Design of PID Controller for Higher Order Discrete Systems Based on Order Reduction Employing ABC Algorithm

Abstract

This paper proposes a new computational simple scheme for Model Order Reduction to design a discrete PID controller for higher order linear time invariant discrete systems. Artificial Bee Colony (ABC) optimization algorithm is employed for both order reduction and controller design. First a successful reduced order model is obtained for original higher order discrete system using ABC optimization algorithm which is based on the minimization of integral square error between the original and reduced order models pertaining to step input. Then a PID controller is designed for reduced order model, based on the minimization of integral square error between the desired response and actual response, pertaining to a unit step input using ABC algorithm. Finally the designed PID controller is connected to the original higher order discrete system to get the desired specifications. The validity of the proposed method is illustrated through a numerical example.

Keywords: Discrete system, Model order reduction, PID controller, Integral square error, Artificial Bee Colony algorithm.