Abstract: To achieve high-precision speed control of permanent magnet synchronous motor (PMSM) for NC machine tool, a robust control method using extended sliding mode observer was designed, which considered the combined disturbance of load torque and circuit and magnetic circuit. Firstly, the model of PMSM with compound disturbance was established. Then the compound disturbance was taken as the extended state, and the extended sliding mode observer was designed to realize the accurate estimation of speed, rotational acceleration and compound disturbance, and the analysis of convergence and stability were carried out. Finally, a new sliding mode approach law was proposed to overcome chattering, which realized the robust control of PMSM under compound disturbance. The simulation results show that the tracking errors of speed and acceleration of the proposed robust control method are only 0.1 r/s and 0.05 r/s², the tracking errors of speed and acceleration of the extended sliding mode observer are only 0.08r/s and 0.04 r/s², and the estimation error of compound disturbance is only 0.03 r/s². In the test experiment, the maximum tracking error of the proposed method for motor speed is only 0.3 r/min, compared with other methods, which has better practicability, faster response speed and higher control accuracy.