Order Reduction of Discrete Systems using Step Response Matching

Abstract

A conceptually simple and new method for the model order reduction of linear time invariant discrete system is presented. The proposed method uses the concept of dominant poles retention in the low order model and exact matching of steady-state parts of the transient responses of low and high order models. Zeros of the reduced order system are determined by matching the transient parts at a few selected points of step responses of reduced and high order systems. Selection of points in the step response curve is based on the fact that only the prominent stages like starting point, first undershoot, and peak overshoot are considered. These being well defined points, when chosen, can be applied to most of the systems and give satisfactory results, in terms of minimum integral error function between the original high order system (OHOS) and the reduced low order system (RLOS). When the transient response is without undershoot or overshoot, a different strategy is suggested. Stability of the RLOS is always assured in the proposed method. A number of examples have been tried using the method and a comparative analysis with existing methods highlights its relevance.