MINIMAL REALISATION AND MODEL REDUCTION FOR LINEAR DYNAMIC SYSTEMS

Abstract

The aim of this thesis is two-fold ; firstly to present a method for obtaining the Minimal Realization of Linear Dynamic Systems & secondly to discuss frequency domain methods for model reduction The realization of a rational transfer function-(matrix) into a minimal system of first order differential equations is a fundamental problem in linear system theory. This formulation in the form of state equations has many practical applications. For example, it provides a straight forward approach to studying the behaviour of the system by simulating it on an analogue or a digital computer. Further more the realization provides a method of synthesizing a transfer function by use of operational amplifier circuits. Finally there are many design techniques and computational algorithms developed exclusively for state equations.In order to apply these techniques and algorithms, transfer functions must be realized. It is a well established fact that the complexity of physical systems make their exact analysis a rather difficult and possibly a non desirable task ,mainly due to the difficult economic and computational considerations involved.This makes apparent the need for using model order reduction methods to obtain adequate reduced order model(s) which constitute a good approximation of the original system. The techniques to obtain the reduced order models in time domain are complex and require optimization while reduced order models in frequency domain can be obtained with less effort.Now the minimal realization of these reduced order models in frequency domain directly gives the reduced order models in state space form(i.e. time domain) without using optimization techniques. In this work ,Software based on Rosenbrock's system matrix formulation has been developed for the on line determination of minimal realizations of transfer functions (matrices). Then the frequency domain methods for model reduction namely Pade Approximation Method ,Stability Equation Method •and Dominant Poles Retention Method (with Pade Approximation Technique) have been carried out on a digital computer.And then these reduced order models are obtained in state space form using minimal realization algorithm. (