International Journal of Computer Applications (0975 – 8887) Volume 42– No.17, March 2012 20 Application of Genetic Algorithm for Tuning of Reduced Ordered Robust PID Controller and Computer Simulations Muhammad Ejaz Department of Electronics Engg, Faculty of Engineering, International Islamic University Islamabad, Pakistan ABSTRACT Robust controllers designed via H ∞ Loop Shaping are complicated and are of order higher than that of the plant. It is very difficult to implement these controllers in practical engineering applications. To overcome this problem, Genetic Algorithm is used to approximate a robust PID controller from H ∞ Loop Shaping controller so that the difficulties in implementation of higher order controller can be avoided. General Terms Application of Genetic Algorithm in Robust Control System. Keywords Robust controller, H ∞ Loop Shaping, Weight selection, Genetic Algorithm, PID Controller and Missile control system. 1. INTRODUCTION H∞ Loop Shaping controller design method is a frequency domain technique to design robust controllers for the system which have uncertainty in their parameters and disturbance interferences. While designing robust controller not only robust stability is sufficient for designing control system, but also the other performances specifications of the closed loop controlled system such as rise time, settling time, overshoot and steady state error, etc. are also important considerations to be satisfied. Loop Shaping is a graphical technique for designing a controller to achieve robust stability and performance for a stable and minimum phase systems. In this approach, designer plots the singular value plot of open loop plant and carries out its analysis with view to its stability and performance specification and then accordingly designs pre and or post compensator to be used as weighting function to get desired shape of open loop plot curve of the system. In this way loop shaping approach is closely related to H  control design method in which the designer tries to minimize the maximum singular value of the plant. By shaping the plants loop function, H  loop-shaping methods actually minimize peak of maximum singular i.e. H  norm of the closed loop system‟s sensitivity and complimentary sensitivity function [1]. In H ∞ Loop Shaping design method first the designer selects the suitable weights i.e. pre and or post compensator by utilizing the classical method of loop shaping satisfying good performance and stability specifications and then H ∞ robust controller is designed using H ∞ Loop Shaping design method to deal with both robust stability and robust performance specifications for control system [2]. In this method resulting controllers are of order higher than that of the original plant. So many difficulties arise when these higher order controllers are implemented in practical engineering applications due to their hardware implementation [3]. Therefore controllers with lower orders are preferable in terms of computing efforts and being cost effective. In this paper, Genetic Algorithm based technique is used for tuning of fix-order and fix structure PID controller from complicated and higher order H ∞ Loop Shaping controller so that the difficulties arising in implementation of higher order controller can be avoided. This method is easy to use and the resulting PID controller has given good results in both time and frequency domains as shown in computer simulations. 1.1 Previous work related to low order control design H PID controller has been designed for plants like Pneumatic Servo-system using Genetic Algorithm in reference [4] and Genetic Algorithm based PI controller for Boiler system is designed in reference [5]. New sufficient LMI conditions for low order controller design were presented in reference [6]; however some degree of conservatism was introduced due to the conditions only being sufficient. An algorithm that combines a randomization algorithm with a coordinate descent cross-decomposition algorithm is presented in reference [7]. Particle Swarm Optimization (PSO) has been applied to design the fixed-structure robust H ∞ loop shaping controller in reference [8]. 1.2 Motivation For H  PID Controller PID controllers are extensively used in industries due to their simplicity in tuning and ease of implementation. Their easy method of tuning and simple structure leads to quick designs [9]. That is why these are most popular and commonly used fixed-structure and fixed-order controllers. These advantages make PID controllers an attractive option. A completely different approach worth mentioning is to compute the full order H ∞ controller and then apply model reduction techniques using Genetic Algorithm to get a low order controller. In this way it is possible to design a lower order fixed-order, fixed-structure and at the same time optimal and robust controller. 2. H  LOOP SHAPING A robust controller design technique, so called H ∞ Loop shaping methods was first introduced by Macfarlane and Glover [10]. H ∞ loop-shaping design procedure provides a framework for designing robust controllers that not only gives robust stability but also robust performance at the same time. In this robust control design procedure, the designer first of all shapes the open-loop plant G(s) with the weighting functions, so called pre-compensator W 1 to satisfy performance and