Robust Control System Design: Advanced State Space Techniques

308 Pages·2003·2.09 MB·English

by  Aman Ullah

Robust Control
System Design
Advanced State
Space Techniques
Second Edition, Revised and Expanded
Chia-Chi Tsui
DeVly Znstitute of Technology
Long Island City, New York, U.S.A.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
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caused or alleged to be caused by this book. The material contained herein is not
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ISBN: 0-8247-4869-7
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Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
CONTROL ENGINEERING
A Series of Reference Books and Textbooks
Editors
NEIL MUNRO, PH.D., D.Sc.
Professor
Applied Control Engineering
University of Manchester Institute of Science and Technology
Manchester, United Kingdom
FRANK L. LEWIS, PH.D.
Moncrief-O'Donnell Endowed Chair
and Associate Director of Research
Automation & Robotics Research Institute
University of Texas, Arlington
1. Nonlinear Control of Electric Machinery, Darren M. Dawson, Jun Hu,
and Timothy C. Burg
2. Computational Intelligence in Control Engineering, Robert E. King
3. Quantitative Feedback Theory: Fundamentals and Applications, Con-
stantine H. Houpis and Steven J. Rasmussen
4. Self-Learning Control of Finite Markov Chains, A. S. Poznyak, K. Najim,
and E. Gomez-Ramirez
5. Robust Control and Filtering for Time-Delay Systems, Magdi S. Mah-
moud
6. Classical Feedback Control: With MATLAB, Boris J. Lurie and Paul J.
Enright
7. Optimal Control of Singularly Perturbed Linear Systems and
Applications: High-Accuracy Techniques, Zoran Gajic' and Myo-Taeg
Lim
8. Engineering System Dynamics: A Unified Graph-Centered Approach,
Forbes T. Brown
9. Advanced Process Identification and Control, Enso lkonen and
Kaddour Najim
10. Modern Control Engineering, P. N. Paraskevopoulos
11. Sliding Mode Control in Engineering, edited by Wilfrid Perruquetti and
Jean Pierre Barbot
12. Actuator Saturation Control, edited by Vikram Kapila and Karolos M.
Grigoriadis
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
13. Nonlinear Control Systems, Zoran Vukic, Ljubomir KuljaCa, Dali
DonlagiC, Sejid Tesnjak
14. Linear Control System Analysis and Design with MATLAB: Fifth Edition,
Revised and Expanded, John J. D’Azzo, Constanfine H. Houpis, and
Stuart N. Sheldon
15. Robot Manipulator Control: Theory and Practice, Second Edition, Re-
vised and Expanded, Frank L. Lewis, Darren M. Dawson, and Chaouki
T. Abdallah
16. Robust Control System Design: Advanced State Space Techniques,
Second Edition, Revised and Expanded, Chia-Chi Tsui
Additional Volumes in Preparation
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
To Susan
and
James and Shane
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Series Introduction
Many textbooks have been written on control engineering, describing new
techniques for controlling systems, or new and better ways of mathematic-
ally formulating existing methods to solve the ever-increasing complex
problems faced by practicing engineers. However, few of these books fully
addresstheapplicationsaspectsofcontrolengineering.Itistheintentionof
this new series to redress this situation.
The series willstressapplications issues, and notjust the mathematics
of control engineering. It will provide texts that present not only both new
and well-established techniques, but also detailed examples of the
application of these methods to the solution of real-world problems. The
authors will be drawn from both the academic world and the relevant
applications sectors.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Therearealreadymanyexcitingexamplesoftheapplicationofcontrol
techniques in the established fields of electrical, mechanical (including
aerospace), and chemical engineering. We have only to look around in
today’s highly automated society to see the use of advanced robotics
techniques in the manufacturing industries; the use of automated control
and navigation systems in air and surface transport systems; the increasing
use of intelligent control systems in the many artifacts available to the
domestic consumer market; and the reliable supply of water, gas, and
electrical power to the domestic consumer and to industry. However, there
are currently many challenging problems that could benefit from wider
exposure to the applicability of control methodologies, and the systematic
systems-oriented basis inherent in the application of control techniques.
This series presents books that draw on expertise from both the
academicworldandtheapplicationsdomains,andwillbeusefulnotonlyas
academically recommended course texts but also as handbooks for
practitioners in many applications domains. Robust Control Systems is
another outstanding entry in Dekker’s Control Engineering series.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Preface
This second edition of Robust Control System Design introduces a new
design approach to modern control systems. This design approach
guarantees, for the first time, the full realization of robustness properties
ofgeneralizedstatefeedbackcontrolformostopen-loopsystemconditions.
State and generalized state feedback control can achieve feedback system
performance and robustness far more effectively than other basic forms of
control.Performanceandrobustness(versusmodeluncertaintyandcontrol
disturbance) are mutually contradictory, yet they are the key properties
requiredbypracticalcontrolsystems.Hence,thisdesignapproachnotonly
enriches the existing modern control system design theory, but also makes
possible its wide application.
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
Modern (or state space) control theory was developed in the 1960s.
The theory has evolved such that the state feedback control and its
implementing observer are designed separately (following the so-called
separation principle [Wil, 1995]). With this existing design approach,
although the direct state feedback system can be designed to have good
performance and robustness, almost all the actual corresponding observer
feedback systems have entirely different robustness. In the new design
approach presented here, the state feedback control and its implementing
observeraredesignedtogether.Moreexplicitly,thestatefeedbackcontrolis
designed based on the results of its implementing observer. The resulting
statefeedbackcontrolisthegeneralizedstatefeedbackcontrol[Tsui,1999b].
This fundamentally new approach guarantees—for all open-loop
systems with more outputs than inputs or with at least one stable
transmission zero—the same loop transfer function and therefore the
same robustness of the observer feedback system and the corresponding
direct state feedback system. Most open-loop systems satisfy eitherofthese
two conditions. For all other open-loop systems, this approach guarantees
that the difference between the loop transfer functions of the above two
feedback systems be kept minimal in a simple least-square sense.
Modern and classical control theories are the two major components
of control systems theory. Compared with classical control theory, modern
control theory can describe a single system’s performance and robustness
moreaccurately,butitlacksaclearconceptoffeedbacksystemrobustness,
such asthelooptransfer function ofclassicalcontrol theory. Byfullyusing
theconceptoflooptransferfunctions,theapproachexploitstheadvantages
ofbothclassicalandmoderncontroltheories.Thisapproachguaranteesthe
robustness and loop transfer function of classical control theory, while
designing this loop transfer function much more effectively (though
indirectly) using modern control design techniques. Thus it achieves both
good robustness and performance for feedback control systems.
If the first edition of this book emphasized the first of the above two
advantages (i.e., the true realization of robustness properties of feedback
control), then this second edition highlights the second of the above two
advantages—the far more effective design of high performance and
robustness feedback control itself.
Auseful control theory shouldprovide general andeffective guidance
on complicated control system design. To achieve this, the design
formulation must fully address both performance and robustness. It must
also exploit fully the existing design freedom and apply a general, simple,
and explicit design procedure. The approach presented here truly satisfies
these requirements. Since this book concentrates on this new design
approachanditsrelevantanalysis,otheranalyticalcontroltheoryresultsare
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.
presented with an emphasis on their physical meanings, instead of their
detailed mathematical derivations and proofs.
The following list shows several of the book’s most important results.
With the exception of the third item, these results are not presented in any
other books:
1. Thefirstgeneraldynamicoutputfeedbackcompensatorthatcan
implement state or generalized state feedback control, and its
designprocedure.Thefeedbacksystemofthiscompensatoristhe
first general feedback system that has the same robustness
properties of its corresponding direct state feedback system
(Chapters 3 to 6).
2. A systematic, simple, and explicit eigenvalue assignment proce-
dure using static output feedback control or generalized state
feedback control (Section 8.1). This procedure enables the
systematic eigenvector assignment procedures of this book, and
is general to most open-loop system conditions if based on the
generalized state feedback control of this book.
3. Eigenvector assignment procedures that can fully use the
freedom of this assignment. Both numerical algorithms and
analytical procedures are presented (Section 8.2).
4. A general failure detection, isolation, and accommodation
compensator that is capable of considering system model
uncertainty and measurement noise, and its systematic design
procedure (Chapter 10).
5. The simplest possible formulation, and a truly systematic and
generalprocedure,ofminimalorderobserverdesign(Chapter7).
6. Solution of the matrix equation TA (cid:1) FT = LC [matrix pair
(A, C) is observable and eigenvalues of matrix F are arbitrarily
assigned]. This solution is general and has all eigenvalues of F
and all rows of T completely decoupled (F is in Jordan form).
This solution uniquely enables the full use of the remaining
freedom of this matrix equation, which is fundamentally
important in most of the basic design problems of modern
control theory (Chapters 5 to 8, 10).
7. The basic design concept of generating a state feedback control
signal without estimating all state variables, and the general-
izationofthisdesignconceptfromfunctionobserversonlytoall
feedback compensators (Chapters 3 to 10).
8. The complete unification of two existing basic feedback
structures of modern control theory—the zero input gain state
Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.