STABLE REDUCED ORDER MODELS FOR DISCRETE TIME SYSTEMS

Abstract

The work presented in the dissertation deals with algorithms for model reduction of single input single output discrete time systems in z-transfer function and comparison of results among algorithms for best suitable stable reduced model of given higher order system. Reduction of higher order system transfer function to low order models has been an important area in the control engineering environment for many years. In the model reduction, finding the low order model of given higher order system transfer function, which reflects the dominant characteristics of original system, normally step responses matching are performed There are several different approaches for the reduction of discrete time systems. Here three different such type of algorithms are discussed, namely Markov and H-parameter matching (MHM), Genetic Algorithm (direct search method), and combination of above both algorithms. First algorithm requires error function in terms of reduced model variables, Pascal triangle. Markov parameters will dictate transient response and h-parameters will dictate the later part of response including steady state response. By making use of these variables we find out the reduced model parameters. Second algorithm is direct search optimization technique. It directs searching for reduced model variables in space in proper steps and also avoids local minima. Third algorithm is combination of both first and second algorithm. It has the advantages of both algorithms and these are explained in detail in chapter 5. The advantages of the proposed algorithms are that characteristics of original system can be preserved in reduced models and in the reduced models are always stable provided, the original system stable. In each algorithm, general formulation, steps involved and flow charts for reducing nth order system to rth order are explained with numerical example