Linear Time invariant Discrete Multi-variable System Model Reduction using Particle Swarm Optimization

摘要

In this paper, a particle swarm optimization approach for obtaining a lower order approximant of a given absolutely stable higher order linear time invariant discrete multi-variable system has been dealt. A linear transformation z = p + 1 is used to analyze the problem in p-domain. A simple auxiliary scheme has been suggested for obtaining the transfer function of the initial lower order model by maintaining the transient gain ratio and steady state gain ratio of the original higher order system in p-domain. Particle swarm optimization (PSO) is used to obtain a better lower order approximant for the individual single input single output (SISO) system that reflects the characteristics of the corresponding higher order system that constitute the given multi-input multi-output (MIMO) system in p-domain. The integral square error is used as an objective function for selecting the best lower order model. Applying reverse transformation p = z-1 the final transfer function matrix of the lower order MIMO model in z-domain is declared. A numerical example illustrates the proposed methodology.