A fractional-order modeling approach for a permanent magnet synchronous motor speed servo system is proposed applying a method combining electromagnetic part modeling and mechanical part modeling. Based on the proposed fractional-order model and system identification scheme, system identification experiments are performed on the electromagnetic part and the mechanical part of the permanent magnet synchronous motor speed servo system, respectively. The fractional-order model parameters of these two parts are identified with these experimental results, and the fractional-order model of the permanent magnet synchronous motor speed servo system is integrated from these two parts. Simulations and experiments in open-loop and closed-loop are performed based on the obtained fractional-order model and integer-order model. The advantage of the proposed fractional-order model for the permanent magnet synchronous motor speed servo system is demonstrated by the simulation and experimental results.

A simplified fractional order PID (FOPID) controller is proposed by the suitable definition of the parameter relation with the optimized changeable coefficient. The number of the pending controller parameters is reduced, but all the proportional, integral, and derivative components are kept. The estimation model of the optimal relation coefficient between the controller parameters is established, according to which the optimal FOPID controller parameters can be calculated analytically. A case study is provided, focusing on the practical application of the simplified FOPID controller to a permanent magnet synchronous motor (PMSM) speed servo. The dynamic performance of the simplified FOPID control system is tested by motor speed control simulation and experiments. Comparisons are performed between the control systems using the proposed method and those using some other existing methods. According to the simulation and experimental results, the simplified FOPID control system achieves the optimal dynamic performance. Therefore, the validity of the proposed controller structure and tuning method is demonstrated.

The fractional order PID (FOPID) controller has been found to have the potential to provide more flexibility in the design options than the integer order PID (IOPID) controller. However, in the FOPID controller design practice, investigations are still required in selecting the achievable design specifications and controller parameters. In order to obtain a practical tuning method for the FOPID controller, taking the first order plus integral systems as the plants, the complete achievable regions of the design specifications are collected and analyzed. In addition, the selectable integral and derivative orders of the FOPID controller are also collected and modeled. With the prior knowledge obtained, a synthesis method for the FOPID controller is proposed to make the control system achieve the desired flat-phase characteristic. To verify the effectiveness of the proposed method, the synthesis method is applied to design the FOPID controller for the permanent magnet synchronous motor (PMSM) speed servo system. Simulation and experimental results show that system with the FOPID controller can achieve satisfying tracking performance and disturbance rejection performance.