A synchronous regulator that accurately tracks three-phase commands with arbitrary balanced harmonic content is set forth. The regulator utilizes multiple reference frames to realize both a novel harmonic estimator and an integral feedback controller. The regulator is analyzed and demonstrated in the context of a permanent-magnet synchronous machine drive. The drive utilizes an optimized nonsinusoidal current command to achieve superior efficiency and torque ripple performance but which is dependent upon the commanded waveforms being precisely realized. The multiple reference frame synchronous current regulator proposed herein readily achieves this requirement. A computer simulation and a hardware prototype demonstrate validity of the regulator.