zbMATH — the first resource for mathematics

Sampled-data control systems. Analysis and synthesis, robust system design. (Transl. from the German). (English) Zbl 0639.93001
Communications and Control Engineering Series. Berlin etc.: Springer- Verlag. XIV, 596 p.; DM 169.00 (1985).
[German editions have been published in 1972 and 1983, a Polish translation in 1976.]
Sampled-data control systems are of growing importance. Modern microprocessor technology allows design-flexibility and extensibility in an efficient and economical manner. With the author’s book a modern approach to sampled-data system analysis and design methods is available.
The book is divided into 9 chapters and 4 appendices. In the first chapter the structure of sampled data systems is described. Typical examples are considered. The controller design problem is defined. Continuous systems are briefly reviewed in chapter 2. Some basic notions and relations are given for later reference. Modelling and linearization is described by considering a physical system (a loading bridge). This system is used as an illustrating example in nearly all following chapters.
In chapter 3 discretization of continuous mathematical models is considered. z-transform methods and frequency response methods are presented. Stability of closed-loop systems and of systems with a nonlinearity is investigated. Some special sampling problems such as noninstantaneous sampling and nonsynchronous sampling are considered. Chapter 4 and chapter 5 are devoted to state space methods. In Chapter 4 controllability is studied. The influence of the sampling period to controllability and the suitable choice of the sampling period is investigated. Related fields such as bandwith and the design of anti- aliasing filters are discussed. Chapter 5 deals with observability and observer design including disturbance observers. The tools developed in chapter 3 to 5 are used in chapter 6 for synthesis. Important aspects of controller design are listed. Controller structures are discussed. Time domain and frequency domain specifications are discussed.
Whereas the first six chapters cover the relevant subjects which are found in most text books dealing with sampling systems the last three chapters contain new material based on research work of the author. Chapters 7 and 8 are devoted to robust control: Usually the plant is described by a simplified mathematical model. Nonlinearities are often neglected. The parameters are not known exactly. The author proposes to cope with this difficulties by considering several plant models with different parameters. Regions in the space P of the coefficients of the characteristic polynomial are considered. Desired regions which result in “nice stability” are defined. A state-feedback vector k is obtained by mapping the P-space into the k-space. In chapter 8 graphical and numerical design procedures are described and illustrated by examples.
The last chapter is devoted to multivariable systems. Controllability indices are introduced. The concept of finite effect sequences is derived and used for controller design in the multivariable case. Finally, a brief introduction to linear quadratic control is presented. In the four appendices basic material for matrix operations and z-transform methods is summarized. Canonical forms and stability criteria are considered. Two application examples are described.
Though the emphasis of the book is on state space methods, classical techniques are covered completely. The theory is illustrated by numerical examples. At the end of each chapter numerous problems are given. The book is a valuable introduction to sampled-data systems (chapter 1 to 6) and an excellent contribution to the most interesting topics “robust control” and “finite effect sequences” (chapters 7 to 9).
Reviewer: R.Tracht

93-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to systems and control theory
93B50 Synthesis problems
93C57 Sampled-data control/observation systems
93B05 Controllability
93B07 Observability
93B17 Transformations
93B35 Sensitivity (robustness)
93B55 Pole and zero placement problems
93C35 Multivariable systems, multidimensional control systems
93C55 Discrete-time control/observation systems
93D15 Stabilization of systems by feedback