This paper presents a fractional order (FO)-active disturbance rejection control (ADRC) with a FO extended state observer (FOESO) design. Applying this FOESO, a typical second order motion plant can be converted into a $cascadedfractionalorderintegrator$ $(1∕s^{2r};0<r<1)$ with considering all other dynamics and internal/external disturbances as $totaldisturbances$. Therefore, a single proportional controller which is not sensitive to system noise can realize a stable control system. According to the frequency characteristics of equivalent FO system model, the FO-ADRC control system is robust to systematic uncertain dynamics and disturbances. Furthermore, without differential action which is needed for the typical double integrator plant control, the proposed control system achieves good robustness to high-frequency noise. Simulation and experiments on PMSM speed servo system are performed, showing that the proposed FO-ADRC behaves better than integer order ADRC (IO-ADRC) and FOPI controller. This FO-ADRC methodology can be simply extended to general control plants.

本文提出了一种具有 FO 扩展状态观测器 (FOESO) 设计的分数阶 (FO) - 自抗扰控制 (ADRC)。应用此 FOESO，可以将典型的二阶运动设备转换为$C\mathrm{一种}秒C\mathrm{一种}d\mathrm{电子}dFr\mathrm{一种}C吨\mathrm{一世}○n\mathrm{一种}升○rd\mathrm{电子}r\mathrm{一世}n吨\mathrm{电子}Gr\mathrm{一种}吨○r$ $(1∕{秒}^{2r};0<r<1)$ 将所有其他动态和内部/外部干扰视为 $吨○吨\mathrm{一种}升d\mathrm{一世}秒吨你r乙\mathrm{一种}nC\mathrm{电子}秒$. 因此，对系统噪声不敏感的单个比例控制器可以实现稳定的控制系统。根据等效FO系统模型的频率特性，FO-ADRC控制系统对系统的不确定动态和扰动具有鲁棒性。此外，没有典型双积分器设备控制所需的微分作用，所提出的控制系统对高频噪声具有良好的鲁棒性。对 PMSM 速度伺服系统进行了仿真和实验，表明所提出的 FO-ADRC 的性能优于整数阶 ADRC（IO-ADRC）和 FOPI 控制器。这种 FO-ADRC 方法可以简单地扩展到一般控制工厂。