Nonlinear Control of Engineering Systems: A Lyapunov-Based Approach

409 Pages·2003·10.878 MB·English

by  Warren E. Dixon, Aman Behal, Darren M. Dawson, Siddharth P. Nagarkatti (auth.)

Control Engineering
Series Editor
William S. Levine
Department of Electrical and Computer Engineering
University of Maryland
College Park, MD 20742-3285
USA
Editorial Advisory Board
Okko Bosgra William Powers
Delft University Ford Motor Company (retired)
The Netherlands USA
Graham Goodwin Mark Spong
University of Newcastle University of Illinois
Australia Urbana-Champaign
USA
Petar Kokotovic
University of California lori Hashimoto
Santa Barbara Kyoto University
USA Kyoto, Japan
Manfred Morari
ETH
ZUrich, Switzerland
Warren E. Dixon
Arnan Behal
Darren M. Dawson
Siddharth P. Nagarkatti
Nonlinear Control
of Engineering Systems
A Lyapunov-BasedApproach
Springer Science+Business Media, LLC
Warren E. Dixon AmanBehal
Oak Ridge National Laboratory Clemson University
Engineering Science and Department of Electrical and
Technology Division Computer Engineering
Oak Ridge, TN 37831 Clemson, SC 29634-0915
USA USA
Darren M. Dawson Siddharth P. Nagarkatti
Clemson University MKS Instruments
Department of Electrical and Advanced Technology Group
Computer Engineering Methuen, MA 01844
Clemson, SC 29634-0915 USA
USA
Library of Congress Cataloging-in-Publication Data
Nonlinear Control of engineering systems: a Lyapunov-based approach 1 Warren E. Dixon
... let ai.].
p. cm. - (Control engineering)
Includes bibliographical references and index.
ISBN 978-1-4612-6581-8 ISBN 978-1-4612-0031-4 (eBook)
DOI 10.1007/978-1-4612-003 1-4
1. Automatic control. 2. Nonlinear control theory. 3. Lyapunov functions. I. Dixon,
Warren E., 1972-II. Control engineering (Birkhliuser)
TJ213.N568 2003
629.8'36-dc21
2003045389
CIP
Printed on acid-free paper.
102003 Springer Science+Business Media New York
Originally published by Birkhliuser Boston in 2003
Softcover reprint of the hardcover 1st edition 2003
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher Springer Science+Business Media, LLC,
except for brief excerpts in connection with reviews or scholarly analysis.
Use in connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use of general descriptive names, trade names, trademarks, etc., in this pUblication, even if the former
are not especially identified, is not to be taken as a sign that such names, as understood by the Trade Marks
and Merchandise Marks Act, may accordingly be used freely by anyone.
ISBN 978-1-4612-6581-8 SPIN 10852085
Typeset by the authors.
987 6 5 4 3 2 1
To my beautiful son, Ethan Noel Dixon
-Warren
To my parents, Swaran and Ashwani K. Behal
-Arnan
To my faithful wife, Dr. Kim Dawson
-Darren
To my loving wife, Meghana S. Nagarkatti
-Siddharth
Contents
Preface xiii
1 Introduction 1
1.1 Pitfalls of Linear Control ...... 1
1.1.1 Limitations of Linearization . 2
1.1.2 Dangers of Destabilization. . 6
1.2 Lyapunov-Based Control. . . . . . . 9
1.2.1 Exact Model Knowledge Example 9
1.2.2 Simulation Results 11
1.2.3 Adaptive Example 14
1.2.4 Simulation Results 15
1.3 Summary 18
References . . . . . 18
2 Mechanical Systems 21
2.1 Introduction. . . . 21
2.2 Autobalancing Systems 23
2.2.1 System Model. . 24
2.2.2 Control Objective 27
2.2.3 Adaptive Control . 28
2.2.4 DCAL-Based Adaptive Control 30
2.2.5 Experimental Setup and Results 39
viii Contents
2.3 Dynamically Positioned Ships . . . . . . . . . 47
2.3.1 System Model ............. . 47
2.3.2 Adaptive Full-State Feedback Control 50
2.3.3 Adaptive Output Feedback Control. 53
2.3.4 Simulation Results 60
2.4 Euler-Lagrange Systems 63
2.4.1 System Model. . . 63
2.4.2 Control Objective 68
2.4.3 Quaternion-Based Control. 69
2.4.4 UUV Extension. . . . . . . 73
2.4.5 Simulation Results ..... 77
2.5 Background and Further Reading . 83
References . . . 85
3 Electric Machines 91
3.1 Introduction.. 91
3.2 Induction Motor ... 94
3.2.1 System Model. 95
3.2.2 Control Objective 96
3.2.3 Standard IFOC Control 97
3.2.4 Improved IFOC Control 98
3.2.5 Adaptive Extension .. 103
3.2.6 Experimental Setup and Results 105
3.3 Switched Reluctance Motor 109
3.3.1 System Model. . . . . . . . 110
3.3.2 Control Objective ..... 111
3.3.3 Adaptive Tracking Control 111
3.3.4 Commutation Strategy. . . 118
3.3.5 Experimental Setup and Results 123
3.4 Active Magnetic Bearings . . . 128
3.4.1 System Model. . . . . . 129
3.4.2 AMB Tracking Control 134
3.4.3 Commutation Strategy. 139
3.5 Background and Further Reading. 141
References . . 143
4 Robotic Systems 149
4.1 Introduction........... 149
4.2 Learning Control Applications. 151
4.2.1 General Problem .... 153
4.2.2 Robot Control Problem 156
Contents ix
4.2.3 Experimental Setup and Results 162
4.3 Position and Force Control Applications 165
4.3.1 System Model ........ . 166
4.3.2 Control Objective ..... . 172
4.3.3 Full-State Feedback Control 173
4.3.4 Output Feedback Control . . 178
4.3.5 Experimental Setup and Results 183
4.4 Visual Servo Control Application 187
4.4.1 System Model ......... . 187
4.4.2 Control Objective ...... . 191
4.4.3 Adaptive Control Development 192
4.4.4 Redundant Robot Extension 198
4.4.5 Camera-in-Hand Extension .. 200
4.4.6 Experimental Setup and Results 204
4.5 Background and Further Reading. 213
References . . . . 215
5 Aerospace Systems 223
5.1 Introduction... 223
5.2 Attitude Tracking ... 225
5.2.1 System Model. 226
5.2.2 Control Objective 231
5.2.3 Adaptive Full-State Feedback Control 231
5.2.4 Adaptive Output Feedback Controller 234
5.2.5 Simulation Results ...... . 240
5.3 Energy /Power and Attitude Tracking. 240
5.3.1 System Model ... 243
5.3.2 Control Objective 243
5.3.3 Adaptive IPACS 245
5.3.4 Stability Analysis. 247
5.3.5 Simulation Results 248
5.4 Formation Flying . . . . . 252
5.4.1 System Model ... 253
5.4.2 Control Objective 256
5.4.3 MSFF Control . . 257
5.4.4 Stability Analysis. 257
5.4.5 Simulation Results 259
5.5 Background and Further Reading. 260
References . . . . . . . . . . . . . . 264
x Contents
6 Underactuated Systems 269
6.1 Introduction. . . . . . 269
6.2 Overhead Crane Systems 271
6.2.1 System Model. . . 271
6.2.2 Open-Loop Error System 273
6.2.3 Control Design and Analysis 276
6.2.4 Experimental Setup and Results 283
6.3 VTOL Systems ...... 287
6.3.1 System Model. . . . . . . 288
6.3.2 Control Objective · ... 290
6.3.3 Open-Loop Error System 291
6.3.4 Control Development. . . 292
6.3.5 Closed-Loop Error System. 294
6.3.6 Stability Analysis. . . . . . 295
6.3.7 Simulation Results . . . . . 299
6.3.8 Automotive Steering Extension 302
6.3.9 Surface Vessel Extension. 306
6.4 Satellite Systems ..... 310
6.4.1 System Model. . . . . . . 311
6.4.2 Control Objective · ... 311
6.4.3 Open-Loop Error System 313
6.4.4 Kinematic Control · ... 314
6.4.5 Closed-Loop Error System . 315
6.4.6 Stability Analysis. . . . . . 315
6.4.7 Axisymmetric Satellite Extension . 318
6.4.8 Simulation Results . . . . . 320
6.5 Background and Further Reading . 324
References . ............. 330
Appendices 335
A Mathematical Background 337
References . . . . . . . . . · ........ .......... 344
B Supplementary Lemmas and Definitions 345
B.1 Chapter 2 Lemmas . . . . . . . . . . . . . ...... 345
B.l.1 Convolution Operations for Torque Filtering 345
B.1.2 Control Signal Bound 346
B.1.3 Control Signal Bound 347
B.1.4 Control Signal Bound 349
B.1.5 Inequality Proofs . . . 354
Contents Xl
B.1.6 Control Signal Bounds .. . 357
B.1.7 Matrix Property ..... . 358
B.2 Chapter 3 Definitions and Lemmas 359
B.2.1 Supplemental Definitions . 359
B.2.2 Stability Analysis for Projection Cases. 359
B.2.3 Dynamic Terms for a 6-DOF AMB System 361
B.2.4 Partial Derivative Definitions 363
B.3 Chapter 4 Lemmas . . . . . . . . . . . . . . . . 364
B.3.1 Inequality Lemma . . . . . . . . . . . . 364
B.3.2 Stability Analysis for Projection Cases. 366
B.3.3 Boundedness Lemma ......... . 367
B.3.4 State-Dependent Disturbance Bound . 369
B.3.5 Matrix Property .... . 372
BA Chapter 5 Lemmas ....... . 373
BA.1 Skew-Symmetry Property 373
BA.2 Control Signal Bound .. 374
B.5 Chapter 6 Definitions and Lemmas 375
B.5.1 Definitions for Dynamic Terms 375
B.5.2 Linear Control Law Analysis . 376
B.5.3 Coupling Control Law Analysis 387
B.5.4 Matrix Property 389
References . 389
Index 391