GA Cascaded P-PD Control on Ball and Beam System with Two-Stage Objective Function

Abstract

This paper proposed a two-stage objective function with genetic algorithm (GA) based tuning on two controller schema - a PD/cascaded P-PD control on a traditional ball and beam system, serving as a prototype for a friction fruit conveyor system. The ball and beam system governed under such controllers is excited with step input, the corresponding system performance factors are captured - rise time, settling time and overshoot. A probabilistic random search on optimum controller parameters is carried with GA method, multiple cost functions - ISE, IAE, ITSE and ITAE, with are evaluated to form a performance cost matrix, which is the first stage of the objective function. The optimum parameter search stops with two conditions; one is that the maximum number of chromosome generation is reached, and the other one is that the performance cost stops improving consecutively for ten generations. The second stage of the objective function is proceeded to decide the found optimum controller parameter solution. The result is decided by taking account of the previously captured performance factors. These factors are normalized and combined with a heuristic weight set to determine a minimum decision cost. The minimum cost chromosome, with ITSE, is the optimum from global found solution space. With two-stage objective function, the GA tuned cascaded P-PD control result on the ball and beam system, meets all system requirements and is satisfactory. Such method can be later implemented on the friction fruit conveyor system for fruit position control and sorting applications.