Type-1 and Type-2 fuzzy Sets to Control a Nonlinear Dynamic System

Abstract

This paper is related to the simulation, in Matlab environment, of a robot manipulator controlled by both type-1 and interval type-2 fuzzy controllers, in which a modification in Karnik-Mendel algorithm has been proposed. To calculate the output of interval type-2 fuzzy system there is a main step called type-reduced; this operation is based on Karnik-Mendel algorithm, which uses arithmetic mean to calculate the control output. In this work, we propose to change the arithmetic mean by harmonic one. The performances of modified interval type-2 controller and type-1 fuzzy controller with and without noises are compared in terms of integral of squared error. The proposed modification in type reduction of Karnik-Mendel algorithm for interval type-2 fuzzy set shows best performance. Indeed, the amount of error in case of modified interval type-2 fuzzy controller is less two times than type-1 fuzzy controller.