Dynamic Fuzzy Membership Intervals with Two-Stage Objective Function for Ball and Beam System based on GA Tuning
Joseph K. P. Tsoi, Nitish D. Patel, Akshya Kumar Swain, Xu Huang · 2020
This paper proposed a two-stage objective function with genetic algorithm (GA) to refine an additional fuzziness layer on dynamic membership intervals of Type-I fuzzy logic control(FLC). The refined dynamic membership intervals Type-I FLC is applied on a traditional ball and beam system, serving as a prototype for a friction fruit conveyor system. The ball and beam system governed under Type-I FLC 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 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 ITAE, is the optimum from global found solution space and sets fixed intervals on the dynamic membership range of Type-I FLC. With two-stage objective function, improved rise time and settling time performance are indicated on the GA tuned Type-I FLC dynamic membership intervals on the ball and beam system than the conventional Type-I FLC, and is satisfactory.