Inherent Design Limitations for Periodic and Sampled-Data Feedback Systems

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Fruedenberg 9414822 The objectives of this proposal are to advance the current state of sampled-data and periodic control systems. Contributions will be made to theory, applications, and pedagogy. A theory of inherent design limitations for sampled-data and periodic feedback systems will be developed to describe robustness and performance tradeoffs due to nonminimum phase zeros, unstable poles, and time delays in the analog plant. Various methodologies have been proposed for circumventing design limitations present in linear time invariant systems by purposely introducing sampling or other forms of periodic control. The theory to be developed will be used to critique these methodologies. The theory of design limitations takes intersample behavior into account, and shows that some of the purported advantages of sampling for overcoming design limitations are illusory because they only consider behavior at sampling instants. The techniques to be used in developing the results are the Bode and Poisson integrals from complex variable theory in conjunction with methods developed in the early 1950's for computing the response of an analog signal in a sampled-data system to a sinusoidal input. Particular emphasis is placed upon the fact that the discrete frequency response depends on aliased high frequency components of the analog response. This dependence is responsible for sensitivity and robustness difficulties due to high frequency model error. The theoretical portion of the proposed research will be carried out in collaboration with Rick Middleton of the University of Newcastle, Australia. Contributions to applications will be made in two areas. First, analysis techniques will be developed for assessing the quality of a sampled-data control design using frequency response plots instead of simulations. Second, models of inherently hybrid will be constructed for the purpose of assessing their bandwidth limitations and degree of design difficulty. Such systems are found in automotive applications, where the engine firing event is inherently discrete, and in sensing devices such as CCD cameras and Optical Multichannel Analyzers which are used in plasma processing. This work supports ongoing applications projects at the University of Michigan in the areas of automotive emission control and semiconductor manufacturing. Contributions to pedagogy arise from the used of techniques taught in standard textbooks to analyze inherent limitations and intersample behavior. The theory to be developed fills a gap in pedagogy that currently exists between the theory of analog and of sampled-data feedback systems. ***