In order to solve the problems of slow dynamic response and weak robustness of the integer order PI controller in the double closed-loop vector control system of permanent magnet synchronous motors, an off-line parameter tuning method of outer speed loop and inner current loop of the system is proposed by using dragonfly algorithm and fractional order PI control. The parameter to be optimized is regarded as the spatial position of the best individual that the dragonfly searches for the food source in the search space, and the error performance index ITAE is used as its target fitness function. Simulation and experimental comparisons of motor speed regulation performance of traditional engineering experience tuning integer order PI, dragonfly algorithm for integer order PI, dragonfly algorithm for fractional order PI, and particle swarm algorithm for fractional order PI, respectively. The results show that the dragonfly algorithm optimized fractional-order PI controller has the advantages of improving the system′s dynamic response performance, reducing the amount of overshoot, and enhancing the robustness, proving the superiority of the optimization strategy.