Fuzzy Static Sliding Mode Control for a Nonlinear Benchmark System

Abstract

This paper is mainly about the control of a ball and beam system, which is an underactuated benchmark, where an ordinary static sliding mode controller and a fuzzy static sliding mode controller are proposed. Stability analysis of the system for both ordinary and fuzzy surfaces is studied in detail. As many researchers have investigated the control of such underactuated problems but there still exist the chattering phenomenon or wide range of tracking errors as problematic issues. The proposed control laws use complete nonlinear model without omitting the centrifugal term. However, for reducing the tracking errors, the Takagi-Sugeno fuzzy approach has been utilized on the sliding surface. The motivation of this paper is to suggest a method in which the unmodeled dynamics do not affect the robustness of the system and with the same control input, the tracking errors of states decrease considerably. Besides, stability for both ordinary static and fuzzy static sliding surfaces still remains. Simulation results indicate that the ordinary static sliding mode controller can converge the system's states to their desired values while the fuzzy static sliding mode controller can also reduce the effects of chattering immensely and improves the system tracking error.