Optimal Sliding Mode Control with Iterative Learning Compensation for Torque Ripple Suppression in PMSM Speed Regulation

This paper addresses torque ripple in permanent magnet synchronous motor (PMSM) under constant-speed operation, caused by interactions among 6 k-th order flux harmonics, PWM sampling delays, and mechanical resonances. An enhanced control scheme is proposed by integrating a closed-loop PD-type iterative learning control (ILC) into an optimal sliding mode speed controller (OSMC). The ILC uses the electrical period as the iteration cycle and updates both reference speed and torque commands in real time, generating compensatory current components to progressively attenuate periodic disturbances while preserving the speed loop’s dynamic responsiveness and robustness. First, an equivalent torque transfer model of the OSMC-PMSM closed-loop system is developed. Then, the convergence criterion of the OSMC-ILC scheme in the iteration domain is derived, along with systematic guidelines for gain selection and anti-windup design. MATLAB/Simulink simulations show that the proposed method reduces torque ripple by 53% compared to conventional PI-ILC. The results confirm the complementary benefits of sliding mode control and iterative learning, providing a compact and effective approach to micro-vibration suppression in high-performance PMSM servo systems.