A Two-Degree-of-Freedom Controller Design Satisfying Separation Principle with Fractional Order PD and Generalized ESO

This paper proposes a two-degree-of-freedom fractional-order proportional-derivative (FOPD) controller with a general extended state observer (GESO) to achieve both optimal speed tracking and disturbance rejection performance for a typical permanent magnet synchronous motor (PMSM) 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 trade-off on tracking performance and disturbance robustness of the typical traditional 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 paper. Simulation illustration and experimental validation are performed to demonstrate that the proposed FOPD-GESO controller is superior to the typical integer-order PID (IOPID) controller and integer order active disturbance rejection control (IOADRC) with a typical extended state observer in terms of speed tracking, anti-load disturbance and robustness to internal uncertainties.