REDUCED ORDER MODELLING WITH AND WITHOUT TIME DELAY

Abstract

The work presented in the dissertation deals with time domain (i.e., based on a state space equations of the original system) and frequency domain (i.e., based on a transfer function description of the original system) model reduction techniques with and without time delay, for single-input single-output linear time invariant dynamic systems. In time domain, Modal Analysis Approach of order reduction, its mathematical development, three basic methods of this approach and the new ideas, i.e., (i) to handle repeated and complex eigen values, (ii) criterion for selecting the order of reduced system, (iii) Modal analysis approach with equivalent lag, which are introduced in this approach, are discussed in detail alongwith numerical examples, results and discussions. In frequency domain, the mixed methods are given to solve the problem of Pade approximation technique and CFE based reduced models respectively, which turn out to be occasionally unstable for a stable high order system. The denominator poles are chosen from the Routh-Hurwitz stability array while the numerator dynamics are determined so that the initial few quotients of continued fraction expansions of the original and reduced systems are the same or so that the initial few time moments of the respective systems are identical in the Pade sense. In one method, a general formulation is given for reducing an n`h order system to a r`h order model with an additional time delay term. The comparison between the proposed time delay methods and the existing technique [11], is also discussed with the help of numerical examples. Finally the work ends with the new method of order reduction without time delay in which the dominant poles are retained according to the order to be reduced to and zeroes are synthesized by zero spectrum analysis method.