Table Of ContentAdaptive Control ofNonsmooth
Dynamic Systems
Springer-Verlag London Ltd.
Gang Tao and Frank L. Lewis (Eds)
Adaptive Control
of Nonsmooth
Dynamic Systems
With 102 Figures
, Springer
Gang Tao, PhD
Department of Electrical and Computer Engineering, University of Virginia,
Charlottesville, VA 22903, USA
Frank 1. Lewis, PhD
Automation and Robotics Research Institute, University of Texas at Arlington,
Fort Worth, TX 76118, USA
ISBN 978-1-84996-869-0 ISBN 978-1-4471-3687-3 (eBook)
DOI 10.1007/978-1-4471-3687-3
British Library Cataloguing in Publication Data
Adaptive control of nonsmooth dynamie systems
I.Adaptive control systems
I.Tao, Gang II.Lewis, Frank L. (Frank Leroy), 1949-
629.8'36
Library of Congress Cataloging-in-Publication Data
Adaptive control of nonsmooth dynamie systems / Gang Tao and Frank L. Lewis (eds.).
p.cm.
Includes bibliographieal references.
1. Adaptive control systems. 2. Dynamics. I. Tao, Gang. 11. Lewis Frank L.
TJ217.A3192001
629.8'36--dc21 2001020311
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Originally published by Springer-Verlag London limited in 2001
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Preface
Nonsmooth nonlinearities such as backlash, dead-zone, component failure,
friction, hysteresis, saturation and time delays are common in industrial con
trol systems. Such nonlinearities are usually poorly known and may vary
with time, and they often limit system performance. Control of systems with
nonsmooth nonlinearities is an important area of control systems research. A
desirable control design approach for such systems should be able to accom
modate system uncertainties. Adaptive methods for the control of systems
with unknown nonsmooth nonlinearities are particularly attractive in many
applications because adaptive control designs are able to provide adaptation
mechanisms to adjust controller parameters in the presence of parametric,
structural and environment al uncertainties. Most adaptive or nonlinear con
trol techniques reported in the literature are for linear systems or for some
classes of systems with smooth nonlinearities, but not for nonsmooth nonlin
earities. The need for effective control methods to deal with nonsmooth non
linear systems has motivated growing research activities in adaptive control
of systems with such common practical nonsmooth nonlinearities. Recently,
there have been many encouraging new results on adaptive control problems
with backlash, dead-zone, failures, friction, hysteresis, saturation, and time
delays. This book, entitled Adaptive Control of Nonsmooth Dynamic Systems,
is aimed at reflecting the state of the art in designing, analyzing and imple
menting adaptive control methods which are able to accommodate uncertain
nonsmooth nonlinearities in industrial control systems.
Backlash, dead-zone, component failure, friction, hysteresis, saturation,
and time delays are the most common nonsmooth nonlinearities in industrial
control systems. Backlash, a dynamic (with memory) characteristic, exists in
mechanical couplings such as gear trains, and always limits the accuracy of
servo-mechanisms. Dead-zone is a static input-output relationship which for
a range of input values gives no output; it also limits system performance.
Dead-zone characteristics are often present in amplifiers, motors, hydraulic
valves and even in biomedical actuation systems. Failures of different types in
actuators, sensors and other components of a control system can cause major
system performance deterioration. Friction exists wherever there is motion
or tendency for motion between two physical components. Friction can cause
a steady-state error or a limit cycle near the reference position and stick-slip
vi Preface
phenomenon at low speed in the conventional linear control of positioning
systems.
Hysteresis, another dynamic characteristic, exists in electromagnetic and
piezoelectric actuators which are used for micromotion control and high
accuracy positioning. Saturation is always a potential problem for actuators of
control systems-all actuators do saturate at some level. Actuator saturation
affects the transient performance and even leads to system instability. Time
delays are also important factors to deal with in order to improve control
system performance such as for teleoperations and in real-time computer
control systems.
Although backlash, dead-zone, failure, friction, hysteresis, saturation, and
time delay characteristics are different, they are all nonsmooth in nature.
Therefore, most existing adaptive control methods are not applicable. Unfor
tunately these nonlinearities can severely limit the performance of feedback
systems if not compensated properly. Moreover, adaptive control of dynamic
systems with each of these nonsmooth characteristics is a control problem
that needs a systematic treatment. It makes the control problem even more
challenging when there are more than one nonlinear characteristic present in
the control system.
In this book it will be shown how nonsmooth nonlinear industrial charac
teristics can be adaptively compensated and how desired system performance
is achieved in the presence of such nonlinearities. The book has 16 chapters
on issues including system modeling, control design, analysis of stability and
robustness, simulation and implementation:
Chapter One: New Models and Identiftcation Methods for Backlash
and Gear Play, by M. Nordin, P. Bodin and P.-O. Gutman
Chapter Two: Adaptive Dead Zone Inverses for Possibly Nonlinear
Control Systems, by E.-W. Bai
Chapter Three: Deadzone Compensation in Motion Control Systems
Using Augmented Multilayer Neural Networks, by R. R. Selmic and
F. L. Lewis
Chapter Four: On-line Fault Detection, Diagnosis, Isolation and Ac
commodation of Dynamical Systems with Actuator Failures, by M.
A. Demetriou and M. M. Polycarpou
Chapter Five: Adaptive Control of Systems with Actuator Failures,
by G. Tao and S. M. Joshi
Chapter Six: Multi-mode System Identification, by E. 1. Verriest
Chapter Seven: On Feedback Control of Processes with "Hard" Non
linearities, by B. Friedland
Chapter Eight: Adaptive Friction Compensation for Servo Mecha
nisms, by J. Wang, S. S. Ge and T. H. Lee
Preface vii
Chapter Nine: Relaxed Controls and a Class of Active Material Ac
tuator Models, by A. Kurdila
Chapter Ten: Robust Adaptive Control of Nonlinear Systems with
Dynamic Backlash-like Hysteresis, by C.-Y. Su, M. Oya and X.-K.
Chen
Chapter Eleven: Adaptive Contral of a Class of Time-delay Systems
in the Presence of Saturation, by A. M. Annaswamy, S. Evesque, S.-I.
Niculescu and A. P. Dowling
Chapter Twelve: Adaptive Contral for Systems with Input Con
straints: A Survey, by J.-W. John Cheng and Y.-M. Wang
Chapter Thirteen: Robust Adaptive Contral of Input Rate Con
strained Discrete Time Systems, by G. Feng
Chapter Fourteen: Adaptive Contral of Linear Systems with Poles in
the Closed Lejt Half Plane with Constrained Inputs, by D. A. Suarez
Cerda and R. Lozano
Chapter Fifteen: Adaptive Control with Input Saturation Constraints,
by C.-S. Zhang
Chapter Sixteen: Adaptive Control of Linear Systems with Unknown
Time Delay, by C.-Y. Wen, Y.-C. Soh and Y. Zhang
The authors of the chapters in this book are experts in their areas of inter
est and their chapters present new solutions to important issues in adaptive
control of industrial systems with nonsmooth nonlinearities such as backlash,
dead-zone, failure, friction, hysteresis, saturation, and time delay. These solu
tions result from recent work in these areas and are believed to be attractive to
people from both academia and industry. Adaptive control of nonsmooth dy
namical systems is theoretically challenging and practically important. This
book is the first book on adaptive control of such systems, addressing all
these nonsmooth nonlinear characteristics: backlash, dead-zone, failure, fric
tion, hysteresis, saturation and time delays. Such a book is also aimed at
motivating more research activities in the important field of adaptive control
of nonsmooth nonlinear industrial systems.
Recent advances in adaptive control of nonsmooth dynamic systems have
shown that those practical nonsmooth nonlinear characteristics such as back
lash, dead-zone, component failure, friction, hysteresis, saturation and time
delays can be adaptively compensated when their parameters are uncertain,
as is common in real-life control systems. Rigorous designs have been given for
selecting desirable controller structures to meet the control objectives and for
deriving suitable algorithms to tune the controller parameters for control of
systems with uncertainties in dynamics and nonsmooth nonlinearities. There
have been increasing interest and activities in these areas of research, as ev
idenced by recent conference invited sessions and journal special issues on
viii Preface
related topics. It is clear that this is a promising direction of research and
there have been many encouraging results. Given the practical importance
and theoretical significance of such research, it is time to summarize, unify,
and develop advanced techniques for adaptive control of nonsmooth dynamic
systems.
Since this book is about some important and new areas of adaptive con
trol research, its contents are intended for people from both academia and
industry, including professors, researchers, graduate students who will use this
book for research and advanced study, and engineers who are concerned with
the fast and precision control of motion systems with imperfections (such as
backlash, dead-zone, component failure, friction, hysteresis, saturation and
time delays) in mechanical connections, hydraulic servovalves, piezoelectric
translators, and electric servomotors, and biomedical actuators systems. The
book can be useful for people from aeronautical, biomedical, civil, chemical,
electrical, industrial, mechanical and systems engineering, who are working
on aircraft flight control, automobile control, high performance robots, ma
terials growth process control, precision motor control, radar and weapons
system pointing platforms, VLSI assembly. The adaptive system theory de
veloped in this book is also of interest to people who work on communication
systems, signal processing, real-time computer system modeling and control,
biosystem modeling and control.
The first editor would like to gratefully acknowledge the partial support
from National Science Foundation under grant ECS-9619363 and National
Aeronautics and Space Administration under grant NCC-1342 to this project.
He would also like to thank his graduate student Xidong Tang for his editorial
assistance on this project. The second editor acknowledges the vital support
of the Army Research Office under grant DAAD19-99-1-0137.
Gang Tao
Charlottesville, Virginia
Frank L. Lewis
Fort Worth, Texas
Contents
Contributors .................................................. xvii
1. N ew Models and Identification Methods for Backlash and
Gear Play
Mattias Nordin, Per Bodin and Per-Olo! Gutman . . . . . . . . . . . . . . . 1
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Backlash Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.1 Physical Model for the Shaft Torque T . . . . . . . . . . . . . . 2
2.2 Phase Plane Backlash Model. . . . . . . . . . . . . . . . . . . . . . . 6
2.3 The Dead Zone Model. ... . ... . .. .. .... .... .... . . . 8
2.4 Model Simulation Comparisons .................... 9
3. Model for Backlash with Rubber ......................... 11
3.1 Shaft Model for Backlash with Rubber. . . . . . . . . . . . .. 12
3.2 Simulations and Measurements: Backlash with Rubber 14
4. Describing Function Analysis ............................ 16
4.1 DIDF Calculations for the Phase Plane Model. . . . . .. 18
4.2 Phase Plane vs. Dead Zone Model. . . . . . . . . . . . . . . . .. 19
5. A Backlash Gap Estimation Method . . . . . . . . . . . . . . . .. . . . .. 21
5.1 Preliminaries and Assumptions. . . . . . . . . . . . . . . . . . . .. 22
5.2 Describing Function Analysis for Identification . . . . . .. 23
5.3 The Estimation Method . . . . . . . . . . . . . . . . . . . . . . . . . .. 25
5.4 Simulation Experiments. . . . . . . . . . . . . . . . . . . . . . . . . .. 26
6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 29
2. Adaptive Dead Zone Inverses for Possibly
Nonlinear Control Systems
Er-Wei Bai. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 31
x Contents
2. Problem Formulation ................................... 33
3. Adaptive Dead Zone Inverse . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34
4. Adaptive Dead Zone Inverse for Linear Control Systems. . . .. 42
4.1 With Known G(s) ... .... .. ... . ...... . . .... .... . .. 42
4.2 With Unknown G(s) . .... .. .. .... . . .... .... .... . .. 45
5. Extension to Nonlinear Control Systems. . . . . . . . . . . . . . . . . .. 45
6. Concluding Remark. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 47
3. Deadzone Compensation in Motion Control Systems Using
Augmented Multilayer Neural Networks
Rastko R. S elmic and Frank L. Lewis ......................... 49
1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 50
2. Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 51
2.1 Dynamics of Mechanical Motion Tracking Systems. . .. 51
3. Neural Networks For Deadzone Compensation. . . . . . . . . . . . .. 52
3.1 Background on Neural Networks ................... 53
3.2 NN Approximation of Continuous Functions . . . . . . . .. 54
3.3 NN Approximation of Jump Functions . . . . . . . . . . . . .. 55
3.4 Structure of Augmented Multilayer NN ............. 59
3.5 Simulation of the Augmented Multilayer NN . . . . . . . .. 60
4. Compensation of Deadzone Nonlinearity.. . . . . . . . . . . . . . . . .. 61
4.1 Deadzone Nonlinearity . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61
4.2 NN Deadzone Precompensator .. .......... . ..... . .. 62
5. NN Controller With Deadzone Compensation . . . .. . . . . . . . .. 66
5.1 Tracking Controller with NN Deadzone Compensation 66
6. Simulation of NN Deadzone Compensator ................. 71
7. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 77
8. Appendix. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 81
4. On-line Fault Detection, Diagnosis, Isolation and Accommo
dation of Dynamical Systems with Actuator Failures
Michael A. Demetriou and Marios M. Polycarpou . . . . . . . . . . . . . .. 85
