Chaos Control Using PID and Lead Compensator Based on Fuzzy Gain Scheduling Technique

Abstract

In this paper, a new method for tracking a desired path in nonlinear chaotic systems is presented. This method is based on using fuzzy gain scheduling in designing PID controller and Lead compensator. Using two standard controllers, PID and Lead, instead of complicated and costly nonlinear controllers is the main advantage of the proposed control system. PID controller has a stabilizing role whereas Lead compensator improves the performance of the system to track the desired path properly. To determine the PID and Lead gains, the nonlinear system is linearized around some working points which are the points of the desired path in specified times, and the gains are designed for each linearized system. Using a Sugeno system as a fuzzy gain scheduler, PID and Lead gains are determined in each time and are applied to the control system to make the nonlinear system track the desired path. To verify the presented method, Duffing equation as a chaotic system is considered to be controlled to which the proposed procedure is applied. Simulation results show the effectiveness of fuzzy gain scheduling in making the nonlinear system track different desired paths more smoothly.