An Intelligent and Robust Single Input Interval Type-2 Fuzzy Logic Controller for Ball and Beam System

Abstract

The Ball and Beam system (BBS) is a nonlinear and unstable system which resembles with many real-time complicated systems. Providing an appropriate beam angle to give the stability to the ball on the beam in a specific position, is a challenging task for the control system researchers. In this paper a robust interval type-2 fuzzy logic controller (IT2FLC) is designed. The dimension of the rule base is reduced by using signed distance method. This signed distance method makes the IT2FLC to a Single input Interval Type-2 Fuzzy logic Controller (SIIT2FLC). The type-2 fuzzy sets resolve the problem of determining membership functions in type-1 fuzzy systems. The membership function of a type-2 fuzzy set is three dimensional, where third dimension is the value of membership function at each point on its two dimensional domain that is called its footprint of uncertainty (FOU). The ability of FOU to represent more uncertainties enables one to cover the input and output domains with less number of fuzzy sets. This SIIT2FLC gives the smooth 2-D control surface and robustness to the system. The simulation work is carried out in simulink environment of MATLAB (7.8.0) software. The simulation results are also validated in the real-time implementation of the BBS, designed by Googol Technology. Experimental results show that the performance of the proposed controller is better than the single input type-1 fuzzy logic controller in terms of transient and steady state response. The ability of handling uncertainty (robustness) of proposed controller has been checked by applying a disturbance signal to the position sensor’s output and also by parameter variation of the BBS.