Order reduction of discrete system models employing mixed conventional techniques and evolutionary techniques

Abstract

A single-input single-output discrete system of high order is reduced to a second order in this paper employing two approaches: an indirect approach using conventional techniques and a direct approach using evolutionary techniques. In the indirect approach, the discrete system is transformed to a continuous system and reduced to a lower order by Padê approximation (by matching Time Moments or Markov parameters) combined with Routh approximation for ensuring stability and inverse transformed back to a lower order discrete system. In the evolutionary approach, the discrete system is reduced to a lower order discrete function and optimized based on minimization of ISE as the objective function using Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) independently. The step responses of reduced order discrete systems obtained by the conventional and evolutionary approaches are compared to determine the best solution.