Optimized fuzzy PD cascade controller: A comparative analysis and design

In this study, we develop a design methodology for a fuzzy PD cascade controller for a ball & beam system by using particle swarm optimization (PSO). The ball & beam system is a well-known control engineering experimental setup, which consists of servo motor, beam, and ball. This system exhibits a number of interesting and challenging properties when being considered from the control perspective. The ball & beam system determines the position of ball through the control of a servo motor. The displacement change of the position of ball leads to the change of the angle of the beam which determines the position angle of a servo motor. Consequently the variation of the position of the moving ball and the ensuing change of the angle of the beam results in the change of the position angle of a servo motor. We introduce a fuzzy PD cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller arranged in a cascaded architecture. Auto-tuning of the parameters of the controller (scaling factors) as well as fuzzy rules of each fuzzy PD controller is realized with the use of the PSO. Moreover the comparative analysis of results of optimization realized by PSO and GA based on SGA (Serial Genetic Algorithms) is discussed from the viewpoint of control performance. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as reference value, which enters into the inner controller as the 2nd controller of the two cascaded controllers. The optimization process takes advantage of a rapid convergence of PSO being used here as a generic search mechanism. A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy PD cascade controller and the conventional PD cascade controller whose design exploited serial genetic algorithms.