Time-Varying Sliding Modes for Second and Third Order Systems

A principal objective of control engineering is to design control systems which are robust with respect to external disturbances and modelling uncertainty. This objective may be well achieved using the sliding mode technique - which is the main subject of

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Andrzej Bartoszewicz, Aleksandra Nowacka-Leverton

Time-Varying Sliding Modes for Second and Third Order Systems

ABC

Series Advisory Board P. Fleming, P. Kokotovic, A.B. Kurzhanski, H. Kwakernaak, A. Rantzer, J.N. Tsitsiklis

Authors Prof. Andrzej Bartoszewicz Institute of Automatic Control Technical University of Łód´z 18/22 Stefanowskiego St. 90-924 Łód´z Poland E-Mail: [email protected]

Dr. Aleksandra Nowacka-Leverton Institute of Automatic Control Technical University of Łód´z 18/22 Stefanowskiego St. 90-924 Łód´z Poland E-Mail: [email protected]

ISBN 978-3-540-92216-2

e-ISBN 978-3-540-92217-9

DOI 10.1007/978-3-540-88063-9 Lecture Notes in Control and Information Sciences

ISSN 0170-8643

Library of Congress Control Number: 2008910998 c 2009 

Springer-Verlag Berlin Heidelberg

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 any other way, 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. Violations are liable for prosecution under the German Copyright Law. 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. Typeset & Cover Design: Scientific Publishing Services Pvt. Ltd., Chennai, India. Printed in acid-free paper 543210 springer.com

Acknowledgments Contents

Our work presented in this book was developed with the kind support of the Polish State budget provided in the years 2008 – 2010, under the research project “Design of the switching surfaces for the sliding mode control of dynamic plants” (N N514 300035). This work was also possible due to the generous help of the Foundation for Polish Science (FNP). The financial assistance of the Foundation, given to the second author of this monograph, Aleksandra Nowacka-Leverton under the Young Researcher Support program, is gratefully acknowledged. Furthermore, a few projects sponsored by the Polish State Committee for Scientific Research and Polish Ministry of Science and Higher Education in the past 12 years, also helped initiate and – to some extent – develop many ideas reported in this book. The research reported in this monograph has benefited greatly from collaboration with a number of PhD students and many friends at Institute of Automatic Control, Technical University of ŁódĨ, Poland. Therefore, we wish to thank all of them for their encouragement, cooperation and stimulating discussions while we were preparing this book. In particular, we wish to thank Prof. Piotr Ostalczyk for his comments on essential parts of the book, and Ms.