Finite-time tracking control for the ball and beam system based on a new fast terminal decoupled sliding mode control in the presence of matched and mismatched uncertainties

Abstract

This paper presents a novel decoupled sliding mode controller for finite-time position tracking in ball-and-beam systems in the presence of matched and mismatched uncertainties. The proposed controller employs two fast terminal sliding surfaces and a novel coupling variable to ensure rapid and simultaneous convergence of all sliding surfaces to zero. A new reaching law is introduced to minimize chattering while ensuring finite-time asymptotic stability. Additionally, a finite-time extended state observer is employed to estimate disturbances and system states within a finite time frame, without requiring prior knowledge of uncertainty bounds. Furthermore, the finite-time convergence stability of the closed-loop system is proved in the Lyapunov framework. The control signal design is simplified, as it requires knowledge of only a small known portion of the system dynamics rather than the entire dynamics. The proposed method is validated through simulations and hardware-in-the-loop experiments, demonstrating enhanced robustness, faster convergence, and significantly reduced chattering compared to existing approaches.