A New Model Reduction Technique for Linear Systems

Abstract

A new method of reduction of high order linear time-invariant systems to low order is presented. New algorithms are proposed to obtain the reduced order model. When a zero-leading row appears in the α-table of the Routh Approximation method, the models cannot be formulated as the α-parameter will be indefinite. In this paper, new α-β tables are formulated in a way different from the Routh's table to overcome this problem. The new technique is simple and direct since it involves no computation of eigen values and residues and avoids the use of recursive formulae unlike in the Routh Approximation Methods. It always gives a stable reduced order model if the original system is stable. The method is illustrated with several numerical examples. The frequency response of the proposed model is more closely following that of the original system than the responses of the models by Routh Approximation and stability equation method. This feature is advantageous in the analysis and design of non-linear systems using frequency domain techniques.