In this article, a speed control scheme based on an analytically designed fractional-order PID with Bode’s ideal cutoff (FOPID-BICO) filter is proposed. The FOPID controller is designed to track the speed references and the BICO suppress is applied to filter the high-frequency noise. Considering the difficulty of parameters tuning of the FOPID controller, a comprehensive analytical design method based on frequency specifications-defined loop-shaping for the FOPID-BICO controller is first proposed for the permanent magnet synchronous motor speed control. The designed speed servo system satisfies five frequency-domain specifications: gain crossover frequency, phase margin, phase crossover frequency, gain margin, and a “flat phase” constraint. Moreover, the influence of phase crossover frequency on control system is fully exposed through the frequency-domain analysis. The proposed designed method ensures that the control system is robust to loop gain variations and guarantees the optimal performance on rejecting noise in high-frequency and disturbance in low-frequency. The effectiveness of the proposed FOPID-BICO controller has been verified by experimental results.

This article proposes a two-degree-of-freedom fractional-order proportional derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal set-speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor servo system. The GESO simplifies the control plant, estimates and actively rejects total disturbances. The FOPD controller achieves fast speed tracking with almost no overshoot. Furthermore, it is verified that the control system with the proposed FOPD-GESO controller design meets the separation principle through mathematical derivation and simulation illustration. It shows that the proposed controller breaks the inherent tradeoff on tracking performance and disturbance robustness of the typical traditional proportional–integral–derivative (PID) control. Meanwhile, a systematic scheme for designing the FOPD-GESO controller to satisfy both frequency-domain and time-domain specifications is proposed in this article. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID controller, integer-order active disturbance rejection control with a typical extended state observer, and fractional-order PID controller in terms of speed tracking, antiload disturbance, and robustness to internal uncertainties.

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.