aude Marzuoli, Sang Hyun Kim, and Timothy Wang. v TABLE OF CONTENTS DEDICATION .................................. iii ACKNOWLEDGEMENTS .......................... v LIST OF TABLES ............................... x LIST OF FIGURES .............................. xi LIST OF SYMBOLS AND ABBREVIATIONS ............. xviii Nomenclature . xviii Subscripts . xix Abbreviations . xx SUMMARY .................................... xxii I INTRODUCTION ............................. 1 1.1 Gas Turbine Engine . .1 1.2 Gas Turbine Engine Modeling . .4 1.3 Gain Scheduled Control . .6 1.4 Model Reference Adaptive Control . .7 1.5 Plug and Play Technology for Engine Control . 10 1.6 Control Software Verification and Certification . 11 1.7 Motivations . 13 1.8 Contributions . 15 1.9 Dissertation Outline . 15 II PHYSICS-BASED MODELING OF A GAS TURBINE ENGINE 17 2.1 Introduction . 17 2.2 Engine Test Apparatus . 17 2.2.1 Testbed Engine . 18 2.2.2 Test Stand and Instrumentation . 18 2.3 Twin Spool Turboshaft Engine Model . 22 vi 2.3.1 Overview . 23 2.3.2 Detailed Description . 24 2.4 Engine Characterization Testing . 29 2.4.1 Experiments . 29 2.4.2 Performance Maps of Engine Components . 30 2.4.3 Data Matching Results . 33 2.5 Open-Loop Simulation Results . 37 2.6 Summary . 41 III GAIN SCHEDULED CONTROL: STABILITY AND VERIFICA- TION ..................................... 43 3.1 Introduction . 43 3.2 Gain Scheduled Control Design . 46 3.2.1 System with Constrained Control Inputs . 56 3.2.2 Controller Interpolation . 58 3.3 Stability and Verification . 59 3.3.1 Stability Analysis . 60 3.3.2 Stability Verification . 63 3.3.3 Towards GS Control Software Verification . 64 3.4 Turboshaft Engine Example . 65 3.4.1 Equilibrium Manifold . 65 3.4.2 Closed-Loop Stability Verification . 69 3.4.3 Bode Plots . 72 3.4.4 Simulation Results . 75 3.4.5 Engine Limit Control Discussion . 82 3.5 Summary . 82 IV GAIN SCHEDULED MODEL REFERENCE ADAPTIVE CON- TROL ..................................... 84 4.1 Introduction . 84 4.2 Mathematical Preliminaries . 86 vii 4.2.1 Projection Operator . 86 4.2.2 Rectangular Saturation Function . 90 4.3 Model Reference Adaptive Control . 91 4.3.1 Problem Formulation . 91 4.3.2 Adaptive Control Design . 93 4.3.3 Model Reference Adaptive Control with Constrained Control Inputs . 99 4.3.4 Towards GS-MRAC Software Verification . 112 4.4 Turboshaft Engine Example . 114 4.4.1 Equilibrium Manifold . 114 4.4.2 Simulation Results . 118 4.4.3 Engine Limit Control Discussion . 126 4.5 Summary . 127 V PLUG AND PLAY TECHNOLOGY CONCEPT FOR GAS TUR- BINE ENGINE CONTROL SYSTEM ................. 128 5.1 Introduction . 128 5.2 Decentralized Linear Parameter Dependent Modeling . 131 5.2.1 Subsystem I: Engine Core . 134 5.2.2 Subsystem II: Engine Fan/Prop . 135 5.3 Decentralized Gain Scheduled Model Reference Adaptive Control . 135 5.3.1 Decentralized Adaptive Control Design . 136 5.3.2 Towards D-GS-MRAC Software Verification . 142 5.4 Plug and Play Technology Concept for Engine Control . 142 5.5 Turboshaft Engine Example . 146 5.5.1 Equilibrium Manifold . 146 5.5.2 Simulation Results . 154 5.5.3 Engine Limit Control Discussion . 170 5.6 Summary . 171 viii VI CONCLUDING REMARKS AND FUTURE RESEARCH ... 172 6.1 Concluding Remarks . 172 6.2 Recommended Future Research . 174 REFERENCES .................................. 176 VITA ........................................ 190 ix LIST OF TABLES 1 Comparison of different MRAC architectures . .9 2 Comparison of control algorithms from the control software verification point of view . 13 3 JetCat SPT5 turboshaft engine specifications [1, 3] . 19 4 Numerical values of the parameters for JetCat SPT5 turboshaft engine simulation . 38 5 Degradation values for engine health parameters as a change from nom- inal values . 114 6 Values for engine PnP test scenarios . 154 x LIST OF FIGURES 1 JetCat SPT5 turboshaft engine [3]. 18 2 CAD drawing of the engine and its mount. 19 3 CAD drawing of the engine exhaust gas path. 20 4 CAD drawing of the variable pitch propeller with its swash plate and bearing blocks. 20 5 CAD drawing of the variable pitch propeller installed on the JetCat SPT5 engine. 20 6 CAD drawing of the engine test setup with its load cell, torque sensor, and shaft adapters. 21 7 Engine test stand configuration. 21 8 JetCat SPT5 engine with variable pitch propeller installed in test stand. 22 9 Schematic turboshaft engine diagram. 23 10 Numerical process of gas turbine engine modeling. 29 11 Compressor map of JetCat SPT5 engine. 31 12 High pressure turbine map of JetCat SPT5 engine. 31 13 Low pressure turbine map of JetCat SPT5 engine. 32 14 Propeller map. 33 15 Comparison of model results to JetCat SPT5 data at 14.6 degree pro- peller pitch angle. 34 16 Comparison of model results to JetCat SPT5 data at 18 degree pro- peller pitch angle. 34 17 Comparison of model results to JetCat SPT5 data at 21.4 degree pro- peller pitch angle. 34 18 Comparison of model results to JetCat SPT5 data at 24.8 degree pro- peller pitch angle. 35 19 Comparison of model results to JetCat SPT5 data at 28.2 degree pro- peller pitch angle. 35 20 Comparison of model results to JetCat SPT5 data at 31.6 degree pro- peller pitch angle. 35 xi 21 Comparison of model results to JetCat SPT5 data at 35 degree pro- peller pitch angle. 36 22 HP and LP spool speeds. 39 23 Fuel and angle control inputs. 39 24 HP and LP spool accelerations. 39 25 Engine thrust. 40 26 Turbine temperature, TSFC, compressor pressure ratio, and compres- sor mass flow rate. 40 27 Compressor map showing the engine operating line for the simulation. 41 28 Pressure, temperature, and spool speed sensor outputs. 41 29 Example of gas turbine engine control architecture. 44 30 Output dependent gain scheduled controller diagram. 56 31 Controller interpolation schematic. 59 32 Stability region. ..