The position control of the ball and beam system using state-disturbance observe-based adaptive fuzzy sliding mode control in presence of matched and mismatched uncertainties

Abstract This paper presents a state-disturbance (S-D) observer-based adaptive fuzzy sliding mode control (AFSMC) to control the ball and beam system (BBS) in the presence of matched and mismatched uncertainties. First, an SMC scheme is designed to an error-based state-space representation of the BBS involving uncertainties. Stability analysis shows that the closed-loop system with the proposed SMC in the presence of uncertainties has global asymptotic stability. Second, a finite-time S-D observer is used to estimate uncertainties, the speed of the ball moving on the beam, and the angular velocity of the beam rotation. In this case, not only does the implementation of the S-D observer-based SMC eliminate the difficulty of access to information of state variables but also it can reach a suitable control input range by selecting smaller control input coefficients. Mathematical proof proves that the closed-loop system reaches the global asymptotic stability using the proposed S-D observer-based SMC in the presence of uncertainties. Finally, an adaptive fuzzy approximator is designed such that if the correct estimation of the boundary of uncertainties is not available, the closed-loop system with the S-D observer-based AFSMC achieves at least the global uniform bounded stability. The simulation and experimental results verify the efficiency of the suggested method compared to similar methods.