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Adaptive Control ofNonsmooth Dynamic Systems
Springer-Verlag London Ltd.
Gang Tao and Frank L. Lewis (Eds)
Adaptive Control of Nonsmooth Dynamic Systems With 102 Figures
, Springer
Gang Tao, PhD Department of Electrical and Computer Engineering, University of Virginia, Charlottesville, VA 22903, USA
Frank 1. Lewis, PhD Automation and Robotics Research Institute, University of Texas at Arlington, Fort Worth, TX 76118, USA
ISBN 978-1-84996-869-0 ISBN 978-1-4471-3687-3 (eBook) DOI 10.1007/978-1-4471-3687-3
British Library Cataloguing in Publication Data Adaptive control of nonsmooth dynamie systems
I.Adaptive control systems I.Tao, Gang II.Lewis, Frank L. (Frank Leroy), 1949-629.8'36
Library of Congress Cataloging-in-Publication Data Adaptive control of nonsmooth dynamie systems / Gang Tao and Frank L. Lewis (eds.).
p.cm. Includes bibliographieal references.
1. Adaptive control systems. 2. Dynamics. I. Tao, Gang. 11. Lewis Frank L. TJ217.A3192001 629.8'36--dc21 2001020311
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© Springer-Verlag London 2001 Originally published by Springer-Verlag London limited in 2001
Softcover reprint ofthe hardcover 1st edition 2001
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Preface
Nonsmooth nonlinearities such as backlash, dead-zone, component failure, friction, hysteresis, saturation and time delays are common in industrial control systems. Such nonlinearities are usually poorly known and may vary with time, and they often limit system performance. Control of systems with nonsmooth nonlinearities is an important area of control systems research. A desirable control design approach for such systems should be able to accommodate system uncertainties. Adaptive methods for the control of systems with unknown nonsmooth nonlinearities are particularly attractive in many applications because adaptive control designs are able to provide adaptation mechanisms to adjust controller parameters in the presence of parametric, structural and environment al uncertainties. Most adaptive or nonlinear control techniques reported in the literature are for linear systems or for some classes of systems with smooth nonlinearities, but not for nonsmooth nonlinearities. The need for effective control methods to deal with nonsmooth nonlinear systems has motivated growing research activities in adaptive control of systems with such common practical nonsmooth nonlinearities. Recently, there have been many encouraging new results on adaptive control problems with backlash, dead-zone, failures, friction, hysteresis, saturation, and time delays. This book, entitled Adaptive Control of Nonsmooth Dynamic Systems, is aimed at reflecting the state of the art in designing, analyzing and implementing adaptive control methods which are able to accommodate uncertain nonsmooth nonlinearities in industrial control systems.
Backlash, dead-zone, component failure, friction, hysteresis, saturation, and time delays are the most common nonsmooth nonlinearities in industrial control systems. Backlash, a dynamic (with memory) characteristic, exists in mechanical couplings such as gear trains, and always limits the accuracy of servo-mechanisms. Dead-zone is a static input-output relationship which for a range of input values gives no output; it also limits system performance. Dead-zone characteristics are often present in amplifiers, motors, hydraulic valves and even in biomedical actuation systems. Failures of different types in actuators, sensors and other components of a control system can cause major system performance deterioration. Friction exists wherever there is motion or tendency for motion between two physical components. Friction can cause a steady-state error or a limit cycle near the reference position and stick-slip
vi Preface
phenomenon at low speed in the conventional linear control of positioning systems.
Hysteresis, another dynamic characteristic, exists in electromagnetic and piezoelectric actuators which are used for micromotion control and highaccuracy positioning. Saturation is always a potential problem for actuators of control systems-all actuators do saturate at some level. Actuator saturation affects the transient performance and even leads to system instability. Time delays are also important factors to deal with in order to improve control system performance such as for teleoperations and in real-time computer control systems.
Although backlash, dead-zone, failure, friction, hysteresis, saturation, and time delay characteristics are different, they are all nonsmooth in nature. Therefore, most existing adaptive control methods are not applicable. Unfortunately these nonlinearities can severely limit the performance of feedback systems if not compensated properly. Moreover, adaptive control of dynamic systems with each of these nonsmooth characteristics is a control problem that needs a systematic treatment. It makes the control problem even more challenging when there are more than one nonlinear characteristic present in the control system.
In this book it will be shown how nonsmooth nonlinear industrial characteristics can be adaptively compensated and how desired system performance is achieved in the presence of such nonlinearities. The book has 16 chapters on issues including system modeling, control design, analysis of stability and robustness, simulation and implementation:
Chapter One: New Models and Identiftcation Methods for Backlash and Gear Play, by M. Nordin, P. Bodin and P.-O. Gutman
Chapter Two: Adaptive Dead Zone Inverses for Possibly Nonlinear Control Systems, by E.-W. Bai
Chapter Three: Deadzone Compensation in Motion Control Systems Using Augmented Multilayer Neural Networks, by R. R. Selmic and F. L. Lewis
Chapter Four: On-line Fault Detection, Diagnosis, Isolation and Accommodation of Dynamical Systems with Actuator Failures, by M. A. Demetriou and M. M. Polycarpou
Chapter Five: Adaptive Control of Systems with Actuator Failures, by G. Tao and S. M. Joshi
Chapter Six: Multi-mode System Identification, by E. 1. Verriest
Chapter Seven: On Feedback Control of Processes with "Hard" Nonlinearities, by B. Friedland
Chapter Eight: Adaptive Friction Compensation for Servo Mechanisms, by J. Wang, S. S. Ge and T. H. Lee
Preface vii
Chapter Nine: Relaxed Controls and a Class of Active Material Actuator Models, by A. Kurdila
Chapter Ten: Robust Adaptive Control of Nonlinear Systems with Dynamic Backlash-like Hysteresis, by C.-Y. Su, M. Oya and X.-K. Chen
Chapter Eleven: Adaptive Contral of a Class of Time-delay Systems in the Presence of Saturation, by A. M. Annaswamy, S. Evesque, S.-I. Niculescu and A. P. Dowling
Chapter Twelve: Adaptive Contral for Systems with Input Constraints: A Survey, by J.-W. John Cheng and Y.-M. Wang
Chapter Thirteen: Robust Adaptive Contral of Input Rate Constrained Discrete Time Systems, by G. Feng
Chapter Fourteen: Adaptive Contral of Linear Systems with Poles in the Closed Lejt Half Plane with Constrained Inputs, by D. A. SuarezCerda and R. Lozano
Chapter Fifteen: Adaptive Control with Input Saturation Constraints, by C.-S. Zhang
Chapter Sixteen: Adaptive Control of Linear Systems with Unknown Time Delay, by C.-Y. Wen, Y.-C. Soh and Y. Zhang
The authors of the chapters in this book are experts in their areas of interest and their chapters present new solutions to important issues in adaptive control of industrial systems with nonsmooth nonlinearities such as backlash, dead-zone, failure, friction, hysteresis, saturation, and time delay. These solutions result from recent work in these areas and are believed to be attractive to people from both academia and industry. Adaptive control of nonsmooth dynamical systems is theoretically challenging and practically important. This book is the first book on adaptive control of such systems, addressing all these nonsmooth nonlinear characteristics: backlash, dead-zone, failure, friction, hysteresis, saturation and time delays. Such a book is also aimed at motivating more research activities in the important field of adaptive control of nonsmooth nonlinear industrial systems.
Recent advances in adaptive control of nonsmooth dynamic systems have shown that those practical nonsmooth nonlinear characteristics such as backlash, dead-zone, component failure, friction, hysteresis, saturation and time delays can be adaptively compensated when their parameters are uncertain, as is common in real-life control systems. Rigorous designs have been given for selecting desirable controller structures to meet the control objectives and for deriving suitable algorithms to tune the controller parameters for control of systems with uncertainties in dynamics and nonsmooth nonlinearities. There have been increasing interest and activities in these areas of research, as evidenced by recent conference invited sessions and journal special issues on
viii Preface
related topics. It is clear that this is a promising direction of research and there have been many encouraging results. Given the practical importance and theoretical significance of such research, it is time to summarize, unify, and develop advanced techniques for adaptive control of nonsmooth dynamic systems.
Since this book is about some important and new areas of adaptive control research, its contents are intended for people from both academia and industry, including professors, researchers, graduate students who will use this book for research and advanced study, and engineers who are concerned with the fast and precision control of motion systems with imperfections (such as backlash, dead-zone, component failure, friction, hysteresis, saturation and time delays) in mechanical connections, hydraulic servovalves, piezoelectric translators, and electric servomotors, and biomedical actuators systems. The book can be useful for people from aeronautical, biomedical, civil, chemical, electrical, industrial, mechanical and systems engineering, who are working on aircraft flight control, automobile control, high performance robots, materials growth process control, precision motor control, radar and weapons system pointing platforms, VLSI assembly. The adaptive system theory developed in this book is also of interest to people who work on communication systems, signal processing, real-time computer system modeling and control, biosystem modeling and control.
The first editor would like to gratefully acknowledge the partial support from National Science Foundation under grant ECS-9619363 and National Aeronautics and Space Administration under grant NCC-1342 to this project. He would also like to thank his graduate student Xidong Tang for his editorial assistance on this project. The second editor acknowledges the vital support of the Army Research Office under grant DAAD19-99-1-0137.
Gang Tao Charlottesville, Virginia
Frank L. Lewis Fort Worth, Texas
Contents
Contributors .................................................. xvii
1. N ew Models and Identification Methods for Backlash and
Gear Play
Mattias Nordin, Per Bodin and Per-Olo! Gutman . . . . . . . . . . . . . . . 1
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Backlash Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Physical Model for the Shaft Torque T . . . . . . . . . . . . . . 2
2.2 Phase Plane Backlash Model. . . . . . . . . . . . . . . . . . . . . . . 6
2.3 The Dead Zone Model. ... . ... . .. .. .... .... .... . . . 8
2.4 Model Simulation Comparisons .................... 9
3. Model for Backlash with Rubber ......................... 11
3.1 Shaft Model for Backlash with Rubber. . . . . . . . . . . . .. 12
3.2 Simulations and Measurements: Backlash with Rubber 14
4. Describing Function Analysis ............................ 16
4.1 DIDF Calculations for the Phase Plane Model. . . . . .. 18
4.2 Phase Plane vs. Dead Zone Model. . . . . . . . . . . . . . . . .. 19
5. A Backlash Gap Estimation Method . . . . . . . . . . . . . . . .. . . . .. 21
5.1 Preliminaries and Assumptions. . . . . . . . . . . . . . . . . . . .. 22
5.2 Describing Function Analysis for Identification . . . . . .. 23
5.3 The Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
5.4 Simulation Experiments. . . . . . . . . . . . . . . . . . . . . . . . . .. 26
6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
2. Adaptive Dead Zone Inverses for Possibly
Nonlinear Control Systems
Er- Wei Bai. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
x Contents
2. Problem Formulation ................................... 33
3. Adaptive Dead Zone Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
4. Adaptive Dead Zone Inverse for Linear Control Systems. . . .. 42
4.1 With Known G(s) ... .... .. ... . ...... . . .... .... . .. 42
4.2 With Unknown G(s) . .... .. .. .... . . .... .... .... . .. 45
5. Extension to Nonlinear Control Systems. . . . . . . . . . . . . . . . . .. 45
6. Concluding Remark. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47
3. Deadzone Compensation in Motion Control Systems Using
Augmented Multilayer Neural Networks
Rastko R. S elmic and Frank L. Lewis ......................... 49
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
2. Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
2.1 Dynamics of Mechanical Motion Tracking Systems. . .. 51
3. Neural Networks For Deadzone Compensation. . . . . . . . . . . . .. 52
3.1 Background on Neural Networks ................... 53
3.2 NN Approximation of Continuous Functions . . . . . . . .. 54
3.3 NN Approximation of Jump Functions . . . . . . . . . . . . .. 55
3.4 Structure of Augmented Multilayer NN ............. 59
3.5 Simulation of the Augmented Multilayer NN . . . . . . . .. 60
4. Compensation of Deadzone Nonlinearity.. . . . . . . . . . . . . . . . .. 61
4.1 Deadzone Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4.2 NN Deadzone Precompensator .. .......... . ..... . .. 62
5. NN Controller With Deadzone Compensation . . . .. . . . . . . . .. 66
5.1 Tracking Controller with NN Deadzone Compensation 66
6. Simulation of NN Deadzone Compensator ................. 71
7. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
8. Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81
4. On-line Fault Detection, Diagnosis, Isolation and Accommo
dation of Dynamical Systems with Actuator Failures
Michael A. Demetriou and Marios M. Polycarpou . . . . . . . . . . . . . .. 85
Contents xi
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85
2. Problem Formulation ................................... 87
3. Adaptive Diagnostic Observers . . . . . . . . . . . . . . . . . . . . . . . . . .. 89
3.1 Properties and Analysis of Detection/Diagnostic Ob-server. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 91
4. Fault Accommodation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 95
5. Special Case: Vector Second-order Systems ................ 96
6. Examples and Numerical Results ......................... 102
7. Conclusions ............................................ 108
References ............................................. 108
5. Adaptive Control of Systems with Actuator Failures
Gang Tao and Suresh M. Joshi ............................... 111
1. Introduction ........................................... 111
2. Problem Statement ..................................... 113
3. Plant-Model State Matching Control ...................... 115
3.1 Basic Plant-Model Matching Conditions ............. 116
3.2 Actuator Failure Compensation .................... 117
4. Adaptive State Tracking Control ......................... 119
5. Compensation Designs for Parametrizable Time-varying Fail-
ures .................................................. 123
5.1 Plant-Model Matching Control Design .............. 124
5.2 Adaptive Contral Design .......................... 126
6. Compensation Designs for Unparametrizable Time-varying
Failures ............................................... 128
6.1 Stabilizing Control ............................... 128
6.2 Adaptive Control Design .......................... 131
7. Plant-Model Output Matching Control .................... 133
7.1 State Feedback Designs ........................... 133
7.2 Output Feedback Design .......................... 142
8. Adaptive Output Tracking Control ....................... 145
8.1 State Feedback Designs ........................... 145
8.2 Output Feedback Design .......................... 151
9. Concluding Remarks .................................... 153
References ............................................. 155
xii Contents
6. Multi-mode System Identification
Erik 1. Verriest ............................................. 157
1. Introduction ........................................... 157
2. Subspace Identification Degradation ...................... 160
2.1 Total Least Squares Identification .................. 160
2.2 Degradation in Bi-modal Systems .................. 162
3. Multi-mode ARMA Identification ......................... 163
3.1 Determination of the Mode Parameters ............. 164
3.2 Resolution of the Mode Parameters ............... " 167
4. Multi-mode State Space Identification ..................... 172
4.1 Mode Transitions and Transition Modes . . . . . . . . . . . .. 172
4.2 Identifiability Canonical Form .................... " 174
4.3 Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 177
5. Markov Chain and Hybrid Modeling ..................... 177
5.1 Hidden Markov Model Identification ................ 179
5.2 Hybrid System Modeling .......................... 183
6. Applications ........................................... 184
6.1 Adaptive Control of Nonlinear and Nonsmooth Systems184
6.2 Fault Detection and Isolation ...................... 185
7. Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 186 8. Conclusions ............................................ 187
References ............................................. 189
7. On Feedback Control ofProcesses with 'Hard' Nonlinearities
Bernard Friedland .......................................... 191
1 Introduction ........................................... 191
2 The State-dependent Algebraic Riccati Equation Method .... 192
3 Modeling Hard Nonlinearities ............................ 193
4 Controlling Systems with State Variable Constraints ........ 195
4.1 Illustrative Examples ............................. 195
5 Friction and Backlash Control ............................ 199
5.1 Illustrative Example .............................. 199
5.2 Backlash Control ................................. 205
6 Conclusions ............................................ 208
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
Contents xiii
8. Adaptive Friction Compensation for Servo Mechanisms
J. Wang, S. S. Ge and T. H. Lee ............................. 211
1. Introduction ........................................... 211
2. Friction Models ........................................ 215
2.1 Static models .................................... 215
2.2 Dynamic models ................................. 220
3. Adaptive Friction Compensation ......................... 222
3.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
3.2 Statie Friction Model Based Adaptive Controller Design222
3.3 LuGre Friction Model Based Adaptive Controller Design225
4. Simulation Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
4.1 Statie Model Based Adaptive Control . . . . . . . . . . . . . . . 234
4.2 Dynamic LuGre Friction Model Based Adaptive Control235
5. Conclusion ............................................ 246
Referenees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
9. Relaxed Controls and a Class of Active Material Actuator
Models
A ndrew K urdila . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
1. Introduetion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249
2. The Governing Dynamical Equations ..................... 252
2.1 Infinite Dimensional Struetural Systems ............. 253 2.2 The Control Influenee Operator .................... 255
2.3 Existenee and Uniqueness of Solutions .............. 258
3. Convergent Approximations ............................. 261
3.1 Finite Dimensional Approximation ................. 261
3.2 Approximation of Hysteresis Operator .............. 264
Referenees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
10. Robust Adaptive Control of Nonlinear Systems with Dy
namic Backlash-like Hysteresis
Chun- Yi Su, Masahiro Oya and Xinkai Chen ................... 273
1. Introduetion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
2. Problem Statement ..................................... 274
xiv Contents
3. Backlash-like Hysteresis Model and Its Properties .......... 275
4. Lyapunov-based Control Structure ........................ 276
5. Function Approximation Using Gaussian Functions ......... 278
6. Adaptive Controller Design .............................. 280
7. Simulation Studies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283
8. Conclusion ............................................ 286
Appendix ............................................. 286
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288
11. Adaptive Control of a Class of Time-delay Systems in the
Presence of Saturation
A. M. Annaswamy, S. Evesque, S.-I. Niculescu and A. P. Dowling 289
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
2 Statement of the Problem ............................... 290
3 The Controller in the Presence of Saturation ............... 291
3.1 A First-order Plant ............................... 292
3.2 Output Feedback with n* = 1 ...................... 293
3.3 Output Feedback with n * = 2 . . . . . . . . . . . . . . . . . . . . . . 296
3.4 A Low Order Adaptive Controller . . . . . . . . . . . . . . . . . . 297
4 The Adaptive Controller in the Presence of a Delay ......... 298
4.1 The Controller without Saturation Constraints ....... 298
4.2 The Controller in the Presence of Saturation and
Time-delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
5 Simulation Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 6 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308
References ............................................. 310
12. Adaptive Control for Systems with Input Constraints - A
Survey
J.- W. John Cheng and Yi-Ming Wang . ........................ 311
1. Introduction ........................................... 311
2. History of the Constrained Control Theory ................ 312
2.1 Existence of Stabilizing Magnitude Constrained Control312
2.2 Designs of Effective Magnitude Constrained Control .. 313
Contents xv
3. Adaptive Constrained Control. ........................... 316
3.1 Adaptive Control Designs with Input Magnitude Con-
straint .......................................... 317
3.2 Adaptive Control Design with Input Magnitude and
Rate Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
4. Conclusions ............................................ 328
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
13. Robust Adaptive Control of Input Rate Constrained Dis
crete Time Systems
Gang Feng . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
2. Rate Constrained Pole Placement Adaptive Control ......... 334
2.1 Plant Model ..................................... 334
2.2 Pole Placement Control ........................... 335
2.3 Rate Constrained Pole Placement Adaptive Control .. 336
3. Stability Analysis ....................................... 341
4. A Simulation Example .................................. 344
5. Conclusions ............................................ 347
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
14. Adaptive Control ofLinear Systems with Poles in the Closed LHP with Constrained Inputs
Dionisio A. Suarez-Cerda and Rogelio Lozano .................. 349
1. Introduction ........................................... 349
2. Control of Systems with Constrained Inputs ............... 351
2.1 Plants with no Poles at the Origin .................. 351
2.2 Double Integrator ................................ 352
2.3 Plant with an Integrator and a Stable Pole .......... 353
3. Adaptive Control of Second-order Plants with Constrained
Input ................................................. 354
3.1 Plant Parameter Identification ..................... 354
3.2 Adaptive State Observation ........................ 355
4. Simulations Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
xvi Contents
5. Conclusions ............................................ 358
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
15. Adaptive Control with Input Saturation Constraints
Cishen Zhang . .............................................. 361
1. Introduction ........................................... 361
2. Amplitude Constrained Direct Adaptive ControI ........... 362
3. Stability of Amplitude Constrained Adaptive Control Systems 366
4. Amplitude Constrained Adaptive Contral of Type-1 Plants .. 370
5. Rate Constrained Direct Adaptive Contral ................. 373
6. Stability of Rate Constrained Direct Adaptive Control Systems374
7. Rate Constrained Adaptive Control of Stable Plants ........ 379
8. Conclusion ............................................ 380
References ............................................. 380
16. Adaptive Control of Linear Systems with Unknown Time Delay
Changyun Wen, Yeng Chai Soh and Ying Zhang ................ 383
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383
2. System Models ......................................... 384
3. Adaptive Control Scheme ................................ 388
3.1 Parameter Estimator ............................. 389
3.2 Contral Law Synthesis ............................ 391
4. Stability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
5. Conclusion ............................................ 400
References ............................................. 400
Index ......................................................... 403
Contributors
A. M. Annaswamy Adaptive Control Laboratory
Department of Mechanical Engineering Massachusetts Institute of Technology
Cambridge, MA 02139, USA
Er-Wei Bai Department of Electrical and Computer Engineering The University of Iowa
Iowa City, IA 52242, USA
Per Bodin Space Systems Division Swedish Space Corporation
S-l71 04 Solna, Sweden
Xinkai Chen Department of Information Science Tokyo Denki University Hatoyama-machi, hiki-gun Saitama 350-0394, Japan
J.-W. John Cheng Department of Mechanical Engineering
National Chung Cheng University
Chia Yi, 621, Taiwan, R.O.C.
Michael A. Demetriou Department of Mechanical Engineering
Worcester Polytechnic Institute Worcester, MA 01609-2280, USA
xviii Contributors
A. P. Dowling Department of Engineering University of Cambridge
Cambridge, UK
S. Evesque
Department of Engineering University of Cambridge
Cambridge, UK
Gang Feng
Department of Manufacturing Engineering and Engineering Management City University of Hong Kong
Tat Chee Ave., Kowloon Hong Kong
Bernard Friedland Department of Electrical and Computer Engineering New Jersey Institute of Technology
Newark, NJ 07102, USA
S. S. Ge Department of Electrical and Computer Engineering National University of Singapore 117576, Singapore
Per-Olof Gutman Agricultural Engineering Technion - Israel Institute of Technology
Haifa 32000, Israel
Suresh M. Joshi
Mail Stop 161 NASA Langley Research Center
Hampton, VA 23681, USA
Andrew Kurdila
Department of Aerospace Engineering, Mechanics and Engineering Science
University of Florida
Gainesville, FL 32611-6250, USA
T. H. Lee Department of Electrical and Computer Engineering National University of Singapore 117576, Singapore
Frank L. Lewis
Automation and Robotics Research Institute The university of Texas at Arlington
Fort Worth, Texas, USA
Rogelio Lozano
Heudiasyc UMR CNRS 6599 Universit de Technologie de Compigne
BP 20529 60205 Compigne cedex, France
S.-1. Niculescu
HEUDIASYC University of Compiegne Compiegne, France
Mattias N ordin
Metals and Mining Division
ABB Automation Systems AB S-721 67 Västeras, Sweden
Masahiro Oya Department of Control Engineering Kyushu Institute of Technology 1-1 Sensui, Tobata, Kitakyushu, 804-8550, Japan
Marios M. Polycarpou
Contributors xix
Department of Electrical and Computer Engineering and Computer Science University of Cincinnati
Cincinnati, OH 45221-0030, USA
Rastko R. Selmic
Signalogic, Inc.
9617 Wendell
Dallas, Texas 75243, USA
xx Contributors
Yeng Chai Soh School of Electrical and Electronic Engineering Nanyang Technological University
N anyang Ave. 639798, Singapore
Chun-Yi Su Department of Mechanical Engineering
Concordia University Montreal, Quebec, H3G IM8, Canada
Dionisio A. Suarez-Cerda Instituto de Investigaciones Electricas Av. Reforma No. 113, Col. Palmira
62490 Temixco, Morelos, Mexico
Gang Tao Department of Electrical and Computer Engineering University of Virginia Charlottesville, VA 22903, USA
Erik I. Verriest School of Electrical and Computer Engineering Georgia Institute of Technology Atlanta, GA 30332-0250, USA
J. Wang Department of Electrical and Computer Engineering National University of Singapore Singapore 117576
Yi-Ming Wang
Department of Mechanical Engineering
National Chung Cheng University
Chia Yi, 621
Taiwan, R.O.C.
Changyun Wen School of Electrical and Electronic Engineering
Nanyang Technological University
N anyang Ave. 639798, Singapore
Cishen Zhang Department of Electrical and Electronic Engineering
The University of Melbourne VIC 3010, Australia
Ying Zhang Division of Automation Technology
Gintic Institute of Manufacturing Technology
638075, Singapore
Contributors xxi