Vibration suppression and fixed-time precision tracking of flexible-link manipulators under actuation limits and unknown disturbances

This paper presents a novel fast fixed-time nonsingular sliding mode controller designed to enhance target tracking accuracy and reduce vibrations in flexible-link manipulators. The core innovation lies in simultaneously addressing model uncertainties, external disturbances, and actuator saturation by incorporating them into the system’s dynamics, thereby overcoming the inherent complexity and design challenges. Beyond this simultaneous handling, the proposed sliding surface itself incorporates new functions that improve upon previous sliding mode designs. Furthermore, actuator saturation, uncertainties, and disturbances are all explicitly considered within the dynamic equations themselves, not added as afterthoughts. The proposed paper integrates three key contributions. First, a new nonsingular fast terminal sliding surface is designed, which uses improved functions to ensure rapid convergence of tracking errors while avoiding singularity issues. Second, a nonlinear extended state observer (NESO) is combined with an auxiliary function to actively estimate and compensate for aggregated disturbances, model uncertainty, and input saturation. Third, an adaptive mechanism is embedded to eliminate the requirement for prior knowledge of uncertainty bounds, making the controller more practical and robust in real-world applications. The proposed method is compared with intelligent control strategies. Closed-loop stability is guaranteed using Lyapunov theory, with theoretical proof of fixed-time tracking error convergence to zero, independent of initial conditions. Effectiveness and robustness are validated via comparative simulations against a state-of-the-art benchmark and experiments on a Speedgoat real-time machine.