Abstract: Due to the simple structure and strong robustness, the sliding mode observer is widely used in sensorless control of permanent magnet synchronous motor(PMSM), but the inherent chattering of the sliding mode observer will affect the control performance of the system. A high order logarithmic sliding mode observer(HOLnSMO) is proposed based on extended back electromotive force model of PMSM by improving sliding mode surface and control law, which achieves finite-time convergence and smooth estimation of back electromotive force. In addition, to improve the precision of rotor position and speed estimation, an expanded state observer based on a three-order super-twisting sliding model method is designed at the phase-locked loop link and the speed chattering is effectively suppressed. The stability of the system is proved according to Lyapunov stability theory. Finally, the proposed sensorless control strategy is proved to have good speed estimation accuracy, dynamic performance and strong robustness by comparative experiments.