A variable exponential approaching law is designed, which shortens the approaching time of the traditional approaching law sliding surface and improves the speed of the system. On the basis of variable exponential approaching law, aiming at the shortcomings of traditional PID control, a sliding mode switching function with a given speed as a variable is proposed. A simulation model of a permanent magnet synchronous linear motor was built through theoretical analysis, and the model was verified. Through verification, an improved sliding mode switching function is obtained, whether there is overshoot when following given speeds, and the rapidity is good. When following a dynamic given speed, the following rapidity is good and the error is small. When there is system disturbance and load disturbance, the system has better robustness.

permanent magnet synchronous linear motor，variable exponential approaching law， improved sliding mode switching function