Particle swarm optimisation based proportional integral and derivative (PID) controller design for linear discrete time system using reduced order model

Abstract

Design of proportional integral and derivative (PID) controller for a higher order discrete system is presented in this paper. The design and tuning of PID controller parameters proportional gain Kp, integral gain Ki and derivative gain Kd are complex and time consuming process for a higher order system. To overcome this, an approximate second order equivalent model is obtained for the higher order system which preserves the stability and retains the characteristics of original system. The proposed method of model reduction uses the advantages of Routh stability array and Particle swarm optimization (PSO). PID controller is designed using reduced order model and is cascaded with the original system. The performance specifications of the closed loop system with the designed controller are analysed. The proposed algorithm is illustrated through numerical examples.   Key words: Cumulative error index, model reduction, particle swarm optimisation, proportional integral and derivative (PID) controller, Routh array, stability.