Fuzzy-PID Controller Optimization: A Differential Evolution Approach

This paper addresses the problem of Fuzzy Proportional-Integral-Derivative control tuning based on a differential evolution technique. Two different constrained optimisation approaches are considered. One where solely the controller scaling factors are adjusted, and another for which both the scaling factors and membership functions width are optimised. The cost function is expressed in terms of the system closed loop performance, with the plant dynamics described by a nonlinear model. The formulation includes a set of constraints, namely bounds on scaling factors, control actions and on the system outputs. For the second approach additional constraints for the membership functions width are also considered. Experimental results carried out on a Multi-Input Multi-Output benchmark system favour the optimisation of both gains and membership functions width.