MODEL SIMPLIFICATION OF LARGE ORDER CONTROL AND GUIDANCE SYSTEMS

Abstract

The first step in the analysis of any system is the formulation of its mathematical model. Mathematical model may be represented either in terms of a state variable description or an input-output description in the form of a transfer function. The dimension of the system matrix or the order of the transfer function is extremely large in case of space guidance systems, many process control systems, and in certain other types of systems. This results in computational difficulties and inhibits a proper under standing of many important aspects cf the inherent dynamic mechanism of the system. In such cases it is desirable tc simplify the system equations or reduce the order of the system transftr function. A basic requirement of a reduced order model is that it should behave very much similar to the original large order system. This thesis is concerned with the above mentioned problem of simplification of large order systems. The existing techniques of simplification have been reviewed. These may be classified into two oategories (a) Time domain techniques, and (b) Frequency domain tech niques. More emphasis is given to the latter in this review since the contribution of this thesis is in the frequency domain techniques. A new algorithm is evolved for the computation of moments from a given transfer function. This finds applica tion in the moment matching technique of simplification of large order systems. This algorithm is suitable for being programmed in a digital computer. Two new simplification techniques have been suggested in the frequency domain. The first one is a modification of the usual moment matching technique and it yields a super ior reduced order model. The second technique uses Chebychev polynomials for deriving the transfer function of a reduced order model. A recent technique of reduction based on transforma tion to Schwarz canonical form has been examined in detail. It is then shown that essentially this technique relies on the approximation of moments and hence may be termed as a frequency domain method. A critical study of the continued fraction technique of simplification has been made. It is shown that this technique is actually a special case of the moment matching technique. Finally, some suggestions are given for further work in this field.