Second-order non-singular terminal sliding mode barrier function-based adaptive robust tip trajectory tracking of a two-link flexible manipulator

This article addresses the chattering-free finite-time control problem of a planar two-link flexible manipulator in the presence of uncertainties and external disturbances. First, a barrier-function-based adaptive second-order non-singular terminal sliding mode controller is developed. Unlike conventional approaches, the proposed method simultaneously ensures tip-trajectory tracking and tip-deflection suppression without requiring prior knowledge of disturbance bounds. Second, a higher-order sliding framework is established by combining a tracking-error-based first-order sliding surface with a second-order non-singular terminal sliding manifold, thereby guaranteeing singularity-free finite-time convergence. Then, adaptive barrier functions are employed to restrict the tracking errors within a prescribed neighborhood and to prevent controller gain overestimation. Furthermore, modal analysis is incorporated to identify the natural frequencies and modal characteristics of the flexible manipulator under no-payload, nominal-payload, and maximum-payload conditions. Lyapunov stability analysis confirms the closed-loop stability and error convergence. Finally, comparative results verify that the proposed controller achieves superior tracking performance, smoother control action, reduced control effort, and enhanced vibration suppression compared with state-of-the-art methods.