Lecture Notes in Control and Information Sciences Editors: M. Thoma · M. Morari 298 Springer Berlin Heidelberg NewYork Hong Kong London Milan Paris Tokyo Youngjin Choi Wan Kyun Chung PID Trajectory Tracking Control for Mechanical Systems With 22 Figures and 12 Tables 13 Series Advisory Board A. Bensoussan · P. Fleming · M.J. Grimble · P. Kokotovic · A.B. Kurzhanski · H. Kwakernaak · J.N. Tsitsiklis Authors Dr. Youngjin Choi Korea Institute of Science and Technology (KIST) Intelligent Robotics Research Center Sungbuk-Gu, Seoul, 136-791, Korea E-Mail:
[email protected] Prof. Wan Kyun Chung Pohang University of Science and Technology (POSTECH) Dept. of Mechanical Engineering San 31, Hyoja-Dong Pohang, 790-784, Korea E-Mail:
[email protected] ISSN 0170-8643 ISBN 3-540-20567-5 Springer-Verlag Berlin Heidelberg New York Cataloging-in-Publication Data applied for A catalog record for this book is available from the Library of Congress. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at . This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under German Copyright Law. Springer-Verlag is a part of Springer Science+Business Media springeronline.com © Springer-Verlag Berlin Heidelberg 2004 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Data conversion by the authors. Final processing by PTP-Berlin Protago-TeX-Production GmbH, Berlin Cover-Design: design & production GmbH, Heidelberg Printed on acid-free paper 62/3020Yu - 5 4 3 2 1 0 I would like to dedicate this book to my parents, to my daughter Yuhyun and to my wife Seoyoung. - Dr. Youngjin Choi For Jinhwa and Kiseo, my family. - Dr Wan Kyun Chung Preface Though PID control has a long history as much as its life force since Ziegler and Nichols published the empirical tuning rules in 1942, surprisingly, it has never been changed in the structure itself. The strength of PID control lies in the simplicity, lucid meaning, and clear effect. Though it must be a widely accepted controller for mechanical control systems, it is still short of theoretical bases, e.g., optimality, performance tuning rules, automatic performance tuning method, and output feedback PID control have not been clearly presented for mechanical control systems. These subjects will be thoroughly discussed in this book. There are many books of PID controller for the purpose of process control, but it is hard to find a book on the characteristics of PID control for mechanical systems. In the first place, when nonlinear optimal control theory is applied to mechanical systems, a class of Hamilton-Jacobi (HJ) equations is derived as a result of optimization. There are two methods to solve a class of HJ