Type-2 fuzzy self-tuning of modified fractional-order PID based on Takagi–Sugeno method

Abstract

In this paper, Takagi–Sugeno (TS) fuzzy technique is combined with interval type-2 fuzzy sets (IT2-FSs) to design a new adaptive self-tuning fractional-order PID (FOPID) controller. TS fuzzy technique is used to construct a modified FOPID controller (TSMFOPID). IT2-FSs are used as a tuner for TSMFOPID to update their gains under parameter uncertainty change and to compensate the controlled system undesired effects of the sudden disturbances. Three types of IT2-FSs tuning methods are used for TSMFOPID. The first one is to tune the proportional–integral–derivative gains of the TSMFOPID. The second one deals with tuning the fractional orders of integral and derivative effects. The last one tunes the five parameters of the TSMFOPID. The responses of the fractional orders of the integral and derivative actions on the controlled system driven by TSMFOPID are given and discussed. The three tuning methods via IT2FST for TSMFOPID controller are applied to load frequency control as a case study of a power system comprising a single area. Comparative studies of the tuning type-1 fuzzy sets (T1FSTs) and IT2FST methods for controlled system using TSMFOPID are carried out and the results are discussed. The results prove that the proposed IT2FST for TSMFOPID controller is very useful for considered application over disturbance changes and parameter uncertainties.