An inverse controller design method for interval type-2 fuzzy models

Recently, it has been demonstrated that interval type-2 (IT2) fuzzy sets and systems are powerful tools in representing and controlling nonlinear systems. Thus, an inverse IT2 fuzzy model (FM) based controller might be an efficient way to control nonlinear processes. In this context, IT2-FM inversion methods have been proposed and successfully implemented in control system design. In this study, an analytical methodology has been developed to form the exact inverse of a certain class of IT2-FM. The proposed inversion methodology consists of two main steps, decomposing the IT2-FM into submodels and then finding the inverse of each possible activated interval type-2 fuzzy submodel. In order to form the inverse IT2-FM controller, the analytical formulation of the interval type-2 fuzzy submodel output is tried to be reached for an inverse solution since the IT2-FM output cannot be presented in a closed form due to the Karnik–Mendel type reduction method. Thus, to form the exact inverse type-2 fuzzy model, an iterative algorithm based on an analytical methodology is proposed to overcome this problem. The proposed inverse controller is embedded into a nonlinear internal model control scheme to provide an effective closed loop control performance in the presence of modelling mismatches and disturbances. Comparative simulation studies have been given where the beneficial sides of the proposed inverse controller are shown clearly in comparison to its type-1 and conventional counterpart.