ANALYSIS AND DESIGN OF CONTROL SYSTEMS USING REDUCED ORDER MODELS

Abstract

The objective of this thesis is to develop new methods of model order reduction for single input single output (SISO), multi-input multi-output (MIMO) continuous and discrete time

systems and compare them with existing methods. This has been attempted for systems described by transfer functions or state space models. Frequency domain and mixed time and frequency domain methods have been proposed. These methods remove some of the inherent difficulties associated with other model order reduction methods. Some of the developed methods are completely new, while in some other cases available techni ques have been modified for removing their drawbacks. The reduced order models are utilized for designing controllers for SISO and MIMO continuous time systems. The performance of the original system with the designed controller is examined. Performance comparisons are also made by using controllers designed on the basis of original high order system. In classical reduction methods based on continued fract ion expansion (CFE), Pade approximation and the time moment matching, the approximation being mostly about a single frequ ency point (s=0), the reduced order models obtained may suffer from three serious drawbacks: (1) The reduced models may be unstable although the original sy s tem is stable. (2) The low accuracy in the mid and high frequency ranges. (3) It may exhibit non minimum phase characteristics. The mixed methods proposed in this thesis are devoid of the above shortcomings.

The thesis is organised as under The introductory first chapter is followed by a review of frequency domain model order reduction techniques included in the second chapter. New methods developed for reduction of SISO scalar systems are given in the third chapter. This chapter also discusses extension of the scalar methods to the mu1tivariable case. Development of exclusively new methods suitable for the model order reduction of multivariable sys tems have been included in Chapter four. Chapter five elabo rates new methods for the reduction of discrete time scalar systems which have also been extended to the multivariable case. Chapter six extends the methods developed in Chapter four, for the reduction of discrete time MIMO systems. The reduced order models obtained in the previous chapters are employed in Chapter seven, for the design of controllers for both SISO and MIMO systems using the principle of approximate model matching. The concluding chapter highlights the contri butions made in the thesis.