Switching funnel transformation function-based discrete-time sliding-mode control for servo systems with time-varying external disturbances

This paper proposes a switching funnel transformation function-based discrete-time sliding-mode control with lower cost to prevent the issue of control failure caused by time-varying external disturbances leading to tracking errors exceeding the performance boundary. This scheme employs an offline spectral regularization-based neural network with good generalization capability to approximate the unknown nonlinear dynamics and modeling errors in the system, resulting in a more accurate discrete-time system model. Based on the discrete-time system model with time-varying external disturbances, a novel discrete-time switching funnel transformation function-based sliding surface is proposed to solve the problem when the tracking error exceeds performance boundaries. The discrete-time funnel boundaries are switched through a predefined event-triggered mechanism, ensuring that the tracking error remains within the performance boundaries at all times, thereby avoiding control failure. Furthermore, a time-varying sliding mode variable reaching rate is proposed to reduce control cost. Finally, theoretical analysis demonstrates that the tracking error remains within a smaller funnel region compared to the predefined one, and the sliding-mode variable ultimately stays within a bounded sliding-mode boundary. Experimental results on SCARA verify the effectiveness of the proposed method.