Evolutionary optimization of interval mathematics-based design of a TSK fuzzy controller for anti-sway crane control

Abstract A hybrid method combining an evolutionary search strategy, interval mathematics and pole assignment-based closed-loop control synthesis is proposed to design a robust TSK fuzzy controller. The design objective is to minimize the number of linear controllers associated with rule conclusions and tune the triangular-shaped membership function parameters of a fuzzy controller to satisfy stability and desired dynamic performances in the presence of system parameter variation. The robust performance objective function is derived based on an interval Diophantine equation. Thus, the objective of a fuzzy logic-based control scheme is to place all the closed-loop control system characteristic polynomial coefficients within desired intervals. The reproduction process in the proposed Evolutionary Algorithm (EA) is based on the arithmetical crossover, uniform and non-uniform mutation along with gene deletion/insertion mutation ensuring a diversity of genomes sizes, as well as a diversity in the parameter space of membership functions. The proposed algorithm was implemented to design a fuzzy logic-based anti-sway crane control system taking into consideration the rope length and the mass of a payload variation. The results of experiments conducted using the EA for different conditions assumed for system parameter intervals and desired closed-loop system performances are compared with results achieved using the iterative procedure which is also described in the paper.