APPLIED NONLINEAR CONTROL. Jean-Jacques E Slotine WeipingLi

Transcription

1 APPLIED NONLINEAR CONTROL Jean-Jacques E Slotine WeipingLi

2 Applied Nonlinear Control JEAN-JACQUES E. SLOTlNE Massachusetts Institute of Technology WEIPING LI Massachusetts Institute of Technologv Prentice Hall Englewood Cliffs, New Jersey 07632

3 Library of Congress Cataloging in Publication Data Siotine, I.-I. E. (Jean-Jacques E.) Applied nonlinear control/jean-jacques E. Siotine,Weiping Li p. em. Includes bibliographical references. ISBN , Nonlinear control theory. I. Li, Weiping. QA S '312-dc20 II. Title CIP Editorial/production supervision and interior design: JENNIFER WENZEL Cover design: KAREN STEPHENS Manufacturing Buyer: LORI BULW[N 1991 by Prentice-Hall, Inc. A Division of Simon & Schuster Englewood Cliffs, New Jersey All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Printed in the United States of America ISBN Prentice-Hall International (UK) Limited, London Prentice-Hall of Australia Pty. Limited, Sydney Prentice-Hall Canada Inc., Toronto Prentice-Hall Hispanoamericana, S.A., Mexico Prentice-Hall of India Private Limited, New Delhi Prentice-Hall of Japan, Inc.. Tokyo Simon & Schuster Asia Pte. Ltd., Singapore Editora Prentice-Hall do Brasil, Ltda., Rio de Janeiro

4 Contents Preface xi 1. Introduction Why Nonlinear Control? 1.2 Nonlinear System Behavior 1.3 An Overview of the Book 1.4 Notes and References Part I: Nonlinear Systems Analysis Introduction to Part I Phase Plane Analysis Concepts of Phase Plane Analysis Phase Portraits Singular Points Symmetly in Phase Plane Portraits Constructing Phase Portraits 2.3 Determining Time from Phase Portraits 2.4 Phase Plane Analysis of Linear Systems 2.5 Phase Plane Analysis of Nonlinear Systems 2.6 Existence of Limit Cycles 2.7 Summary 2.8 Notes and References 2.9 Exercises vii

5 viii 3. Fundamentals of Lyapunov Theory Nonlinear Systems and Equilibrium Points 3.2 Concepts of Stability 3.3 Linearization and Local Stability 3.4 Lyapunov's Direct Method Positive Definite Functions and Lyapunov Functions Equilibrium Point Theorems Invariant Set Theorems System Analysis Based on Lyapunov's Direct Method Lyapunov Analysis oflinear Time-Invariant Systems Krasovskii's Method The Variable Gradient Method Physically Motivated Lyapunov Functions Pelformance Analysis Control Design Based on Lyapunov's Direct Method 3.7 Summary 3.8 Notes and References 3.9 Exercises Advanced Stability Theory Concepts of Stability for Non-Autonomous Systems 4.2 Lyapunov Analysis of Non-Autonomous Systems Lyapullov'S Direct Methodfor Non-Autonomous Systems Lyapullov Analysis oflinear Time-Varying Systems * The Linearization Methodfor Non-Autono~ousSystems los ]] * Instability Theorems 4.4 * Existence of Lyapunov Functions 4.5 Lyapunov-Like Analysis Using Barbalat's Lemma Asymptotic Properties offunctions and Their Derivatives Barbalat's Lemma Positive Linear Systems PR and SPR Transfer Functions The Kalman-Yakubovich Lemma Positive Real Transfer Matrices The Passivity Formalism Block Combinations Passivity in Linear Systems

6 4.8 * Absolute Stability * Establishing Boundedness of Signals * Existence and Unicity of Solutions Summary Notes and References Exercises 154 ix 5. Describing Function Analysis Describing Function Fundamentals An Example ofdescribing Function Analysis Applications Domain Basic Assumptions Basic Definitions Computing Describing Functions Common Nonlinearities In Control Systems Describing Functions of Common Nonlinearities Describing Function Analysis of Nonlinear Systems The Nyquist Criterion andits Extension Existence oflimit Cycles Stability oflimit Cycles Reliability ofdescribing Function Analysis Summary Notes and References Exercises 188 Part II: Nonlinear Control Systems Design 191 Introduction to Part II Feedback Linearization Intuitive Concepts Feedback Linearization And The Canonical Form Input-State Linearization Input-Output Linearization Mathematical Tools Input-State Linearization of SISO Systems 236

7 x 6.4 Input-Output Linearization of SISO Systems 6.5 * Multi-Input Systems 6.6 Summary 6.7 Notes and References 6.8 Exercises Sliding Control Sliding Surfaces A Notational Simplification * Filippov,s Construction ofthe Equivalent Dynamics Pe/fect Peiformance - At a Price Direct 1mplementations ofswitching Control Laws 7.2 Continuous Approximations of Switching Control Laws 7.3 The Modeling/Perfonnance Trade-Offs 7.4 * Multi-Input Systems 7.5 Summary 7.6 Notes and References 7.7 Exercises Adaptive Control Basic Concepts in Adaptive Control Why Adaptive Control? What 1s Adaptive Control? How To Design Adaptive Controllers? Adaptive Control of First-Order Systems 8.3 Adaptive Control of Linear Systems With Full State Feedback 8.4 Adaptive Control of Linear Systems With Output Feedback Linear Systems With Relative Degree One Linear Systems With Higher Relative Degree Adaptive Control ofnonlinear Systems 8.6 Robustness of Adaptive Control Systems 8.7 * On-Line Parameter Estimation Linear Parametrization Model Prediction-Error-Based Estimation Methods The Gradient Estimator The Standard Least-Squares Estimator

8 8.7.5 Least-Squares With Exponential Forgetting Bounded-Gain Forgetting Concluding Remarks and Implementation Issues Composite Adaptation Summary Notes and References Exercises 389 xi 9. Control of Multi-Input Physical Systems Robotics as a Prototype Position Control Trajectory Control Adaptive Robot Trajectory Control The Basic Algorithm * Composite Adaptive Trajectory Control Putting Physics in Control High-Frequency Unmodeled Dynamics Conservative and Dissipative Dynamics Robotics as a Metaphor Spacecraft Control The Spacecraft Model Attitude Control Summary Notes and References Exercises 433 BIBLIOGRAPHY 437 INDEX 459

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