Relative Stability using Simplified Routh Approximation Method (SRAM)

Abstract

A new Simplified Routh Approximation Method (SRAM) for model reduction of high order linear time-invariant systems is proposed. The Routh Approximation Methods for model reduction discussed in literature are based on α and β parameters. This paper presents a new method (SRAM) for model reduction involving only α-parameters to make the method simple. The proposed method is a direct method for deriving a k^th-order approximant. The main advantage is that, in order to find the parameters of the k^th-order approximant, it will no longer be necessary to previously obtain those of all p^th-order approximants (p⩽k-1) as is the case with Routh Approximation Methods [3, 5, 6]. The additional advantageous feature of SRAM is that it always gives a stable reduced order model if the original system is stable. New algorithms are proposed to obtain the numerator and denominator polynomials of the reduced order models using only α-parameters, thus avoiding the use of β-parameters and recursive formulae. The method is illustrated with several numerical examples. The frequency response of the proposed model by SRAM closely follows that of the original system. This feature is very useful for the analysis and design of nonlinear systems using frequency domain techniques. It is also shown how SRAM can easily be applied for obtaining the relative stability parameter values. The proposed procedure is purely analytical, simple and direct.