Supercritical Sliding Mode Control for Position Tracking of PMSM With Disturbance Rejection

In highly dynamic environments, such as industrial automation systems with frequent load changes or electric vehicles, ensuring both robustness and high-precision control remains challenging, particularly in the position control of permanent magnet synchronous motors. Sliding-mode control (SMC) is widely used for its robustness, but traditional SMC methods often suffer from chattering and slow convergence, limiting overall system performance. To address these limitations, this study proposes a robust SMC approach incorporating a novel nonlinear sliding surface inspired by the supercritical pitchfork bifurcation concept. Additionally, a new reaching law is introduced to attenuate chattering and ensure fast convergence of the sliding variable to zero within a finite time. The proposed method also integrates a proportional-integral observer (PIO) with the equivalent-input disturbance (EID) framework to enhance disturbance rejection under both matched and mismatched uncertainties. The stability of the proposed controller was verified using Lyapunov stability analysis, and its performance was validated through simulations and real-world experiments. Comparative evaluations demonstrated that the proposed reaching law significantly reduces chattering amplitude by over 50 % and improves convergence speed by approximately 5.6 times faster than conventional methods. Furthermore, the system's disturbance-rejection capability under matched and mismatched uncertainties is enhanced through the PIO+EID structure. These results confirmed the robust performance of the controller under unknown disturbances. This paper is accompanied by a video that demonstrates the proposed control strategy and provides a comparison with traditional controllers.