Differential Evolution algorithm for model reduction of SISO discrete systems

Reduction of Single Input Single Output (SISO) discrete systems into Reduced Order Model (ROM), using a conventional and a bio-inspired evolutionary technique is presented in this paper. In the conventional technique, mixed advantages of Modified Cauer Form (MCF) and differentiation are used. In this method, the original discrete system is first converted into equivalent continuous system by applying bilinear transformation. The denominator of the equivalent continuous system and its reciprocal are differentiated successively and the reduced denominator of the desired order is obtained by combining the differentiated polynomials. The numerator is obtained by matching the quotients of MCF. Finally, the reduced continuous system is converted back into discrete system using inverse bilinear transformation. In the evolutionary technique method, Differential Evolution (DE) optimization technique is employed to reduce the higher order model. DE method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical example.