MODEL REDUCTION OF DISCRETE TIME SYSTEMS IN FREQUENCY DOMAIN

Abstract

The work presented in the dissertation deals with frequency domain method for the model reduction of single input single output discrete time systems in z-transfer function. Reduction of higher order systems transfer function to lower order model. has been an important subject area in the control engineering environment for many years. In the model order reduction, find the low order model of higher order system, which reflect the dominant characteristic of original system. For the matching the characteristic of original and reduced system, normally step responses matching are done to consider the low order model approximate to high order system. There are two approaches for the reduction of discrete time system, namely the direct method and indirect method. The indirect • method used some transformation and then reduction is carried in the transformed domain. First the z-transfer for function are transformed into - the w-domain by the bilinear transformation z= (l+w)/ (1-w). Then model reduction method Routh approximation is used respectively to reduce the order of the transfer function. The transformed model is then converted in the z-domain. The direct method do not required any transformations. A bilinear Schwarz approximation method is presented for the direct model reduction of discrete-time system. Both the approaches are discussed in the dissertation and the comparison with existing is carried out. The advantages of the proposal method are that frequency domain characteristics of the original systems can be preserved in the reduced models and the reduced models are always stable provided, the original models are stable. In each method, a general formulation and step for reducing nth order system to an rth order model along with numerical example, result and discussion are given.