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UBC Theses and Dissertations

Identification and parameter optimizaiton of linear systems with time delay Robinson, William Reginald

Abstract

Analog computer methods are developed for iterative parameter optimization and continuous identification of linear systems with time delay. A unified treatment of structural sensitivity analysis is presented. New results are presented on the simultaneous generation of the second-order sensitivity functions for a class of systems. To test the theory, a simple controller is proposed for a linear time-invariant process with time delay. The controller parameters are to be adjusted so that the process output closely approximates some desired output, while remaining insensitive to fluctuations in the plant delay. For this purpose, an iterative procedure is used to minimize a combined error-sensitivity performance index. Two continuous identification methods are presented. The first of these is an output error method derived using structural sensitivity analysis, while the second is an equation error method. It is assumed that processes to be identified can be represented by linear differential-difference equations. Unknown parameters in these equations are determined by a steepest descent technique. Both methods are applied for the first time to the important problem, of identifying constant and time varying time delays. The two methods are compared, and the equation error method is found to be superior. It is shown that this method is stable in the linear region in parameter space, and is always stable if all process delays are known. Techniques leading to a more economical implementation of the equation error method are presented.

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