A novel non-singular fixed-time terminal sliding mode control method for multi-input multi-output systems subject to uncertainties

This paper introduces a novel fixed-time non-singular terminal sliding mode control (NFTTSM) method for addressing the trajectory tracking problem in multi-input multi-output systems subject to uncertainties. First, a fixed-time disturbance observer (FTDO) is designed to compensate for system parameter uncertainties and external disturbances. Subsequently, a variable-gain fixed-time reaching law (VGFTRL), formulated based on a decision function, is proposed to ensure the rapid convergence of the sliding mode variable to the sliding surface, thereby enhancing system robustness. Furthermore, a novel non-singular terminal sliding mode (NNTSM) surface, constructed using the hyperbolic tangent function, is introduced to guarantee that the system state converges to zero within a fixed time along the sliding surface, effectively improving control accuracy while mitigating singularity issues. Building upon FTDO, VGFTRL, and NNTSM, a non-singular fixed-time terminal sliding mode (NFTTSM) controller is developed to ensure that the system state tracks the desired trajectory within a fixed time, with the proposed control scheme ensuring that the tracking time remains independent of initial conditions, thereby offering enhanced control performance. The fixed-time convergence property of the proposed methodology is rigorously established through theoretical analysis. Finally, a manipulator system is applied to validate the feasibility and superiority of the proposed approach, confirming its effectiveness in handling system uncertainties while ensuring precise and robust trajectory tracking.