Optimum approximation of high-order systems by low-order models†

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Abstract
A method has been proposed for the determination of optimum low-order models for a high-order system which minimize a specified error criterion for a given order of the model. The method is based on the pattern-search algorithm of Hooke and Jeeves. Starting from an approximate first or second-order model, an optimum model of that order is determined, and the process is continued with the order increasing progressively. As an example of the application of the method, optimum second-order models of a seventh-order system have been obtained using a number of different criteria for optimization. A third and a fourth-order optimum model have then been derived for a given criterion.

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