Table Of ContentCONTRIBUTORS TO THIS VOLUME
DARE AFOLABI
M. D. ARDEMA
GEORGE BOJADZIEV
DONG DA
FAYEZM.DAMRA
HENRYK FLASHNER
JONATHAN Ε. GAYEK
RAMESH S. GUTTALU
SHIVP.JOSHI
JAE H.KIM
YEONG CHING LIN
OSITA D. I. NWOKAH
ANDRZEJ OLAS
H.ALI PAK
W. Ε. SCHMITENDORF
KAVEH SHAMS A
G. F. SHANNON
ROWMAU SHIEH
ROBERTE. SKELTON
J. M. SKOWRONSKI
R. J. STONIER
THOMAS L. VINCENT
C. N. WHEELER
C. WILMERS
CONTROL AND
DYNAMIC SYSTEMS
ADVANCES IN THEORY
AND APPLICATIONS
Edited by
C. T. LEONDES
School of Engineering and Applied Science
University of California, Los Angeles
Los Angeles, California
and
College of Engineering
University of Washington
Seattle, Washington
VOLUME 35: ADVANCES IN CONTROL MECHANICS
PART 2 OF 2
ACADEMIC PRESS, INC.
Harcourt Brace Jovanovich, Publishers
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London Sydney Tokyo Toronto
This book is printed on acid-free paper. @
Copyright © 1990 By Academic Press, Inc.
All Rights Reserved.
No part of this publication may be reproduced or transmitted in any form or
by any means, electronic or mechanical, including photocopy, recording, or
any information storage and retrieval system, without permission in writing
from the publisher.
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United Kingdom Edition published by
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Library of Congress Catalog Card Number: 64-8027
ISBN 0-12-012735-0 (alk. paper)
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90 91 92 93 9 8 7 6 5 4 3 2 1
Dedicated to
Drs. George Leitmann and Angelo Miele
appreciation for their many contributions over the
CONTRIBUTORS
Numbers in parentheses indicate the pages on which the authors' contributions begin.
Daré Afolabi (137), School of Engineering and Technology, Purdue University,
Indianapolis, Indiana 46202
M. D. Ardema (235), Santa Clara University, Santa Clara, California
George Bojadziev (215), Mathematics and Statistics Department, Simon Fraser
University, Burnaby, B. C, Canada V5A IS6
Dong Da (65), School of Aeronautics and Astronautics, Purdue University, West
Lafayette, Indiana 47907
Fayez M. Damra (137), School of Aeronautics an Astronautics, Purdue Univer-
sity, West Lafayette, Indiana 47907
Henryk Flashner (xiii, 43), Department of Mechanical Engineering, University of
Southern California, Los Angeles, California 90089-1453
Jonathan E. Gayek (31), Department of Mathematics, Trinity University, San
Antonio, Texas 78284
Ramesh S. Guttalu (xiii), Department of Mechanical Engineering, University of
Southern California, Los Angeles, California 90089
Shiv P. Joshi (87), Aerospace and Mechanical Engineering, University of Ari-
zona, Tucson, Arizona
Jae H. Kim (65), School of Aeronautics and Astronautics, Purdue University,
West Lafayette, Indiana 47907
ix
χ CONTRIBUTORS
Yeong Ching Lin (87), Aerospace and Mechanical Engineering, University of
Arizona, Tucson, Arizona
Osita D. I. Nwokah (137), School of Mechanical Engineering, Purdue University,
West Lafayette, Indiana 47907
Andrzej Olas (1), Oregon State University, Department of Mechanial Engineer-
ing, Corvallis, Oregon 97331
H. Ali Pak (273), Department of Mechanial Engineering, University of Southern
California, Los Angeles, California 90089-1453
W. E. Schmitendorf (165), Mechanical Engineering, University of California,
Irvine, Irvine, California 92714
Kaveh Shamsa (43), Department of Mechanical Engineering, University of
Southern California, Los Angeles, California 90089-1453
G. F. Shannon (295), Associate Professor of Electrical Engineering, University of
Queensland, St Lucia, Queensland, Australia
Rowmau Shieh (273), Department of Mechanial Engineering, University of
Southern California, Los Angeles, California 90089-1453
Robert E. Skelton (65), School of Aeronautics and Astronautics, Purdue Univer-
sity, West Lafayette, Indiana 47907
J. M. Skowronski (xiii, 235), Department of Mechanical Engineering, University
of Southern California, Los Angeles, California 90089
R. J. Stonier (185, 255), Department of Mathematics & Computing, Capricornia
Institute of Advanced Education, Rockhampton, Queensland, Australia 4702
Thomas L. Vincent (87), Aerospace and Mechanical Engineering, University of
Arizona, Tucson, Arizona
C. N. Wheeler (255), Tarong Power Station, Nanango, Queensland, Australia
4610
C. Wilmers (165), Institute for System Dynamics and Control, University of
Stuttgart, Stuttgart, Federal Republic of Germany
PREFACE
Modern technology makes possible amazing things in control and dynamic
systems and will continue to do so to an increasing extent with the passage of
time. It is a fact, however, that control systems go back over the millennia, and
while rudimentary in earlier centuries, they were, generally, enormously effec-
tive. A classic example of this is the Dutch windmill. In any event, this is true
today, and, as just noted, amazing things are now possible. As a result, this vol-
ume and the previous one, Volumes 35 and 34, respectively, in the series Control
and Dynamic Systems, are based on a National Science Foundation-Sponsored
Workshop on Control Mechanics, i.e., control system development using analyti-
cal methods of mechanics and active control of mechanical systems. Publication
of the presentations at this workshop in this Academic Press series has made it
possible to expand them into a format which will facilitate the study and utiliza-
tion of their significant results by working professionals and research workers on
the international scene.
Ordinarily, the preface to the individual volumes in this series presents a sum-
mary of the individual contributions in the respective volumes. In the case of
these two volumes, this is provided by the Introduction, which follows immedi-
ately.
xi
INTRODUCTION
The articles in this volume were presented at the National Science
Foundation-Sponsored Second Workshop on Control Mechanics, held at the
University of Southern California, Los Angeles, January 23-25,1989. This work-
shop is the second in a series devoted to promoting control mechanics, i.e., con-
trol system development using analytical methods of mechanics and active con-
trol of mechanical systems.
Research in control mechanics is motivated by the demands imposed on mod-
ern control systems. The tasks of modern industry in areas like high technology
manufacturing, construction and control of large space structures, and aircraft
control can be accomplished only by precisely controlled and highly autonomous
mechanical systems. These systems are inherently nonlinear due to simultaneous
high speed large motions of multiple interconnected bodies and their complex
interactions with the environment. In addition, weight limits imposed by space-
based systems and power constraints lead to highly flexible structures. High
speed operation combined with structural flexibility necessitates inclusion of both
nonlinear effects and vibrational modes in control law development. Conse-
quently, one needs to apply methods of analytical mechanics to develop an ade-
quate mathematical representation of the system. Then the underlying global
characteristics of the equations of motion must be employed to develop sophisti-
cated multivariable, possibly nonlinear, control laws.
The theme of the above-mentioned promotion of control mechanics is covered
by a wide scope of papers in mechanical systems control theory presented at the
workshop. The topics are arranged in two volumes—seven papers in the first and
thirteen papers in the second. The first two chapters of Part 1 deal with micro-
burst, a severe meteorological condition pertinent to aircraft control. These two
chapters consider the problem of stable control of an aircraft subjected to wind-
shear caused by microburst. New results concerning control of an aircraft under
windshear conditions are given by G. Leitmann and S. Pandey in the first chapter.
xiii
xiv INTRODUCTION
The problem of control during windshear was first posed and has been exten-
sively studied by A. Miele, who kindly accepted the invitation of C. T. Leondes
to present a review of his results in the second chapter. In the third chapter, M.
Corless addresses the issue of designing controllers for uncertain mechanical sys-
tems which are robust against unmodelled flexibility. Results concerning robust
control design without matching conditions are presented by M. S. Chen and M.
Tomizuka in the fourth chapter. Their results are applicable to SISO systems with
disturbances or modelling errors that are either bounded or that have a cone-
bounded growth rate. In the fifth chapter, S. Hui and S. H. Zak deal with the ro-
bust control problem using the variable structure control method. They present a
methodology to design controllers and state observers and analyze their stability
properties.
W. G. Grantham and A. M. Athalye study the control of chaotic systems in the
sixth chapter. This article is concerned with the numerical chaotic behavior which
can occur under feedback control, even with a stabilizing control law. Part 1 con-
cludes with an article by R. S. Guttalu and P. J. Zufria that considers the problem
of finding zeros of a nonlinear vector function, using methods of dynamical sys-
tems analysis. The role of singularities and their effect on the global behavior of
dynamical systems is studied in detail.
Liapunov design method, an approach often used in control mechanics, is the
first topic considered in Part 2. In the first chapter of Part 2, A. Olas studies the
question of finding recursive Liapunov functions for autonomous systems. This is
a sequel to the novel method of "converging series" presented by him at the First
Control Mechanics Workshop in 1988. In the second chapter, J. E. Gayek dis-
cusses a new approach to verifying the existence of stabilizing feedback control
laws for systems with time-delay by using Liapunov functionals. In the third
chapter, K. Shamsa and H. Flashner use the notions of passivity and Liapunov
stability to define a class of discrete-time control laws for mechanical systems.
Their approach is based on the Hamiltonian structure of the equations of motion,
a characteristic common to a wide class of mechanical systems. Reduction in
dimensionality of models is discussed by R. E. Skelton, J. H. Kim, and D. Da in
the fourth chapter. This problem is of interest for controlling high-order mechani-
cal systems such as large space structures and robotic manipulators with struc-
tural flexibility. Regarding the systems with structural flexibility, a new method
of control via active damping augmentation is introduced by T. L. Vincent, Y. C.
Lin, and S. P. Joshi in the fifth chapter. This study is an extension to two-dimen-
sional structures that the authors presented for beams in the First Control Me-
chanics Workshop. O. D. I. Nwokah, D. Afolabi, and F. M. Damra discuss the
modal stability of imperfect cyclic systems in the sixth chapter. The paper is of
particular value in resolving some of the disagreement in the literature concerning
the qualitative behavior of cyclic systems. In the seventh chapter, W. E.
Schmitendorf and C. Wilmers investigate the problem of developing reduced-
INTRODUCTION xv
order stabilizing controllers. They present a numerical algorithm for designing a
minimum-order compensator to stabilize a given plant.
Most of the papers presented in this workshop are applicable to the analysis
and design of robotic manipulators. This field has recently attracted attention in
developing strategies for coordination control of multi-arm systems, adaptive
control of robots, and control of manipulators with varying loads. A numerical
step-by-step collision avoidance technique is proposed and demonstrated by R. J.
Stonier in the eighth chapter. A theoretical basis for collision avoidance using
Liapunov stability theory is investigated by G. Bojadziev in the ninth chapter. In
the tenth chapter, a new method of using differential game approach to coordina-
tion is proposed by M. Ardema and J. M. Skowronski. A single arm problem us-
ing nonlinear Model Reference Adaptive Control studied by R. J. Stonier and C.
N. Wheeler appears in the next chapter. A path-tracking method for control of
mechanical systems is presented by H. A. Pak and R. Shieh in the twelfth chapter.
In this chapter, a class of optimal feedforward tracking controllers have been pro-
posed using preview and feedback control actions. Finally, our Australian partici-
pants presented a number of applications with this field, specifically on how to
use the robotic manipulators in cane-sugar production analysis, sheep shearing,
and the mining industry. The last-mentioned application is discussed in the final
chapter by G. F. Shannon.
The participants of the workshop are in debt to Professor G. Leitmann for initi-
ating this series of meetings; to Professor L. M. Silverman, Dean of the School of
Engineering at the University of Southern California, for supporting and opening
the workshop; the administrative staff of the Mechanical Engineering Depart-
ment, Ms. G. Acosta and Ms. J. Givens, for their invaluable help; and to the editor
of Control and Dynamic Systems, Professor C. T. Leondes, for inviting these pro-
ceedings for publication. The organizing committee gratefully acknowledges a
grant from the National Science Foundation.
Janislaw M. Skowronski
Ramesh S. Guttalu
Henryk Flashner
