Tuning of mamdani-type pid controllers: A constrained nonlinear optimisation approach

This chapter addresses the Fuzzy PID controller’s tuning problem, by considering a nonlinear constrained optimisation framework based on a differential evolutionary method. Two basic adaptation schemes are evaluated, depending on the controller’s parameters to be adjusted. In one of the approaches, merely the fuzzy-pid controller’s scaling factors are adjusted, while the other considers a joint optimisation of scaling factors and membership functions width. The performance index under minimisation is represented by a quadratic cost function, including the control error and the increment of control action. Constraints on the scaling factors, membership functions, and on the system’s inputs and outputs are incorporated into the optimisation problem. Experiments carried out on a Multi-InputMulti-Output benchmark system favour the joint optimisation of scaling factors and membership functions.