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.
