Derivation and analysis of a self-tuning interval type-2 fuzzy PI controller

In this paper, a self-tuning interval type-2 fuzzy PI controller (IT2 FPIC) is proposed based on the analysis of the close form solution of IT2 FPIC output. Unlike other researches, the analytical derivations of IT2 FPIC output are presented in three error regions in this paper. Analysis has shown that the IT2 FPIC can be seen as a PI controller with variable gains, which are the functions of the inputs and the structure parameters. Then, the relationship between the sizes of footprint of uncertainty (FOU), inputs of the controller and the equivalent PI gains is investigated. On the basis of the above work, a self-tuning IT2 FPIC is proposed. Simulation results show that the proposed controller provides better performance than T1 FPIC and IT2 FPIC.