Reviewed by Petr Zagalak
Automatica, Vol. 36, no. 5, pages 83-84, 2000
"This is a book on practical feedback control and not on system theory generally" is the first sentence of Preface and, I am sure, many a reader will certainly be pleased by that. The authors' aim was to write a book that would also be an introduction to robust control, could be used as a text for graduate courses, and be useful for control engineers. This is quite an ambitious goal which was, in my opinion, successfully realized to a great extent. The book is neither exaggeratedly theoretical, nor an easy-to-read text on control. It provides a lot of insight into the art of practical control design. The H-infinity methods discussed in the book, can be viewed as a generalization of classical design techniques. The book consists of 12 chapters and one appendix, which gives more than five hundred pages of interesting text. The first chapter, Introduction, describes the most important requisites of the scene, that is to say, the main characteristics of the process of control system design are briefly described, linear models and their transfer functions are introduced, the control problem is stated, and signal scaling and linearization are briefly discussed. The basic notation is defined therein, too.
The second chapter is devoted to the classical methods of feedback control for SISO systems. Frequency response, feedback loop, closed-loop stability, closed-loop performance, and elements of the loop-shaping design methods form the core of the chapter. Based on this, the H, formulation of control problems with weighted and mixed sensitivities are introduced. MIMO systems are considered in the third chapter. First, algebra of transfer functions is described and then, based on frequency response, singular values and singular value decomposition are introduced and their properties are discussed briefly. Also discussed is control of MIMO systems, their right half-plane zeros, and the relative gain array of a nonsingular matrix. The need for studying robustness is motivated by examples and the notions like robust stability and robust performance are briefly explained. The rest of the chapter is devoted to the general control problem formulation. This is just an introduction to these important concepts that are reconsidered again in the next chapters. Elements of linear system theory, which is also the title of the chapter, are given in the fourth chapter. The treated material is standard; however, some parts are too brief and could be difficult for certain readers (not only the uninitiated), and therefore to keep a more detailed text on linear system theory handy is recommended.
The first four chapters can be viewed as an introductory part of the book in which many basic ideas and concepts are briefly but clearly explained. The text of each chapter is also well-graduated and hence attention attracting. Just the distribution of the material into individual chapters can be criticized a bit, i.e. most of the material of Chapter 4 could be stated in Chapters 1-3 as well. This particularly concerns the sections on system descriptions, poles and zeros, and stability. Also, some topics treated in the chapter could receive more attention because of their importance in control theory. This namely concerns the Youla-Kucera parameterization of all stabilizing feedback compensators.
Chapters 5 and 6 form another whole that is devoted to analysing performance limitations in SISO and MIMO systems. The central issue here is the concept of input-output controllability (performance targeting, dynamic resilience), the term reflecting the ability of a plant to achieve acceptable control performance, which is in many cases related to the limitations on the bandwidth of the system. The results on the performance limitations analysis are summarized in the form of controllability rules (necessary conditions) that are satisfied if the system is input-output controllable. All the material of Chapter 5 is covered by two examples and many exercises. Basically the same things are considered for MIMO systems in the following chapter. Special attention is paid to the analysis of uncertainty since there is also uncertainty associated with the system directions, the issue which is unique to MIMO systems.
The next two chapters, 7 and 8, provide the reader with an introduction to uncertainty and robustness. SISO systems are studied first. Then, in the eighth chapter, a more general treatment for MIMO systems is developed. The exposition begins with a brief description of sources of uncertainty, models for uncertainty, and how uncertainty is represented in the frequency domain. Based on this, robust stability and robust performance are investigated. The MIMO system analysis is much more complicated as there are internal interactions between inputs and outputs, which may increase sensitivity to uncertainty. Therefore, the structured singular value is defined and the analysis of the effect of uncertainty on stability and performance is studied using this tool. By discussing the mu-synthesis problem the chapter climaxes.
The main topic of Chapter 9 is multivariable controller design. Several methods of synthesis are discussed but the main emphasis is on the H-infinity loop-shaping methods. The chapter begins with a brief review of the role of singular values in MIMO feedback design and a description of the traditional LQG control. Next, the H2, H-infinity mixed-sensitivity H-infinity and signal-based H-infinity, approaches to controller design are introduced. The H-infinity, loop-shaping design procedures are studied in the rest of the chapter.
The process of designing a control system is frequently quite a complicated affair and anyone who has ever been involved in such a process knows that very well. The tenth chapter opens the door to the art of control structure design. Questions like which outputs of the plant should be measured, which ones should be controlled, which inputs should be manipulated, are discussed first. Then the control configuration is considered. Some elements (cascade and decentralized controllers, selectors, etc.) used to build up a specific control configuration are described and their features are studied. Special attention is paid to the sequential design procedure applied to cascade or decentralized control systems and to the stability of decentralized control.
The material of the tenth chapter is not frequently encountered in the textbooks on control. Together with the material of Chapters 5 and 6, this is a part of the book where the authors' pragmatic view and orientation to practical control are revealed the most. The balanced truncation, balanced residualization, and optimal Hankel norm approximation, as the main methods for model reduction, are discussed in Chapter 1 1. Unstable models are briefly mentioned, too. In the last chapter, there are three case studies (helicopter and aero-engine control, distillation process) presented. They will help the reader to fix many important issues introduced in the previous chapters. The book ends with two appendices; the first one gives elements from the matrix and norm theory, the second one contains an example of the Norwegian-style exam; a student project is outlined therein, too.
It is evident, from the above overview of chapters, that the book is really comprehensive, covering a large field of modern control design methods. Hence, the primary question is whether all the presented material is well-balanced. My answer is positive. There are not many points that could be criticized. The book is appealing and has many interesting features. For instance, the gap between the theory of SISO and MIMO systems is substantially reduced introducing the H, loop-shaping methods, strong points are covered by examples and exercises providing additional insight and information on the problems, and the use of the frequency-domain and state-space methods is well-balanced.
A lot of information about the book can also be found on the authors' web pages. This particularly concerns the MATLAB files, solutions to problems, project works, additional exercises, and print errors.
Being quite complete, the book provides many items of information and ideas for the reader. Students and control engineers will find that the book is a valuable text and reference book. Even researchers working in the field can be motivated by some problems hinted therein. In summary, the book is a very good and complete text to the subject of control system design. It even offers a lot of introductory material needed for an undergraduate course on modern control techniques with many examples and exercises. The book is oriented to practical issues of control design and this. together with the clear presentation of the basic concepts, is the strongest point of the book.
Petr Zagalak
Institute Of Information Theory and Automation,
Academy of Sciences of the Czech Republic,
P. 0. Box 18, 182 08 Prague, Czech Republic
E-mail address: zagalak@utia.cas.cz (P. Zagalak)
About the reviewer
Petr Zagalak was born in Czechoslovakia. He received, in 1972, his master degree from the Faculty of Nuclear and Physical Engineering of the Czech Technical University . Since then he has been with the Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic. During 1972-81 he worked at the Computer Center of the Institute. In 1982 he received his doctoral degree from the Academy and got an appointment as a member of research staff of the Institute. He received the Automatica Paper Prize in 1990. His current research interests include mainly algebraic methods of control theory, structure of linear systems, and numerical aspects of polynomial calculus.