The scope of this paper is to present a fuzzy logic control of a class of multi-input multioutput (MIMO) nonlinear systems called “system of ball on a sphere,” such an inherently nonlinear, unstable, and underactuated system, considered truly to be two independent ball and wheel systems around its equilibrium point. In this work, Sugeno method is investigated as a fuzzy controller method, so it works in a good state with optimization and adaptive techniques, which makes it very attractive in control problems, particularly for such nonlinear dynamic systems. The system’s dynamic is described and the equations are illustrated. The outputs are shown in different figures so as to be compared. Finally, these simulation results show the exactness of the controller’s performance. 1. Introduction Recently, several attempts have been made to analyze the dynamic and control of a system containing a ball on a body and its stability which is used in education and research in control field including ball and beam [1], ball on wheel [2, 3], and ball on sphere [4, 5]. This paper investigates particularly a nonlinear system of ball on a sphere [2] whose dynamical equations are extremely nonlinear and their parameters are interdependent in various directions; they have been considered to be two independent ball and wheel systems around the equilibrium point [3]. This system of ball on a sphere is visualized in Figure 1. In the current work, based on the results, a considerably simpler fuzzy control technique for a larger class of these nonlinear systems is proposed [6], such as unmanned vehicles [7, 8] and robot manipulators. It has now been realized that fuzzy control systems theory and methods offer a simple, realistic, and successful alternative for the control of complex, imperfectly modeled, and largely uncertain engineering systems. For this purpose, a combination of fuzzy control technology and advanced computer facility available in the industry provides a promising approach that can mimic human thinking and linguistic control ability, so as to equip the control systems with certain degree of artificial intelligence. Figure 1: A ball on a sphere system. This paper contains the following subjects. First, dynamic and modeling section which presents the dynamic of the modeling and its parameters has been presented. Next, the control law has been investigated and, by means of input-to-state stability theory, a new fuzzy control scheme is designed involving the equations parameters. Following that, the simulation results have been discussed by the graphs and tables,
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