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This paper first analyzes the development of permanent magnet synchronous motor vector control, and then explains the electromechanical energy conversion principle of three-phase permanent magnet synchronous motor from the perspective of electromechanical energy conversion, and deduce the Lagrange motion equation. In addition, the mathematical model of permanent magnet synchronous motor (PMSM) in three phase stationary coordinate system and dq coordinate system is listed. Based on Simulink, a simulation model of speed and current double closed loop vector control system is established. By analyzing the simulation results, the performance of PMSM vector control system is verified.