ORDER -REDUCTION OF DISCRETE SYSTEMS USING RESPONSE MATCHING TECHNIQUES

Abstract

The analysis and design of high order systems is quite tedious and costly. It is therefore desirable that a higher order system be replaced by a lower order system such that the simplified model has enough information to closely approximate the response of the .given system. During the past two decades, various model reduction techniques, for continuous as well as digital control systems have been developed, in both the time and frequency domain. -~ Response matching technique is a .quite popular technique for the order reduction of large-scale systems. In this technique, coefficients of the numerator and denominator of ' the reduced order model are calculated in such a way that the error between a particular. response (step, frequency or impulse) of the original and reduced order system is minimum. In the present work, three different methods of order reduction based on response matching technique aredeveloped. In the methods developed, the difference is due to the two facts (i) type of the response to be matched. (ii) approach of minimizing the error between responses. The first method is based on step response matching. In this method, dominant poles of the reduced order system are retained in the reduced order system and numerator coefficients are calculated to minimize the error between step responses of the original and reduced order system. In second method retention of dominant poles is not done and instead both numerator and 'denominator coefficients are calculated in such a way as to minimize the error between frequency responses of original and reduced order system. The third method is based on impulse response . matching. But instead of matching the response directly - as in case of methods 1 and 2, order reduction is based on weighted impulse response gramians introduced in [27] for linear discrete systems. These gramians are given as functions of the impulse response of the system. These gramians contain the information about the stability and input-output behaviour of the system. The reduced order models are obtained by retaining the states corresponding to the dominant eigenvalues of these gramians.