The design of a fuzzy cascade controller for ball and beam system: A study in optimization with the use of parallel genetic algorithms

Abstract

In this study, we introduce a design methodology for an optimized fuzzy cascade controller for ball and beam system by exploiting the use of hierarchical fair competition-based genetic algorithm (HFCGA). The ball and beam system is a well-known control engineering experimental setup which consists of servo motor, beam and ball and exhibits a number of interesting and challenging properties when considered from the control perspective. The position of ball is determined through the control of a servo motor. The displacement change of the position of ball requires 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 the fuzzy cascade controller scheme which consists of the outer (1st) controller and the inner (2nd) controller in a cascaded architecture. Auto-tuning of the parameters of the controller (viz. scaling factors) of each fuzzy controller is realized with the use of the HFCGA. The set-point value of the inner controller (the 2nd controller) corresponds to the position angle of a servo motor, and is given as a reference value which enters into the inner controller as the 2nd controller of the two cascaded controllers. HFCGA is a kind of a parallel genetic algorithm (PGA), which helps alleviate an effect of premature convergence being a potential shortcoming present in conventional genetic algorithms (GAs). A detailed comparative analysis carried out from the viewpoint of the performance and the design methodology, is provided for the fuzzy cascade controller and the conventional PD cascade controller whose design relied on the use of the serial genetic algorithms.