A New Approach for Interval Type-3 Fuzzy Control of Nonlinear Plants

This article is focused on the implementation Interval Type-3 Fuzzy Logic Systems (IT3FLSs) for control problems with the goal of analyzing their performance and efficiency in the stabilization of nonlinear plants when perturbation is considered on the models. Two control problems are presented in which IT3FLSs allow the design of efficient fuzzy controllers when compared to alternative approaches. The methodology with the implementation of the vertical slices concept is utilized for approximating the results of IT3FLSs in the control problems. Simulation results with type-1, interval type-2, and generalized type-2 are presented and analyzed in comparison with IT3FLSs. To highlight the excellent performance of IT3FLs, two types of perturbations are considered in the models, showing that IT3FLs outperform type-2 and type-1 in control. The parameters of λ(LowerScale)andℓ(LowerLag)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda ({\text{Lower}}\; {\text{Scale}}) \; {\text{and}}\;{\ell}({\text{Lower}}\; {\text{Lag}})$$\end{document} that characterize an IT3FLS are changed manually with the 0.2, 0.5 and 0.9 values. Excellent results are presented with the value of 0.2. Several types of control performance metrics are presented to illustrate the results. The most relevant contribution is showing the potential of interval type-3 in the control area in outperforming alternative approaches.