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.

This article presents four model-based active disturbance rejection controllers aimed at achieving the independent control in terms of servo and regulation for permanent magnet synchronous motor servo system. According to different definitions of total disturbance in system, two full-order model-based extended state observers (ESOs) and two reduced-order model-based ESOs are constructed to estimate and compensate for total disturbance. The independent control feature in terms of servo and regulation is verified, and feedback controllers are chosen and designed using frequency-domain specifications for satisfactory servo performance. Frequency-domain analyses including open loop, closed loop, disturbance rejection, noise suppression, and robustness to plant uncertainties are introduced. Comparative evaluations of disturbance rejection and noise suppression are conducted among the four controllers. Experimental results validate the effectiveness of the proposed approach in achieving independent control, robustness to plant parameters variations, and performance comparisons with other typical active disturbance rejection controller (ADRC) and PI controllers. In addition, a method for observer design is further introduced, which handles periodic disturbances on the basis of the proposed model-based ESO (MESO) framework. The experimental results validated that the proposed method effectively suppresses periodic disturbances.

Impedance control is an important method in robot–environment interaction. In traditional impedance control, the damping force is regarded as a linear viscoelastic model, which limits the description of the dynamic model of the impedance system to a certain extent. For the robot manipulator, the optimal impedance parameters of the impedance controller are the key to improve the performance. In this paper, the damping force is described more accurately by fractional calculus than the traditional viscoelastic model, and a fractional-order impedance controller for the robot manipulator is proposed. A practical and systematic tuning procedure based on the frequency design method is developed for the proposed fractional-order impedance controller. The fairness of comparison between the fractional-order impedance controller and the integer-order impedance controller is addressed under the same specifications. Fair comparisons of the two controllers via the simulation and experiment tests show that, in the step response, the fractional-order impedance controller has a better integral time square error (ITSE) result, smaller overshoot and less settling time than the integer-order impedance controller. In terms of anti-disturbance, the fractional-order impedance controller can achieve stability with less recovering time and better ITSE index than integer order impedance controller.

The current and speed dual-loop control strategy based on field-oriented control for surfaced permanent magnet synchronous motors (SPMSMs) is widely applied in high-performance industrial sectors. This article presents a systematic control framework for the SPMSM dual-loop that includes a resonant-model-based extended state observer and a feedback controller. The proposed control framework is shown to achieve decoupling control between servo (speed/current tracking) and regulation (aperiodic and periodic disturbances rejection) for the dual loop, meaning that the disturbance rejection performance can be independently improved without changing the tracking performance. Resonant-model-based extend state observer is proposed to estimate and compensate for both aperiodic and periodic disturbances, and the corresponding feedback controllers are designed for the inner current-loop and the outer speed-loop. Then, the disturbance rejection systematic analysis method and parameters tuning method are proposed. Compared with the optimal proportional–integral–resonant control and active disturbance rejection control methods, experimental results demonstrate that the proposed control strategy achieves better speed tracking and disturbance rejection performance, decoupling control performance between speed tracking and disturbance rejection, robustness to parameter mismatch, and better periodic disturbance rejection performance.

In this paper, a fractional-order active disturbance rejection controller (FOADRC), combining a fractional-order proportional derivative (FOPD) controller and an extended state observer (ESO), is proposed for a permanent magnet synchronous motor (PMSM) speed servo system. The global stable region in the parameter (K_p, K_d, μ)-space corresponding to the observer bandwidth ω_o can be obtained by D-decomposition method. To achieve a satisfied tracking and anti-load disturbance performance, an optimal ADRC tuning strategy is proposed. This tuning strategy is applicable to both FOADRC and integer-order active disturbance rejection controller (IOADRC). The tuning method not only meets user-specified frequency-domain indicators but also achieves a time-domain performance index. Simulation and experimental results demonstrate that the proposed FOADRC achieves better speed tracking, and more robustness to external disturbance performances than traditional IOADRC and typical Proportional-Integral-Derivative (PID) controller. For example, the J_ITAE for speed tracking of the designed FOADRC are less than 52.59% and 55.36% of the J_ITAE of IOADRC and PID controller, respectively. Besides, the J_ITAE for anti-load disturbance of the designed FOADRC are less than 17.11% and 52.50% of the J_ITAE of IOADRC and PID controller, respectively.