Model approximation of multiple delay transfer function models using multiple-point step response fitting

Abstract

Compared with model approximation for general SISO transfer function models with or without a single constant delay, the approximation problem for SISO transfer function models with multiple delays has received much less attention. In this paper, we attack this problem and thus present a multiple-point step response fitting based approximation method to derive the reduced models. A simple frequency-domain weighted recursive least squares (RLS) algorithm is proposed to determine a set of parameters so that the reduced models can approximate the original models by minimizing the defined frequency-domain squared-error between the step responses of the original and the reduced model. Numerical examples have demonstrated that the proposed approximation approach can not only introduce less dynamic approximation error, but also yield zero steady-state error.