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Torque-ripple reduction methods based on harmonic current injection for permanent magnet synchronous machine (PMSM) drives have been widely discussed, while the performance of torque-ripple-model-based methods is limited due to model accuracy as well as the rotor position errors, and the speed harmonic control-based methods still cannot get rid of the impact of the phase information of speed harmonics, which results in remaining torque ripples and the difficulty in designing speed harmonic controller. In this article, the unique relationships between the quadrature magnitudes of speed harmonics and harmonic currents are derived considering the minimal conduction copper loss by the harmonic currents. Based on that, a novel torque-ripple reduction method based on the speed harmonic control is proposed, wherein a novel speed harmonic controller is presented to regulate the quadrature magnitudes of speed harmonics so that the phase of speed harmonics is avoided in the speed harmonic controller. Also, the proposed speed harmonic controller aims to generate harmonic current references. The proposed methodology is evaluated by experiments and is verified to reduce torque ripples of PMSM drives effectively.