Finite-Time Control of Permanent Magnet Linear Synchronous Motor via Variable Gain Fractional-Order Terminal Sliding Mode Control

This article proposes a variable gain fractional-order terminal sliding mode (VGFOTSM) control for position tracking of the permanent magnet linear synchronous motor. Specifically, practical uncertainties such as mass variation, friction forces, and load disturbances in tracking tasks are addressed. First, a novel fractional-order sliding mode manifold, referred to as the VGFOTSM, is constructed. This approach utilizes a time-varying gain that is automatically adjusted in response to changes in the system state, contingent upon the tracking error. Next, the corresponding reaching law, which enhances robustness, is formulated based on the adaptive robust term. Furthermore, the Lyapunov stability theory is employed to demonstrate the finite-time convergence of the closed-loop system under the VGFOTSM controller, allowing for the calculation of the finite time required to reach a neighborhood near the origin. Finally, experimental results validate the effectiveness and superiority of the proposed control method.