Quantitative feedback theory: fundamentals and applications

620 Pages·2006·32.581 MB·English

by  Garcia-Sanz, Mario, Houpis, Constantine H., Rasmussen, Steven J

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CONTROLENGINEERING
ASeries of Reference Books and Textbooks
Editor
FRANK L. LEWIS, PH.D.
Professor
Applied Control Engineering
University of Manchester Institute of Science and Technology
Manchester, United Kingdom
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,
Constantine H. Houpis and Steven J. Rasmussen
4. Self-Learning Control of Finite Markov Chains, A. S. Poznyak, K. Najim,
and E. Gómez-Ramírez
5. Robust Control and Filtering for Time-Delay Systems,
Magdi S.Mahmoud
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 Gajif
and Myo-Taeg Lim
8. Engineering System Dynamics: A Unified Graph-Centered Approach,
Forbes T. Brown
9. Advanced Process Identification and Control, Enso Ikonen
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
13. Nonlinear Control Systems, Zoran Vukić, Ljubomir Kuljača, Dali Donlagič,
and Sejid Tesnjak
14. Linear Control System Analysis & Design:Fifth Edition, John D’Azzo,
Constantine H.Houpis and Stuart Sheldon
15. Robot Manipulator Control:Theory & Practice, Second Edition,
Frank L.Lewis, Darren M. Dawson, and Chaouki Abdallah
16. Robust Control System Design: Advanced State Space Techniques,
Second Edition, Chia-Chi Tsui
17. Differentially Flat Systems, Hebertt Sira-Ramirez
and Sunil Kumar Agrawal
DK709X_half-series-title.qxd 10/13/05 10:53 AM Page C
18. Chaos in Automatic Control, edited by Wilfrid Perruquetti
and Jean-Pierre Barbot
19. Fuzzy Controller Design: Theory and Applications, Zdenko Kovacic
and Stjepan Bogdan
20. Quantitative Feedback Theory: Fundamentals and Applications,
Second Edition, Constantine H. Houpis, Steven J. Rasmussen,
and Mario Garcia-Sanz
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Quantitative
Feedback Theory
Fundamentals
and Applications
Second Edition
Constantine H. Houpis
Air Force Institute of Technology
Wright-Patterson AFB, Ohio
Steven J. Rasmussen
General Dynamics
Wright-Patterson AFB, Ohio
Mario Garcia-Sanz
Public University of Navarra
Pamplona, Spain
Boca Raton London New York
A CRC title, part of the Taylor & Francis imprint, a member of the
Taylor & Francis Group, the academic division of T&F Informa plc.
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Library of Congress Cataloging-in-Publication Data
Houpis, Constantine H.
Quantitative feedback theory / Constantine H. Houpis, Steven J Rasmussen, Mario Garcia-
Sanz.--2nd ed.
p. cm. -- (Control engineering ; 20)
Includes bibliographical references and index.
ISBN 0-8493-3370-9 (alk. paper)
1. Feedback control systems. I. Rasmussen, Steven J. II. Garcia-Sanz, Mario. III. Title.
IV. Control engineering (Taylor & Francis) ; 20.
TJ216.H69 2006
629.8'3--dc22 2005053836
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Preface
The objective of this text is to bridge the gap between the scientific (theoretical)
and engineering methods of Quantitative Feedback Theory (QFT) by applying this
multivariable robust control system design technique to real-world problems.
Thus, the engineer is at the interface of the real-world with the body of knowledge
and theoretical results available in the technical literature. Professor Isaac M.
Horowitz, the developer of the QFT technique, has continually stressed the
transparency of QFT; that is, the ability to visually relate the implementation of
the design parameters to the real-world problem, from the onset of the design and
throughout the individual design steps. Therefore, it is the purpose of this text to
enable and enhance the ability of the engineering student and the practicing
engineer to bridge the gap between the scientific and engineering methods. In
order to accomplish this goal, the text is void of theorems, corollaries, and/or
theoretical lemmas. In other words, this textbook stresses the engineering
approach and not the scientific approach – this is a textbook for engineers.
Professor Horowitz began developing the Quantitative Feedback Theory
(QFT) in early 1960. Since then great strides have been made in exploiting the
full potential of the QFT technique. It is a frequency domain technique for
designing a class of control systems for nonlinear plants. The abbreviation QFT
should not be confused with the physics topic Quantum Field Theory (QFT). The
catalyst that has propelled Horowitz’s QFT to the level of being a major robust
multiple-input multiple-output (MIMO) control system design method has been
the development and availability of viable QFT computer-aided-design (CAD)
packages. Through the close collaboration of Professor Horowitz with Professor
C.H. Houpis and his graduate students, during the 1980s and the early part of the
90s, successful QFT designs involving structured parametric uncertainty had been
completed and published by the Air Force Institute of Technology (AFIT) MS
thesis students and faculty. During this period, the first multiple-input single-
output (MISO) and MIMO QFT CAD packages were developed at AFIT.
Another major accomplishment was the successful implementation and flight test
of two QFT designed flight control systems, by Captain S.J. Rasmussen, of the Air
Force Wright Laboratory, for the LAMBDA unmanned research vehicle in 1992
and 1993. Also, on April 28, 1995, Dr. Charles Hall of North Carolina State
University, announced that four successful flight tests of QFT flight controllers
had been accomplished.53 Based upon these solid accomplishments, an aerospace
engineering firm began applying the QFT design method in 1995. Other
individuals throughout the world such as Professor E. Eitelberg, Professor E. Boje,
Professor S. Jayasuriya, Professor P.O. Gutman, Professor A. Banos, Dr. D.J.
Balance, Professor P.S.V. Nataraj, Professor O. Yaniv, Professor Y. Chait et al are
also applying QFT to design real-world robust control systems. Professor D.S.
v
vi Preface
Bernstein ably points out the power of the frequency domain analysis, not only for
linear systems, but also for nonlinear systems.76
In 1986 Professor Houpis published a technical report41 which was the first
attempt to bring under one cover the fundamentals of QFT. The second edition2of
this Technical Report (TR) brought the material up to the state-of-the-art, and, like
the first edition, aimed to provide students and practicing engineers with a
document that presented QFT in a unified and logical manner. Refinements based
upon the class testing of the first and second editions are incorporated in this text.
Much of the material in this text is based upon the numerous articles written by
Professor Horowitz, along with his colleagues, and the numerous lectures that he
presented at the Air Force Institute of Technology.
In the summer of 1995 Professor Mario Garcia-Sanz, visiting research
scientist at the Control System Centre, UMIST (UK), attended a QFT seminar
given by Professor Houpis. At that time they started a collaborative effort in
furthering the development of QFT and its application to real-world problems. A
few months later, on his return to Spain, Professor Garcia-Sanz established the
Control Engineering Group at the Public University of Navarra, with QFT as one
of the main lines of research and with full encouragement from Professor
Horowitz in the field. Since then the group works very closely with industry,
especially with the M. Torres Company, CEIT and NASA-JPL. In fact, the group
pioneered the application of QFT design techniques to new challenging real-world
problems such as the control of large variable-speed multipole synchronous wind
turbines, of waste water treatment plants and of multiple spacecraft in formation.
Results of this theoretical and applied work are incorporated in this edition.
Both analog and sampled-data (discrete-time) MISO and MIMO feedback
control systems are covered in detail. Extensive use is made of the MISO and
MIMO QFT CAD packages to assist the reader in understanding and applying the
QFT design technique. A PC MIMO QFT CAD, is available with this text, to be
used with conjunction of the PC version of MATHEMATICA. This is
accomplished by including appropriate examples in each chapter and problems at
the end of each chapter in order to reinforce the fundamentals.
The authors have exerted meticulous care with explanations, diagrams,
calculations, tables, and symbols. The reader is shown how to make intelligent
real-world assumptions based upon mathematics and/or on a sound knowledge of
the characteristics and the operating scenario of the plant to be controlled. The
text provides a strong, comprehensive, and illuminating account of those elements
that have relevance in the analysis and design of robust control systems and in
bridging the gap between the scientific and the engineering methods.
Chapters 2 through 7 present the fundamentals of the QFT technique and the
associated design procedure for the tracking control problem. This is followed by
an extension of the technique to handle external disturbances, the regulator control
problem, for a MIMO system. The remaining chapters focus on bridging the gap
between theory and the real world by presenting engineering rules and the factors
that are involved, such as simulations, implementation, etc., that are important in
Preface vii
implementing a successful robust control system design. Extensive use of the
MISO and MIMO QFT CAD packages (see Appendices C-E) is made for the MISO
and MIMO examples throughout the text.
Chapter 2 discusses the reasons why feedback is required to achieve the
desired system performance. This is followed by presenting an overview of QFT:
the design objectives; what is structured parametric uncertainty and its Bode plot
and Nichols Chart representations; performance specifications; design overview;
and QFT basics. The chapter concludes with an insight into the QFT technique
and the benefits of applying this technique.
As Horowitz and his colleagues have shown, an mxm MIMO control system
can be represented by m2 MISO equivalents. As a result, the QFT technique was
initially developed for MISO control systems and was then extended to MIMO
control systems. Thus, Chapter 3 presents the fundamentals of the QFT design
technique for the analog MISO control system. This is followed by the extension
of this technique to MISO discrete-time control systems in Chapter 4.
Chapter 5 begins with an introduction to MIMO plants having structured
parametric uncertainty. This is followed by the introduction to the QFT MIMO
compensated system formulation and the development of the effective MISO
equivalents of a MIMO system. The remaining portion of the chapter adapts the
MISO analog QFT design technique of Chapter 3 to the QFT robust design
(Methods 1 and 2) of MIMO control systems containing structured parametric
uncertainty. Chapters 5 through 9 and Chapter 11 utilize a diagonal G
compensator/controller matrix whereas Chapter 10 discusses the use of non-
diagonal G matrix (Method 3).
The QFT Method 1 design technique is discussed in detail in Chapter 6.
Aspects such as performance tolerances, sensitivity analysis, simplification of the
single-loop structure, high frequency and stability analyses, equilibrium and trade-
offs, some universal design features, and the determination of bounds are
discussed.
Chapter 7 thoroughly presents the details of Method 2. This method has the
advantage of reducing the amount of over-design inherent in Method 1 and is
applied when the diagonal dominance condition is not satisfied. Design equations
for the 2x2 and the 3x3 MIMO systems are presented with corresponding design
guidelines. The Binet-Cauchy formula is applied to determine if a minimum-phase
(m.p.) effective plant (det P) is achievable.
In Chapter 8 the QFT technique is extended to the design of MIMO control
systems with external disturbance inputs; i.e., the regulator control problem. From
the state-space equations the corresponding plant and disturbance matrices are
derived and the corresponding block diagram representation is shown. Based
upon this formulation, the QFT m2 MISO effective loop equations are derived for
the regulator case. This QFT regulator design technique is applied to a real-world
design example.
The remaining chapters enhance the emphasis of this text: to bridge the gap.
Throughout the preceding chapters the elements that contribute to the
viii Preface
transparency of QFT have been stressed, where applicable. Based upon these
elements, and upon many years of applying the QFT robust control system design
technique to many real-world nonlinear problems, Engineering Rules are
presented in Chapter 9. These rules attempt to bridge the gap between QFT and
the real-world problems.
Chapter 10 is a major contribution to this edition which presents the QFT
design of non-diagonal compensators/controllers G for both tracking and
disturbance rejection problems (Method 3). It introduces a non-diagonal G
decoupling approach based upon a sequential design methodology.
There are a number of factors that contribute to making the decision that a
satisfactory control system design has been achieved. Chapter 11 discusses the
factors that are involved in a control system design cycle, factors that must be kept
in mind from the onset of the design process and which bridge the gap between
theory and the real world.
Time delay strongly limits the achievable performance of systems and
complicates the design of controllers. Traditionally industry has been addressing
this problem by the use of a Smith Predictor Controller (SPC). However, the SPC
is very sensitive to plant model mismatch, and then, in the presence of plant
uncertainty, it may result in a poor performance or an unstable system. Thus,
Chapter 12 introduces a method to design a SPC using the QFT technique for
systems containing time delay with plant uncertainty in both, the rational part and
the time delay.
The concept of Bridging the Gap, discussed in Chapter 9, is exemplified in
Chapter 13 by the discussion of two real-world QFT designed control systems: the
design of a control system for a waste water treatment plant and for a large wind
turbine synchronous generator.
Chapter 14 discusses the utilization of a weighting matrix in conjunction
with control authority allocation in order to enhance the achievement of the
maximum number of the desired system performance specifications. This
utilization is especially useful in systems whose plant model matrix is non-square
and is nonlinear.
Five new appendices have been added that enhance the technical content of
the second edition. Section 2-3.5 is enhanced by Appendix A, Template
Generation. Appendix B, Inequalities Bounds Expressions, provides further
insight in the design procedure given in Section 3-16. Two examples of a non-
diagonal compensator/controller design to supplement the new Chapter 10 are
given in Appendices H (the tracking problem) and I (the disturbance rejection
problem). Appendix J, Elements For Loop Shaping, provides further insight for
the guidelines given in Sections 3-13 and 3-14.
The most effective way of expediting the transfer of QFT knowledge and its
corresponding state-of-the-art material is for all authors on this subject to adhere to
a standard list of QFT symbols. Thus, this text includes a section entitled QFT
Standard Symbols & Terminology.
Preface ix
There are many worthwhile robust multivariable control system design
techniques available in the technical literature, which are based on both the state-
variable approach and on conventional control theory. The applicability of each
design technique may be limited to certain classes of design problems. The
control engineer must have a sufficiently broad perspective to be able to apply the
appropriate technique to the right design problem. Some of the questions that the
control engineer must keep in mind (see Chapter 11) in selecting a design method
are: (a) can it solve a real-world problem? (b) is the method computationally
intensive? (c) can it handle structured parametric uncertainty? (d) which method
yields the lowest order compensator or controller? and (e) will the design method
result in a control system that can be implemented on the target hardware, etc?
For some techniques the designer is assisted by available computer-aided-design
(CAD) packages.
This text presents a control system design based on quantitative feedback
theory (QFT), which is a very powerful design method when plant parameters
vary over a broad range of operating conditions. It incorporates the concept of

designing a robust control system that maintains the desired system performance,
not only over a prescribed region of plant parameter uncertainty, but also with a
degree of control effector failures. The authors believe that this method has
proven its applicability to the design of practical MISO and MIMO control
systems with low order compensators (controllers) with minimal gain. This
textbook provides students of control engineering and the practicing control
engineer with a clear, unambiguous, and relevant account of the QFT technique.
The text is arranged so that it can also be used for self-study by the engineer
in practice. Included are examples of feedback control systems in various areas of
practice (electrical, aeronautical, mechanical, etc.) while maintaining a strong
basic QFT text that can be used for study in any of the various branches of
engineering. The text has been thoroughly class-tested, thus enhancing its value
for classroom and self-study use. The computer-aided-design (CAD) packages of
Appendices C through E are available to assist a control engineer in applying the
QFT design method. The use of QFT CAD packages are stressed throughout the
text. The authors wish to thank John W. Glass of Purdue University for review of
the TOTAL-PC CAD software that accompanies this volume.
The authors wish to express their appreciation for the support and
encouragement of Professor M. Pachter, at the Air Force Institute of Technology,
during the preparation of the 1995 technical report.41 His wealth of knowledge of
the flight control area enhanced its value and his comments with respect to this
text are appreciated.
The authors express their thanks to those students who have used this book
and to the faculty who have reviewed it for their helpful comments and
recommendations. Special recognition is given to Professors E. Eitelberg and E.
Boje for their encouragement and support for this second edition. Appreciation is
expressed to Dr. J.J. D’Azzo, Professor Emeritus of Electrical Engineering, and
Professor Pachter, Air Force Institute of Technology, for the encouragement they
x Preface
have provided in the preparation of this text, as well as to John Glass of Purdue
University, who reviewed the TOTAL-PC software.
Special appreciation is expressed to Professor Horowitz for the association
and his collaboration with Professor Houpis during the period of 1981 through
1992. The personal relationship with him has been a source of inspiration and
deep respect. Appreciation is also expressed to Dr. R.L. Ewing, Air Force
Institute of Technology Research associate, for his work on improving and
maintaining the TOTAL-PC CAD package.
Acknowledgment of Mr. E. Flinn, U.S. Air Force Wright Aeronautical
Laboratories, and his colleagues Mr. J. Morris and Mr. D. Rubertus is made for the
support and encouragement in developing and extending the QFT technique,
during the 1980s. This support and encouragement was maintained by Mr. M.
Davis (retired), Mr. J. Ramage, and Mr. Rubertus (retired) of the Air Force
Research Laboratory. Further acknowledgment must be made of the support of Dr.
S.N. Sheldon and the support given by the European Office of Aerospace
Research and Development of the U.S. Air Force Office of Scientific Research
during the latter part of the 20th century.
The thorough review of the 1st edition manuscript by Professor D. McLean
of the University of Southampton was of immense value and was greatly
appreciated by the authors. Contributions to this second edition were also made by
present and former PhD students of Professor Mario Garcia-Sanz at the Control
Engineering Group of the Public University of Navarra. Special mention is given
to Dr. Xabier Ostolaza, Dr. Juan Carlos Guillen, Dr. Montserrat Gil, Dr. Igor
Egana, Dr. Marta Barreras, and Ms. Irene Eguinoa. Their perception and insight
have contributed to the clarity and rigor of the presentation.
Constantine H. Houpis
Mario Garcia-Sanz
Steven J. Rasmussen