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UBC Theses and Dissertations

Numerical and algebraic methods for computer-aided design of linear and piece-wise linear systems Sarkar, Basanta


A method is presented for linear control system design using functional relations between system parameters and system response. The functional relations are obtained by frequency domain evaluation of an integral performance criterion. The performance criterion is defined as a correlation measure between the responses of a known reference system and the system to be designed. A method is also presented for obtaining algebraic expressions relating the time-domain response of linear and piece-wise linear systems with system parameters. By means of a rational fraction approximation to the exponential e and through use of a known technique for evaluating time-domain convolution integrals, it becomes possible to obtain the time-domain response without the necessity of first having to determine the poles of the system. The time-domain response is obtained as a ratio of polynomials in t with the coefficients as algebraic functions of the system parameters. The extension of the linear design theory to cover non-linear and multivariable systems is given. Several examples are given to illustrate the usefulness of the proposed techniques.

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