Review of the book S. Skogestad and I. Postlethwaite, Multivariable feedback control - Analysis and design, Wiley, 1996.

Reviewed by S. Atique Malik
Review from Int. Jnl. of Robust + Nonlinear Control
Volume: 8
Number: 14
Date of Issue: 15/12/98
This is a graduate level text on the design of multi-variable feedback control systems, using the transfer function approach. It includes a comprehensive MATLAB simulation of a high-purity binary distillation column, that is used to illustrate the design principles put forward in this book. This is one of the highlights of this book, and a feature that makes the book relevant to practising engineers. All of the standard multivariable topics of robustness, H. and u synthesis are dealt with, including the design of the control structure and the means to compute the performance limits of SISO (single-input single-output) and MIMO (multi-input multi-output) systems. The text is clear and concise, and a lot of valuable information is contained in the 559 pages. The reader is not overwhelmed with mathematical formulae, as each of the topics is introduced at a pace suitable for graduate students and experienced engineers. The weakness of the book is simply that it has cloven to the path,of the transfer function type systems, and there is no mention of discrete systems that are more prevalent in practical situations. Time delays are often encountered in the chemical process industry, but the authors do not provide sufficient space to this practical problem. Overall, an excellent book, and highly recommended for both student and practitioner alike.

Chapters 1 and 2 lay the foundation for the main theme of this book, which is that a control system design requires an appreciation of the process operation and the process objectives. From this follows the selection of the control structure and the control algorithms. This makes it easy for the new student to appreciate the place occupied by control theory within the larger sphere of the design of a control strategy. Classical control theory is introduced by considering the analysis of SISO (single- input single-output) systems, via loop shaping. Analysis via two-degree-of-freedom control design is introduced, along with sensitivity analysis. The concepts are illustrated by the design of a simple H-infinity system. This chapter would have been even more valuable with the detailed consideration of a first-order system with dead time. It would appear that the analysis of such systems cannot be easily done, at a simple level, by the transfer function approach used in this book.

Chapter 3 deals with the analysis of multivariable systems. This chapter suffers from a lack of physically meaningful examples, and the level of abstraction causes a break with the pragmatic approach of the first two chapters. Hence, the student will need access to other texts for assistance. The topics discussed in this chapter cover SVD, condition number, and RGA analysis as well as a clear description of the meaning of robustness in MIMO (multiple-input-multiple output) systems. The last topic is clearly explained by a simple example. This chapter therefore provides an introduction to the basic terminology of MIMO systems, and is a starting point to the understanding of the technical literature in this field.

Chapter 4 is a review of linear system theory, and is meant to summarize important results in the application of the transfer function approach to multivariable systems. The usual topics of model representations (state space and transfer function) are dealt with. Coprime factorizations are explained and demonstrated with the help of examples in MATLAB. The state-space realization of simple transfer function representations is discussed too. The discussion does not get into the aspects of minimal and non-minimal realizations, which would have been useful in demonstrating the non-unique nature of state-space realizations. The Padé approximation is not covered in sufficient depth to allow the reader to appreciate its use in the approximation of time delays. This is a rather surprising omission, as time delays are very common in the chemical process control area. While this chapter is very informative, a discussion on right-hand plane zeros and stabilizing controllers would have been beneficial.

Chapters 5 and 6 deal with the practical issue on limits of performance for SISO and MIMO systems. Control structure design is treated as an integral part of control system design, and this makes it a very readable and useful chapter for practising engineers also. Chapters 7 and 8 deal with the issue of uncertainty and robustness. These chapters represent a very abstract and mathematical treatment of the subject, which may be of value to researchers concerned with the theory. They do impede the otherwise smooth flow of the book.

The remainder of the book deals with controller design of H. two-degree-of-freedom controllers, as well as Control Structure Design, in a simple and effective way. Judicious use of Matlab puts the point across very well. These chapters are recommended for their brevity and clarity. An interesting feature of the book is the final chapter on Case Studies on helicopter, aero-engine and distillation column control.

The design of discrete control systems is omitted in this text. This is a weakness from the point of view of application-oriented engineers in the mechanical and chemical fields. As the authors have done such a great job of the transfer function approach, the discrete case could have been covered within two chapters. This extension, with the Matlab code and discussion of the constraints issue, would make this book invaluable for the control engineer. Admittedly, the book would then be far heftier!

S. Atique Malik
Process Control Technology
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Air Products and Chemicals
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USA