(BOOK)-PID Controllers for Time Delay Systems

This monograph presents our recent results on the proportionalintegr derivative PID controller and its design analysis and synthesis The fo cus is on linear timeinvariant plants that may contain a time delay in the feedback loop This setting captures many realworld practical and in dustrial situations The results given here include and complement those published in Structure and Synthesis of PID Controllers by Datta Ho and Bhattacharyya 10 In 10 we mainly dealt with the delayfree case The main contribution described here is the efficient computation of the entire set of PID controllers achieving stability and various performance specifications The performance specifications that can be handled within our machinery are classical ones such as gain and phase margin as well as modern ones such as Hoo norms of closedloop transfer functions Finding the entire set is the key enabling step to realistic design with several design criteria The computation is efficient because it reduces most often to lin ear programming with a sweeping parameter which is typically the propor tional gain This is achieved by developing some preliminary results on root counting which generalize the classical HermiteBiehler Theorem and also by exploiting some fundamental results of Pontryagin on quasipolynomials to extract useful information for controller synthesis The efficiency is im portant for developing software design packages which we are sure will be forthcoming in the near future as well as the development of further capabilities such as adaptive PID design and online implementation

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