A method for controlling operation of a rotary electric machine includes receiving, via a bandwidth-partitioning harmonic compensation regulator (HCR) of a controller, a commanded torque and rotational speed of the electric machine, and calculating, via the HCR in response to enabling conditions, a dq harmonic compensation current and a dq harmonic compensation voltage for one or more predetermined harmonic orders using the commanded torque and the rotational speed. The harmonic compensation current and voltage cancel torque ripple and current ripple in the one or more predetermined harmonic orders. The method may include injecting an acoustic tone at a predetermined harmonic order. The method additionally includes adding the dq harmonic compensation current and voltage to a dq current and voltage command, respectively, to generate adjusted dq current and voltage commands. The electric machine is then controlled using the adjusted dq current and voltage commands.