Constrained Nonlinear‐Based Optimisation Applied to Fuzzy PID Controllers Tuning

Abstract

This paper aims at studying the optimal Fuzzy Proportional–Integral– Derivative controllers' tuning problem by considering two different nonlinear constrained optimisation techniques. One relying on a Hessian‐based analytical approach, and the other based on a differential evolutionary method. In the case of offline implementation, two basic frameworks are under assessment, depending on the controller parameters to be adjusted. For online scaling factors and membership functions' width tuning, its implementation is based on the parallel computation paradigm. The performance index is described by a quadratic cost function, taking as arguments control errors and the increment of control actions. Constraints on the scaling factors, membership functions' width, as well as on the system inputs and outputs are also included in the optimisation problem. Experiments carried out on a benchmark system favour the offline joint optimisation based on the differential evolutionary approach of scaling factors and membership functions' width.