TABLE OF CONTENTS Vladimir Zakian
Abstract. The need for a new conceptual foundation for the design of control systems is explained. A new foundation is proposed, comprising a definition of control and three principles of systems design: the principle of inequalities, the principle of matching and the principle of uniform stability. A design theory is built on this foundation. The theory brings into sharper focus, hitherto elusive but central, concepts of tolerance to disturbances and over-design. It also gives ways of characterising a good design. The theory is shown to be the basis of design methods that can cope with, important and commonly occurring, design problems involving critical systems and other problems, where strict bounds on responses are required. The method of inequalities, that can be used to design such systems, is discussed.
Following a brief examination of the foundation of the conventional framework for the design of control systems, the need for a new framework is identified. The components of the foundation of this new framework are outlined in this section and developed in some detail in the rest of the chapter.
Although control mechanisms have been known since antiquity, two well known papers, Maxwell's (1868) and Nyquist's (1932), have been influential in forming the foundation of what is now the mainstream theory for the design of control systems, with its remarkable successes and, as will be seen, some significant limitations.
