Robust Control Design An Optimal Control Approach Feng Lin Wayne State University USA and Tongji University China Robust Control Design RSP SERIES IN CONTROL THEORY AND APPLICATIONS Series Editor Professor Witold Pedrycz Department of Electrical and Computer Engineering University of Alberta Fuzzy Control and Fuzzy Systems Second Extended Edition Witold Pedrycz Robust Control Design An Optimal Control Approach Feng Lin Wayne State University USA and Tongji University China Copyright 2007 Published by Research Studies Press Limited 16 Coach House Cloisters 10 Hitchin Street Baldock Hertfordshire SG7 6AE John Wiley Sons Ltd The Atrium Southern Gate Chichester West Sussex PO19 8SQ England Telephone cid 2 44 cid 3 1243 779777 Email for orders and customer service enquiries cs books wiley co uk Visit our Home Page on www wiley com This work is a co publication between Research Studies Press Limited and John Wiley Sons Ltd All Rights Reserved No part of this publication may be reproduced 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in regard to the subject matter covered It is sold on the understanding that the Publisher is not engaged in rendering professional services If professional advice or other expert assistance is required the services of a competent professional should be sought Other Wiley Editorial Offices John Wiley Sons Inc 111 River Street Hoboken NJ 07030 USA Jossey Bass 989 Market Street San Francisco CA 94103 1741 USA Wiley VCH Verlag GmbH Boschstr 12 D 69469 Weinheim Germany John Wiley Sons Australia Ltd 42 McDougall Street Milton Queensland 4064 Australia John Wiley Sons Asia Pte Ltd 2 Clementi Loop 02 01 Jin Xing Distripark Singapore 129809 John Wiley Sons Canada Ltd 6045 Freemont Blvd Mississauga ONT Canada L5R 4J3 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books Anniversary Logo Design Richard J Pacifico Library of Congress Cataloging in Publication Data Robust control design an optimal control approach Feng Lin Lin Feng p cm Includes index ISBN 978 0 470 03191 9 cloth 1 Automatic control I Title TJ213 L455 2007 629 8 dc22 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 978 0 470 03191 9 HB 2007020129 Typeset in 10 12pt Sabon by Integra Software Services Pvt Ltd Pondicherry India Printed and bound in Great Britain by TJ International Padstow Cornwall This book is printed on acid free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production To Sherry Robert and Nicholas Contents Preface Notation 1 Introduction 1 1 Systems and Control 1 2 Modern Control Theory 1 3 Stability 1 4 Optimal Control 1 5 Optimal Control Approach 1 6 Kharitonov Approach 1 7 H cid 2 and H2 Control 1 8 Applications 1 9 Use of this Book 2 Fundamentals of Control Theory 2 1 State Space Model 2 2 Responses of Linear Systems 2 3 Similarity Transformation 2 4 Controllability and Observability 2 5 Pole Placement by State Feedback 2 6 Pole Placement Using Observer 2 7 Notes and References 2 8 Problems 3 Stability Theory 3 1 Stability and Lyapunov Theorem 3 2 Linear Systems xi xiii 1 1 5 6 8 9 10 11 12 13 15 16 17 25 33 44 52 63 63 69 69 73 viii CONTENTS 3 3 Routh Hurwitz Criterion 3 4 Nyquist Criterion 3 5 Stabilizability and Detectability 3 6 Notes and References 3 7 Problems 4 Optimal Control and Optimal Observers 4 1 Optimal Control Problem 4 2 Principle of Optimality 4 3 Hamilton Jacobi Bellman Equation 4 4 Linear Quadratic Regulator Problem 4 5 Kalman Filter 4 6 Notes and References 4 7 Problems 5 Robust Control of Linear Systems 5 1 Introduction 5 2 Matched Uncertainty 5 3 Unmatched Uncertainty 5 4 Uncertainty in the Input Matrix 5 5 Notes and References 5 6 Problems 6 Robust Control of Nonlinear Systems 6 1 Introduction 6 2 Matched Uncertainty 6 3 Unmatched Uncertainty 6 4 Uncertainty in the Input Matrix 6 5 Notes and References 6 6 Problems 7 Kharitonov Approach 7 1 Introduction 7 2 Preliminary Theorems 7 3 Kharitonov Theorem 7 4 Control Design Using Kharitonov Theorem 7 5 Notes and References 7 6 Problems 8 H cid 2 and H2 Control 8 1 Introduction 8 2 Function Space 8 3 Computation of H2 and H cid 2 Norms 8 4 Robust Control Problem as H2 and H cid 2 Control Problem 75 85 93 98 98 101 101 105 110 112 120 127 127 133 134 137 145 154 169 170 173 174 176 180 188 210 210 213 213 214 227 231 236 236 239 239 240 244 252 CONTENTS 8 5 H2 H cid 2 Control Synthesis 8 6 Notes and References 8 7 Problems 9 Robust Active Damping 9 1 Introduction 9 2 Problem Formulation 9 3 Robust Active Damping Design 9 4 Active Vehicle Suspension System 9 5 Discussion 9 6 Notes and References 10 Robust Control of Manipulators 10 1 Robot Dynamics 10 2 Problem Formulation 10 3 Robust Control Design 10 4 Simulations 10 5 Notes and References 11 Aircraft Hovering Control 11 1 Modelling and Problem Formulation 11 2 Control Design for Jet borne Hovering 11 3 Simulation 11 4 Notes and References Appendix A Mathematical Modelling of Physical Systems References and Bibliography Index ix 256 273 273 277 277 279 282 287 290 295 297 297 302 304 306 316 317 317 322 330 336 339 351 363 Preface The reasons for writing this book are twofold 1 I want to write a book that summarizes the different approaches to robust control design and 2 I need a textbook that covers the topics of modern control theory suitable for a second control course for senior
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