Second-Order Predefined-Time Nonsingular Sliding Mode Control With Prescribed Performance for Nanopositioning Stage

This article proposes a novel second-order predefined-time nonsingular sliding mode control method aiming to enhance the dynamic performance of a nanopositioning stage under external disturbances and the model uncertainties. The method is capable of achieving fast convergence to the stable region while ensuring submicron-level motion tracking accuracy. First, a novel inequality is proposed to guarantee the predefined-time stability of the system, and a detailed proof is provided. By combining predefined-time control with higher-order sliding mode control, the proposed method effectively reduces chattering, enhances system robustness, and improves applicability. In addition, by integrating a novel predefined-time prescribed performance function, the tracking error converges to a specified region within a predefined-time, avoiding the inherent singularity issue of predefined-time sliding mode control. Meanwhile, it improves both transient and steady-state performance and ensures global predefined-time stability. In addition, this article analyzes the stability of the proposed controller. Finally, the controller’s performance is experimentally validated on the nanopositioning stage. The results demonstrate that the designed controller attains better motion tracking performance, in the presence of external disturbances and the model uncertainties.