METAHEURISTIC-BASED TUNING OF PROPORTIONAL-DERIVATIVE LEARNING RULES FOR PROPORTIONAL-INTEGRAL FUZZY CONTROLLERS IN TOWER CRANE SYSTEM PAYLOAD POSITION CONTROL

This paper proposes the use of metaheuristic optimization algorithms to tune the Proportional-Derivative (PD) learning rules within the framework of Iterative Learning Control applied to low-cost Takagi-Sugeno Proportional-Integral (PI)-fuzzy controllers for tower crane system payload position control. Four PD learning rules are considered: direct rule with current (in the iteration domain) control error, direct rule with previous control error, indirect rule, and open-closed-loop rule. The fuzzy controllers are tuned by the Extended Symmetrical Optimum method applied to the linear PI controllers, and then by the modal equivalence principle. Set-point filters are included for overshoot reduction. A unified design approach is formulated for all four PD learning rules in terms of optimally computing the gains in the iteration domain using metaheuristic optimization algorithms that solve optimization problems with objective functions expressed as the sum of the squared control error multiplied by time, where the two variables are the parameters of the PD learning rules. Seven popular metaheuristic optimization algorithms are implemented. Real-time experimental results from ten iterations of these optimization algorithms support the performance comparison of the fuzzy control systems.