Reduction of large scale linear dynamic SISO and MIMO systems using differential evolution optimization algorithm

Abstract

In this paper, a computationally simple approach is proposed for order reduction of large scale system linear dynamic SISO and MIMO system using differential evolutionary (DE) optimization technique. The method is based on minimizing the integral square error (ISE) between the transient responses of original and reduced order models pertaining to step input. The reduction procedure is simple, efficient and computer oriented. Stability of the reduced order system is always assured in proposed method. The algorithm is illustrated with help of two numerical examples and results are compared with other well known reduction techniques to show its superiority.Keywords--SISO system; MIMO system; model order reduction; differential evolutionary optimization; integral square error. I INTRODUCTIONThe mathematical description of most physical systems leads to higher order differential equations which are difficult to use either for analysis or controller synthesis. It is hence useful and sometimes necessary to find the possibility of finding some equation of the same type that of lower order that may be considered to adequately reflect the dominant characteristics of the system under consideration. This will help to better understanding of the physical system, reduce computational complexity, reduce hardware complexity and simplify the controller design.Several reduction methods are available in literature for reducing the order of large scale linear single and multivariable systems in frequency domain [1][2][3][4][5][6][7][8][9]. Further several methods have also been suggested by combining the features of two different reduction methods [4][5][6]. Recently, numerous methods of order reduction are also available in the literature [3], [5,6] which are based on error minimization by optimization techniques. In spite of having several reduction methods, none always gives the satisfactory results for all the systems.In recent years, one of the most promising research fields has been "Evolutionary techniques", an area utilizing analogies with nature or social systems. Differential evolutionary is branch of Evolution algorithm (EA) developed by Rainer Storn and Kennith Price in 1995 for optimization problem [10]. The differential algorithm is a promising approach for engineering optimization problem. It is a heuristic approach mainly having three advantages; finding the true global minimum regardless of the initial parameters value, fast convergence, and using few control parameters [11]. The DE algorithm is a population based algorithm like genetic algorithm using similar operators; crossover, mutation and selection. The main difference in constructing better solutions is that GA relies on crossover while DE relies on mutation operation. Being simple, fast, easy to use, very easily adapted for integer and discrete optimization, quite effective in non linear constraint optimization including penalty functions and useful for optimizing multi model search spaces are the other important features of DE [12][13].In present work, the ...

A hybrid bacterial foraging and modified particle swarm optimization for model order reduction

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