Fuzzy-PID gains tuning: Differential evolution versus second order analytical algorithms

This paper presents a comparison between two distinct constrained optimisation based approaches for tuning the gains of fuzzy-Proportional-Integral-Derivative controllers. One of the frameworks is based on a second order analytical optimisation approach, while the other relies on a differential evolutionary algorithm. In both methodologies, the cost function is related to the closed loop system performance. The system dynamics is described by a nonlinear model, and the set of constraints to the solution includes bounds on gains, control actions and on the system outputs. Experimental results carried out on a Multi-Input Multi-Output benchmark system illustrate the advantages of using a global optimisation approach.