Many techniques are available for designing linear multivariable analog controllers: pole placement using observer-based controllers, loopshaping, the inverse Nyquist array method, convex optimization in controller parameter space, and so on. One class of techniques is to specify a performance function and then optimize it, and one such performance function is the norm of the closed-loop transfer matrix, suitably weighted. The two most popular norms to optimize are the H-2 and H-infinity norms. The fact that most new industrial controllers are digital provides strong motivation for adapting or extending these design techniques to digital control systems.
This book is intended as a graduate text in linear sampled-data (SD) control systems. The subject of SD control is a subdomain of digital control; it deals with sampled signals and their discrete-time processing, but not with quantization effects nor with issues of real-time software. SD control systems consist of continuous-time plants to be controlled, discrete-time controllers controlling them, and ideal continuous-to-discrete and discrete-to-continuous transformers.
As a prerequisite, the ideal reader would know multivariable analog control design, especially H-2 and H-infinity theory---a user's guide to H-2 and H-infinity theory is presented in Chapter 2. A prior course on digital control at the undergraduate level would also be an asset. Standard facts about state models in continuous and discrete time are collected in the appendix.
Part I (Chapters 2-8) is aimed at first-year graduate students, while Part II (Chapters 9-13) is more advanced. In particular, some of the development in the later chapters is framed in the language of operator theory.
In Part I we present two indirect methods of SD controller design: - Discretize the plant and design the controller in discrete time. - Design the controller in continuous time, then discretize it. These two approaches both involve approximations to the real problem, which involves an analog plant, continuous-time performance specifications, and a SD controller. Part II proposes a direct attack in the continuous-time domain, where SD systems are time-varying (actually, periodic). The main problems addressed are H-2 and H-infinity optimal SD control. The solutions are presented in forms that can readily be programmed in, for example, MATLAB. MATLAB with the mu-Tools toolbox was used for the examples.