## Digital control of dynamic systems. 2nd ed.(English)Zbl 0697.93002

Amsterdam etc: Addison-Wesley Publishing Company. xiv, 837 p. (1990).
The book is about the use of digital computers in order to study dynamic systems and to design real time controllers for such systems. It is a revised version (second edition) of a book originally published in 1980. In the preface of the second edition it is clearly indicated what the differences are. The current book contains chapters on “Nonlinear control” and “Application and practice”, which the original edition did not have. It will be no surprise that most chapters are devoted to linear systems.
It is a well written textbook; the text is easy to follow. Many examples elucidate the text and at the end of each chapter there are exercises. In fact much of the theory is preceded by examples (from various fields of applications), such that the theory follows naturally. In this way the reader is never in doubt whether a theory is useful or not. Very briefly stated one could say that practice comes before mathematics. The authors suggest laboratory work as a supplement to the contents of the book. In this context MATLAB is useful as a package both for design and some matrix calculations. Frequently differences (and pitfalls) between continuous time and discrete time design methods are given. Thus one gets a good feeling for the discretization aspects of a (originally possibly continuous time) design problem. The prerequisites to follow the text are a working knowledge of Laplace transforms, some matrix algebra, and a first course in linear feedback controls.
Let us now consider the contents and then end with some conclusions. Chapter one is a general introduction in which various notions (and their differences) are intuitively explained. Examples of such notions are disturbance rejection, robustness, difference between discrete and digital signals, aliasing. Chapter two deals with the analysis of linear, discrete systems, where the emphasis is on the z-transform. It starts with linear difference equations. Subsequently we get transfer functions and z-transforms, BIBO stability, canonical forms, state space description. Numerical aspects are considered also such as the calculation of $$e^ A$$ where A is a square matrix. Chapter three, we are in the meantime on page 101, deals with sampled-data systems. The impulse modulation was used to represent the sampling process. The subject of Chapter four is: Discrete Equivalents to continuous transfer functions: The digital filter. The techniques presented for the construction of such discrete equivalents are numerical integration, zero-pole mapping and hold-equivalence.
The basic deterministic design methods are presented in Chapters five and six, the root-locus and frequency response methods in Chapter five and the pole placement and estimators in Chapter six. In Chapter five, four design techniques are presented, viz. emulation, root locus, frequency responses, direct transfer function calculation. In Chapter six observability and controllability first show up as technical conditions for the existence of certain inverse matrices in the design process. Later on these concepts are discussed in a broader context. The separation principle and reduced order observers also belong to Chapter six.
In Chapter seven, it starts on page 322, the nonlinear phenomenon of amplitude quantization and its effects on system error and system dynamic response is studied. In Chapter eight identification is introduced. The central technique presented is the maximum likelihood method for parametric identification which was developed as a generalization of least squares. Chapter nine is on multivariable and optimal control. The emphasis is on LQ problems (linear dynamics, quadratic criterion) the Riccati-equation plays a role in the solution. The discretization of a continuous time quadratic criterion leads to a discrete time quadratic criterion in which there are cross terms between the control and the state. This chapter ends with a design of a magnetic-tape-drive. Chapter ten deals with sample rate selection. The selection of the best sample rate is a compromise. Several factors which influence this compromise are discussed. Chapter eleven is on nonlinear control. It discusses linearization, describing functions, equivalent gains, the (false) Aizerman’s conjecture, Lyapunov functions amongst others. The criterion of time optimality is also discussed within this chapter. Other topics briefly dealt with are adaptive control, self-tuning regulators and model reference techniques. In Chapter twelve the application and practice of digital control is discussed by means of a case study of a disk-file head-positioning servomechanism. The basics of hardware implementation of digital control: processors, interfaces, A/D and D/A converters, etc. are covered. Some appendices, a list of references and an index conclude the book.
One will learn a lot from this book; the authors discuss many problems with which the designer of real digital control systems is faced. The mathematics is kept to a minimum. Eigenvalues and eigenvectors belong already to the class of a few unusual or more advanced topics (as written in the preface). Jordan canonical forms are not discussed (in the analysis matrices are diagonalizable). There is no discussion on the convergence of the solution of the differential Riccati-equation to the solution of the corresponding algebraic Riccati equation. This does not mean that the mathematics used is not correct; the statements given are correct and are put in the proper context.
In conclusion, a very readable textbook in which the authors put a lot of practical experience.
Reviewer: G.J.Olsder

### MSC:

 93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory 93B50 Synthesis problems

Matlab