Model Order Reduction of Interval Systems Using Mixed Methods

Abstract

The objective of this thesis is to originate new techniques of model order reduction for single input single output (SISO), multi-input multi-output (MIMO) continuous and discrete time interval systems and compare them with existing techniques. This has been attempted for systems described by transfer function models. Existing model reduction methods for fixed coefficients have been extended to interval systems in frequency domain. The developed methods have intuitive appeal and compare favourably with available techniques. These methods remove some of the inherent difficulties associated with existing model order reduction methods of interval systems. The performance of the original system and reduced order system is examined. The reduced order interval models obtained by the extension of fixed coefficients reduction techniques to interval systems may suffer from the following drawbacks. (1) The reduced interval models may be unstable though the original interval system is stable. (2) It may exhibit non minimum phase characteristics. (3) The reduced interval models produce low accuracy in the mid and high frequency ranges. The proposed methods in the thesis are devoid of these drawbacks. The following advantages are there using proposed methods (1) The error approximation is small. (2) The proposed techniques conserve the original system characteristics such as stability. (3) The proposed methods are computationally efficient. The thesis is organised as under: The introductory first chapter is followed by a review of stability analysis of an interval system included in the second chapter. A review of frequency domain interval iii system model order reduction techniques are given in the third chapter. This chapter also discuss the reasons for failures of extending Routh approximation to interval systems. New mixed methods developed for model reduction of continuous time interval systems are given in chapter four. This chapter also shows the advantage of new techniques when compared with existing reduction techniques for interval systems. In Chapter 5, two modified methods are proposed based on differentiation method and Schwarz approximation method considering dependency property. Chapter six elaborates new methods for the reduction of discrete time interval systems. In chapter 7, interval plant stabilization by using stability boundary locus is discussed briefly. The concluding chapter highlights the contributions made in the thesis.