An extended-state-observer resonant phase-locked loop (ESO-RPLL) method is proposed to suppress speed vibration caused by a nonlinear periodic load during sensorless control of permanent magnet synchronous motors for compressors. In contrast with the traditional phase-locked loop (PLL) with the same poles allocation

the proposed ESO-RPLL has stronger dynamic tracking ability of the rotor position

and can realize a zero steady-state error with respect to the specific harmonic components in the speed command. Then

a load torque estimation and compensation method based on a phase-locked loop extended state observer (PLL-ESO) is designed to compensate the periodic load torque and suppress the speed vibration. The experimental results show that the proposed method can effectively suppress the speed vibration

reduce the system vibration

improve the low-speed performance of compressors.