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Pergamon Press.

Printed in Great Britain.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...*.*** LOWELL 9. KOPPEL: Intmducthm to Control Theorywith &&athms to Process Control. Prentice-Hag 1968. 466 pp. $13.50. EVEN IN a field rapidly ballooning with textbooks it is refreshing to find a significant new contribution. This book is a coherent, well developed introduction to modem deterministic control theory. The author assumes a knowledge of classical feedback control and orients the book toward a graduate course in automatic control. Chapters 1-4 serve two purposes: a review of classical methods for continuous and discrete linear systems; and an introduction to the state variable representation, including such topics as the state transition matrix, controllability and observability. Chapter 5 is devoted to Lyapunov stability theory. The treatment, which by necessity is somewhat limited, especially in the area of nonlinear system stability, is quite clear and readable. In an interesting section the author points out some subtle questions involved in the use of Lyapunov functions to design controllers. Chapter 6, by far the largest in the book, considers the optimization of continuous systems. A thorough analysis of a scalar linearquadratic problem is used to illustrate the variational approach and the nature of the optimal proportional control law. A fairly standard treatment of Pontryagin’s minimum principle follows, including the classic linear-quadratic case. The time optimal control of linear systems is treated in sufficient detail to provide a sound understanding of the problem. Numerical procedures for optimization using the minimum principle and dynamic programming complete Chap. 6. Chapter 7 parallels Chap. 6 in treating optimization of discrete control systems. Discrete dynamic programming and the discrete minimum principle are outlined. The author is careful to point out the weaker nature of the discrete as opposed to the continuous minimum principle, a distinction which has caused some confusion in publications on this subject. A brief treatment of the optimal control of distributed parameter systems appears in Chap. 8. The author restricts his attention to linear hyperbolic systems for which analytical results may be obtained. The final three chapters represent the unique contribution of this book, the application of the theory to “real” processes. Chapter 9 is a short discussion of process modeling via transfer functions. Chapter 10 considers time-optimal control for simulated and real systems and Chap. 11 treats the design of digital process controllers. (Chemical reactors and distilla-

tion are treated as examples.) Those who are concerned with control implementation will find these chapters quite useful, as the author has restricted himself to simple transfer function representation of the processes considered. Several characteristics of the overall style combine to make the book well-suited for use as a textbook. A large part of the learning process is consigned to excellent example problems, liberally included in all the chapters. The parallels between continuous and discrete systems are- stressed, providing a sound approach to the discrete representation. Useful appendices for mathematical background are provided. A firm bridge is established between the classical and the state representations, and physical insight is provided whenever possible, a factor often overlooked in control texts. However, the book is not beyond criticism. The list of references at the end of each chapter is disappointing in view of the vastness of the literature on modem control and stability theory. Perhaps a more serious criticism is the author’s limited treatment of the numerical techniques for optimization of nonlinear systems. Although some space is devoted to this in Chap. 6, the reader is not made fully aware of either the complexity or the new approaches available for this problem. Important techniques such as quasilinearization, invariant imbedding, nonlinear programming and penalty function methods are not even mentioned. No indication is given as to what one might have to do if confronted with, say, a five state variable optimization problem, or, in fact, a classical multivariable compensation problem. In the linear muhivariable case it is stated that if one chooses his example carefully, physical realizability is possible in isolated cases. No attempt at rationalization of design for non-interaction is presented. Since one stated object of the book is to prepare the reader for the current literature on automatic control, and since this literature is today mainly concerned with algorithms for large, nonlinear systems, the author has fallen shortin this respect. Nevertheless, on the whole, this book provides an excellent introduction to control theory: Its huge number of illustrative and practical examples and its integration of the classical and modem approaches distinguishes the book. The flavour of the book is distinctly chemical engineering and it should prove a valuable textbook for graduate control courses as well as for practicing engineers.

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J. H. SEINFELD

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