Tracking Control of Ball on Sphere System Using Tuned Fuzzy Sliding Mode Controller Based on Artificial Bee Colony Algorithm

Abstract

This research is conducted to study the trajectory tracking of a ball on a sphere. Regulating a ball on the upper equilibrium point of a sphere has been studied in previous researches; however, tracking the trajectory of a ball on a sphere is investigated for the first time in this research. To achieve this, an accurate model of the ball on sphere system has been extracted so that firstly, there is a valid dynamical model at the far-reaching points from the upper equilibrium point; and secondly, the designed controller (based on the accurate model) has a good performance, as well. In this research, the proposed controller is a fuzzy sliding mode controller (FSMC) which is robust to the parametric uncertainties. Also, because of the substitution of the fuzzy term instead of the sign function, the chattering about the sliding surface is reduced or eliminated. In addition, to tune the parameters of the fuzzy system, an appropriate objective function has been proposed such that its minimization would cause the decrease in both sliding time and chattering around the sliding surface. Tuning of the fuzzy membership parameters is done using artificial bee colony algorithm, with the aim of minimization of the mentioned objective function. In simulations, ball tracking on three predetermined trajectories on sphere shows superiority of FSMC when compared with sliding mode controller (SMC); in a way that the chattering and RMS of its tracking error in the system output are far less than those of SMC.