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The stator torsional vibration of permanent-magnet brushless AC/DC (BLAC/BLDC) drives with direct torque control (DTC) schemes and alternate torque-ripple compensation strategies is investigated systematically. To facilitate the analysis, a new method to measure the torsional vibration transfer function of the drive system by utilizing the cogging torque as a constant excitation source is proposed. Improved BLAC/BLDC DTC schemes, which account for the influences of nonsinusoidal back electromotive force (EMF), cogging torque, and commutation torque ripples (in the case of BLDC), are developed. Their effectiveness in minimizing low-order stator frame torsional vibration is validated and confirmed experimentally. Experimental investigation reveals that the stator torsional vibration of the prototype machine under conventional BLAC DTC operation is largely attributed to the nonsinusoidal back EMF and cogging torque while that under BLDC DTC operation is mainly caused by the cogging torque and distorted phase current during commutation interval. The torsional vibration spectra in both operating modes consist of harmonics with frequencies which are multiples of six times the fundamental electrical frequency, while their amplitudes are affected by the magnitude of exciting torque harmonics and the torsional vibration transfer function of the stator assembly.