This paper proposes a cooperative strategy that combines virtual DC signal injection maximum torque per ampere (MTPA) with proportional–integral–resonant (PIR) control to mitigate the torque ripple of interior permanent magnet synchronous machines (IPMSMs) caused by inverter nonlinearity. The virtual DC signal is superimposed on the d–q-axis feedback currents to track the optimal current angle accurately, while a PIR controller provides high-gain compensation at the 5th and 7th harmonic frequencies, significantly improving current waveform quality. Experimental results demonstrate that, compared with conventional MTPA and MTPA with virtual signal injection only, the proposed scheme achieves the lowest torque ripple and total harmonic distortion (THD) of the phase current, and realizes higher-precision MTPA operation with a smaller current magnitude under identical load conditions.
Zhang et al. (2026) studied this question.