Research On Permanent Magnet Synchronous Motor Fractional-order Modeling And Speed Control

Generally, there are two ways to improve the performance of the motion control system, one is to build a more accurate plant model and the other is to design a more powerful controller for the system. With the development of the fractional calculus theory and its application in science, engineering and industrial area, it is expected that a more accurate plant model can be built and a more powerful controller can be designed by using fractional calculus. As a result, the control system can obtain better control performance. Thus, the speed control of the permanent magnet synchronous motor(PMSM) is studied using the fractional calculus from two aspects in this paper, motion control system modeling and speed controller design.In the system modeling aspect, based on the composing mechanism, the mathematical model of PMSM is divided into two parts: the electromagnetic part and the mechanical part. Identification experiments are performed on these two parts respectively and the parameters of two parts are identified using numerical fitting method. The fractional order model of PMSM is then obtained by synthesizing the models of two parts. An integer order model is obtained by using the same identification method. Motor speed control simulations and experiments are performed and the deviations between the experimental outputs and simulation outputs of the fractional order model are compared with that of the integer order model. Simulation and experimental results show that the fractional order model obtained in this paper is more accurate and closer to the intrinsic characteristic of the PMSM over the integer order model.In the controller design aspect, the current design methods for the fractional order proportional integral(PIλ) controller are studied and compared. Based on the obtained fractional order model, a tuning method for the fractional order PIλ controller is proposed, combing the frequency-domain method and the time-domain optimization method. Thus, the advantages of two methods are synthesized and the fractional order PIλ speed controller for the PMSM speed-control system is obtained using the proposed tuning method. Motor speed control simulations and experiments are performed to check the dynamic response performance of the system using the fractional order PIλ controller. Simulation and experimental results show that the system using the fractional order PIλ controller can achieve good stability, the robustness to gain variations, better tracking performance and better anti-load disturbance performance over the system using the integer order PI controller.Satisfying more limiting conditions, a tuning method for the fractional order proportional integral derivative(PIλDμ) controller is proposed, combing the frequency-domain method and the time-domain optimization method, taking the advantage of the larger value range of the fractional order PIλDμ controller. More strict limiting conditions are introduced into the controller design method and the fractional order PIλDμ speed controller for PMSM speed control system is obtained. Motor speed-control simulations and experiments are performed to check the dynamic response performance of the system using the fractional order PIλDμ controller. Simulation and experimental results show that, satisfying all the limiting conditions, the system using the obtained fractional order PIλDμ controller can achieve good stability, the robustness to gain variations, better tracking performance and better anti-load disturbance performance over the system using the integer order PID controller.