Transform Methods with Applications to Engineering and Operations ...

446

Book

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL.

SMC-9,

NO.

8, AUGUST 1979

Reviews

Teoria della Regolazione (Theory of Automatic Control)-Arturo Locatelli (Milano, Italy: Hoepli, 1976, 516 pp.). Reviewed by Giuseppe Buja, Instituto di Elettrotecnica e di Elettronica, Universita di Padova, Padova, Italy.

According to the author's presentation, this 500-page book is the outgrowth of successive reelaborations of classroom notes used in a 90-hour course taught at the Politecnico di Milano. The course is primarily addressed to (mature) engineering students at approximately the first or second year graduate level (in the American university system) having familiarity with the basic concepts of linear systems and classical automatic control theory. The aim is to provide control engineers with a working knowledge of the most important modern design techniques of compensators for multivariable linear control systems. The book is addressed not as a research monograph but rather as an effort (probably not yet attempted by others) of giving a unifying and at the same time rather detailed presentation of the most important modern state-space synthesis techniques. Actually, most of the basic recent results (such as pole assignment, various reduced-order observers decoupling, sensitivity theory, and linear optimal control with quadratic performance criterion) are covered in a completely self-contained way. Besides the introduction, the book consists of four chapters, the first three of which (approximately 100 pages each) are dedicated to pole assignment and state reconstructors, decoupling and insensitivity. The last chapter is about 200 pages long and is mainly devoted to optimal control (especially to the linear-quadratic cost problem). Chapter 2 deals with the design of compensators for pole assignment, both in the case of complete information (i.e., the state is totally accessible) and in the partially observable case. After starting and proving Wonham's basic results (using Heymann's simplification in the proof), a detailed discussion of the incomplete information case is given. Luenberger's observers are first introduced, and various reduced-order observations are then discussed, leading to dynamic compensators of order n-rank(C) and n-rank(B) (dual observers of Gopinath). Finally, the author goes through the rather lengthy and technical proofs of the theory of minimal-order observers of Brasch and Pearson. Chapter 3 is dedicated to the decoupling problem. In this part of the book, a noticeable effort is evident to present in an easy readable way the geometrical theories of Basile--Laschi-Marro and Morse-Wonham. The interesting blend of the two approaches presented here may actually be viewed as a personal contribution by the author. Conditions for existence of nondynamic and dynamic compensators to achieve noninteracting control are first carefully discussed, and then the pole assignability for the decoupled blocks is treated. The algorithms for designing these compensators are generally to be found by reading the proofs of the theorems. They are not reported in a self-contained fashion. This policy (which is followed all through the book) is a little questionable and makes the use of the book itself a bit difficult for people interested only in the results.

However, there are a number of nice examples where the theory is applied, and this might be of some help. The argument of Chapter 4 has been a research subject for the Milano group for some years in the past. Some of the topics treated here, like the design of compensators to achieve trajectory and terminal parametric insensitivity, are based on research papers coauthored by the writer of the book. Conditions for existence of such regulators are generally rather severe, and there is little freedom left to assign poles. So, there might be some doubts on the importance given to these topics in a book like this, which is admittedly not a research book. Anyway, the problem is an important one, and it might seem adequate to give the students some feeling for it. Chapter 5 is dedicated to optimal control theory. The point of view taken here is the classical one followed by Kalman in his Bulletin de la Sociedat Math. Mexicana paper and permits a rather straightforward derivation of the Riccati equation and the optimal linear control law. The maximum principle (the usual starting point in many optimal control

is introduced only towards the end of the chapter and is used almost exclusively to discuss time-optimal control for linear systems. The LQ problem is solved and discussed with enough detail even if some recent generalizations of the theory (J. C. Willems' paper in IEEE TAC, 1971) have not been reported. Some space is given also to the treatment of the inverse problem. From the point of view of practical applicability, perhaps the most apparent deficiency of this part of the book is the conspicuous absence of numerical schemes for solving the ARE. In conclusion, the effort to give an unitary view is apparent and makes the book of a pedagogical value and reasonably easy to read, especially if compared with the original papers (this is true especially for C'hapter 3). Main shortcomings are the fact that most of the design algorithms are to be found buried in the proofs of the theorems and not sufficiently "highlighted," and that there is insufficient consideration of numerical

books)

problems.

On the whole, one might say that the main merit of the book is to give up-to-date and very detailed account of the most important design methods known today for linear multivariable control systems'

an

Transform Methods with Applications to Engineering and Operations Research-Eginhard J. Muth (Englewood Cliffs, NJ: Prentice Hall, 1977, 372 pp.). Reviewed by Lokenath Debnath, Mathematics and Physic.s Departments, East Carolina University, Greetnville, NC 27834.

Integral transform methods are simple, effective mathematical mnethods widely used for finding solutions of problems in applied mathematics, physics, engineering, operations research, and other related areas. With reader background in calculus and ordinary differential equations, this

book is a brief introduction to the Laplace transforms and Z-transforms and their applications to simple engineering problems involved with ordinary differential and difference equations. It gives an easy manipulative treatment of the Laplace and Z-transforms rather than a rigorous and systematic theory. It has seven chapters, a short bibliography, and four appendices containing tables of the Laplace transforms and Z-transforms. Chapter 1 deals with an introduction to algebra of complex numbers and the concept of analytic functions. In Chapters 2 and 3, the author considers the elementary properties of the Laplace transforms and the inverse Laplace transforms. The methods of partial-fraction decomposition are used to obtain the inverse Laplace transforms. No attempt is made to discuss the inverse Laplace transforms by the complex integral formula and its evaluation by the method of

residues.

Chapter 4 is devoted to simple applications of the Laplace transform to certain classical problems in electrical circuits, mechanical systems. deflection of beams, and moment generating functions in statistics and operations research. Most of these problems are governed by ordinary linear differential equations. In Chapters 5 and 6, the properties of the Z-transforms and the inverse Z-transforms are systematically discussed with examples. The final chapter deals with applications of the Z-transforms to numerous problems governed by linear difference equations. It includes problems in simple and compound interest, inventory control model, electrical ladder network, time-series analysis, data smoothing. digital filtering, Poisson's process, and discrete probability distributions and mioment functions. The All chapters are provided with numerous problems for book is well written and does not contain any incorrect information or

genierating

solutioin.

IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, VOL.

SMC-9, NO. 8, AUGUST 1979

serious errors. In the opinion of the reviewer, the book seems to be helpful ill-prepared students, but may not be useful and stimulating for wellprepared students of engineering. The following comments are in order. First, the Laplace transforms which are still predominantly used in solving partial differential equations are completely excluded from this book. Second, the treatment of the inverse Laplace transforms without the residue theory of analytic functions is also uninspired. This book would have been more useful and stimulating for engineering students if some interesting recent applications of the transforms were included. In the opinion of the reviewer, this book is not really the top of its kind. It seems to be moderately successful as a

for

text at an

engineering undergraduate level.

Regelungssysteme mit Begrenzungen (Control Systems with Constraints)A. H. Glattfelder (Miunchen: R. Oldenbourg Verlag, 1974, 195 pp.). Reviewed by George M. Siouris, Aerospace Guidance and Metrology Center (AFLC), Newark Air Force Station, Newark, OH 43055. The present study investigates an area of growing interest, namely, techniques for dealing with control systems subjected to constraints. Most often, constrained control problems appear in the automation of indus-

447

Multivariable Control Theory-J. M. Layton (Stevenage, England: Peter Peregrinus, 1976, 236 pp.). Reviewed by Stephen Barnett, School of Mathematics, University of Bradford, Bradford, West Yorkshire, England BD7

lDP.

The aim of this book is to collect a number of recent developments in the theory of deterministic multivariable control systems. It is intended primarily for first-year graduate students who have a basic knowledge of single-input single-output control systems, together with an appropriate background in matrices and complex variable theory. It will also be useful to practicing control engineers wishing to bring themselves up-to-date. The book is divided into three parts, Part I covers fairly standard material on state-space representations; solution of linear equations; controllability, observability, and transfer-function matrices; and Lyapunov stability. The second part, on techniques of feedback controller design, is perhaps the most valuable, since it contains material not previously available within a single volume. After listing desirable properties of a control system, four recently developed approaches to controller design are described: pole assignment, dyadic transfer matrices, inverse Nyquist array, and sequential design. A useful feature is that the author includes his own critical comments on the methods. The third part of the book deals with optimization, including the calculus of variations, Pontryagin's principle, dynamic programming, and hill climbing. The range of topics covered in this relatively short book is remarkable, but despite its conciseness the treatment is generally most readable. Worked examples are given, and there are four or five problems for the reader at the end of each chapter. The book can be recommended as a welcome and timely contribution to the literature in this field.

trial processes. The essential components of such control systems are 1) the plant, 2) the sensor(s), and 3) the controller. The system is controlled by the controller, which compares the measured values to their desired values and adjusts the input variables to the plant. The book grew out of the author's research in control, at the Zurich Federal Institute of Technology during the years 1971-1972. This compact book has the unique quality of being interesting simultaneously to both the student and the specialist in the field. The book contains nine chapters. Chapter 1 opens with introductory material on control, definitions, mathematical, and empirical concepts in Optimization-S. S. Rao (New Delhi: Wiley Eastern, 1978, 711 pp.). control. Chapter 2 gives some examples representative of constrained con- Reviewed by Vimal Singh, Department of Electrical Engineering, Motilal trol systems, chosen from the areas of compressed air supply control, Nehru Regional Engineering College, Allahabad, India 211004. stirred-tank chemical reaction control, and dc machine control. A table with typical plant-transfer functions is also given. Thus an attempt has This book deals with the various optimization methods. It consists of 12 been made in this chapter to provide substance for later chapters by chapters and three appendices. Chapter 1 presents historical development, formulating examples of a wide class of interest. formulates and classifies optimization problems, and enumerates the varChapter 3, on system dynamic behavior demands, includes discussions ious solution techniques. Chapter 2 describes the classical techniques, that of reference signals, demands on the constraint, and demands on the con- is, the techniques of differential calculus in locating the optimum points of trol function. Chapter 4 deals with the design problem of constrained continuous and differentiable functions. control. Topics addressed in this chapter include choice of control setup, Linear programming forms the subject of Chapters 3 and 4. The simplex and the manifestation of the control structure. Chapter 5 discusses initial method is considered in Chapter 3, and some of the advanced topics such conditions and oscillations, auxiliary constraints, the steady state, and as duality theory, decomposition principle, etc., are discussed in Chapter 4. limit cycles. Chapter 6 is a comprehensive summary of key information on The next three chapters present the solution of nonlinear linear operation, procedures for reducing oscillations, and constraints of problems. The situation of a function of a single variable is programming considered in the main control quantity. An excellent feature of this chapter is the practi- Chapter 5, and the methods of unconstrained and constrained optimizacal application of the concepts presented. Chapter 7 is concerned with the tion are discussed in Chapters 6 and 7. relationship between constrained control and optimal systems. Discussed Geometric programming, dynamic programming, and integer programhere are such topics as operating point and state, development of the ming are covered in Chapters 8-10. Chapter 11presents the techniques of closed-loop system, and the relaxation of the assumptions. The applica- stochastic linear, nonlinear, and dynamic programming, and the last chaptions oriented engineer would certainly find this chapter useful. In Chapter ter reviews the critical path method, the program evaluation and review 8, the author treats the behavior of measurements subjected to stochastic technique, game theory, quadratic programming, and the calculus of disturbances. The material in this chapter is concise and informative. iations. Appendix A presents the definitions and properties of convex varand The emphasis here is on the influence of process noise, and the effect of concave functions, B discusses the computational aspects of Appendix measurement noise. The last chapter, Chapter 9, presents a summary and nonlinear programming, and Appendix C gives the proof of the an outlook of this area of control theory. A list of 52 references is included arithmetic-geometric inequality. at the end of the book. The author has made it a point to illustrate each new concept by a The book is well organized and assembled. The student and specialist in complete numerical thus making the concept easy and motivatthis area of control will be delighted by the fine illustrations and will also ing the reader for example, practical engineering applications. find merit in the many sophisticated ideas that are discussed. The book is As regards the coverage of the topics, the book is essentially a complete well motivated and will make an excellent reference for researchers and one. One can excellently run one or two courses based on this book, for students alike. students having a knowledge of differential calculus and matrix theory.