Harmonic currents in magnetically suspended rotor systems are usually caused by mass unbalance and displacement sensor errors, which will produce harmonic vibrations. Repetitive control (RC) is used to eliminate harmonic currents in the control system, but for the magnetic bearing control system, the odd harmonics often dominates, and the characteristics of the even harmonic frequency are not expected to change greatly. At the same time, the ratio of the sampling frequency to the rotor frequency is required to be an integer in the conventional repetitive controller (CRC), which greatly limits its range of application. Therefore, a 3/2-order dual-mode fractional-order repetitive control scheme with a three-parallel structure is proposed. The three branches in the scheme can not only eliminate odd and even harmonics independently, but also improve the robustness of frequency fluctuations. In addition, this method converts the fraction into an integer polynomial by Lagrange interpolation, which can accurately suppress the harmonic current at any frequency. The system delay is reduced to $0.5{N}$ sampling periods, and the system dynamic response rate is accelerated. Simulation results show that the proposed algorithm can effectively achieve harmonic vibration suppression at any frequency.

中文翻译：

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磁悬浮转子谐波振动抑制的3/2阶双模分数重复控制

磁悬浮转子系统中的谐波电流通常是由质量不平衡和位移传感器误差引起的，会产生谐波振动。重复控制(RC)用于消除控制系统中的谐波电流，但对于磁轴承控制系统，奇次谐波往往占主导地位，偶次谐波频率的特性预计不会有很大变化。同时，传统的重复控制器（CRC）要求采样频率与转子频率之比为整数，这极大地限制了其应用范围。因此，提出了一种三并联结构的3/2阶双模分数阶重复控制方案。方案中的三个支路不仅可以独立消除奇偶次谐波，同时也提高了频率波动的鲁棒性。此外，该方法通过拉格朗日插值将分数转换为整数多项式，可以准确抑制任意频率下的谐波电流。系统延迟降低到$0.5{N}$采样周期，系统动态响应速度加快。仿真结果表明，该算法能够有效地实现任意频率下的谐波振动抑制。