Novel Sine-Logarithmic Reaching Law Sliding Mode Control for Permanent Magnet Synchronous Motor

Sliding mode control (SMC) is widely used for permanent magnet synchronous motor (PMSM) drives because of its robustness against disturbances and parameter uncertainties. However, the reaching law still faces a trade-off between fast convergence and chattering suppression. Reaching laws based on the signum function usually provide rapid convergence but induce severe high-frequency oscillations, whereas smooth or exponential modifications may reduce discontinuity at the expense of slower transient response or excessively large control gains. To address these limitations, this paper proposes a novel sine-logarithmic reaching law combined with a power-rate term for PMSM sliding mode control. The proposed structure avoids both the conventional smooth and exponential approximations commonly used in the literature. A theoretical analysis is presented, and the convergence behavior is characterized in terms of practical finite-time stability. The effectiveness of the proposed reaching law is evaluated in MATLAB/Simulink through comparative PMSM simulation studies, including start-up, steady-state, load-disturbance, parameter-variation, and total harmonic distortion (THD) tests against representative reaching laws from the literature. The simulation results indicate that the proposed method provides a favorable trade-off among rapid reaching, chattering attenuation, steady-state accuracy, and harmonic performance. These findings suggest that the proposed reaching law is a competitive alternative for PMSM sliding mode control.