Abstract: To overcome the influence of uncertain torque such as unknown load,mechanical friction and external interference on the speed control accuracy of position sensorless permanent magnet synchronous motors,a back-stepping hyperspiral sliding mode control method was proposed. Firstly,the conversion relationship between the three-phase coordinate system,two-phase rotating coordinate system and two-phase stationary coordinate system of the permanent magnet synchronous motor was analyzed,and a motion mathematical model of the permanent magnet synchronous motor was established. Then,a back-stepping control law was designed for the speed loop to stably track the speed,and the uncertain torque was estimated by the the designed observer in real-time. The compensation current was introduced to suppress the disturbance of uncertain torque to the control system.Finally,a hyperspiral sliding mode control law was designed for the current loop to achieve high-precision control of the motor speed. The simulation results show that the designed observer can accurately estimate the uncertain torque,and the maximum estimated error is only 0.01 N·m. The proposed control law can effectively overcome the influence of uncertain torque and maintain high accuracy of the permanent magnet synchronous motor speed,and the maximum error is only 0.46 r/min,greatly improving the dynamic control performance of the permanent magnet synchronous motor.The test results show that the designed back-stepping hyperspiral sliding mode control law has higher control accuracy,and the RMSE,MAE and MAPE are only 0.317 7 r/min,0.252 5 r/min and 0.03 %,respectively,which exhibits stronger robustness and better engineering applicability.

Key words: permanent magnet synchronous motor, unknown load, uncertain torque, observer, back-stepping control law, hyperspiral sliding mode control law