Abstract：Due to the structural defects of the permanent magnet synchronous motor and various nonlinear factors in the driving circuit, the three-phase current in the motor contains current harmonics of various orders, which are mainly (6k±1) (k is a positive integer) orders. These current harmonics of (6k±1) orders in the natural coordinate system will be displayed as 6k orders after the coordinate is changed to the two-phase rotating coordinate system. At the same time, the transfer function of the repetitive controller has multiple resonance peaks, and its resonance frequency is a multiple relationship. Thus, the repetitive controller is widely used for suppressing the current harmonics of permanent magnet synchronous motors. However, the sampling period of the motor controller is fixed in the actual control system, and the current harmonic frequency changes with the motor speed, causing a fractional delay link in the repetitive controller. The most commonly used method to solve this problem is Lagrange interpolation to approximate the fractional delay link. This paper first analyzes the shortcomings of this method, and then discusses the method of Lagrange interpolation to approximate fractional order with numerical analysis. There are unnecessary specific constraints between Lagrange interpolation coefficients, and a better harmonic suppression effect can be achieved by reasonably configuring the interpolation coefficients. Then, the coefficient in the interpolation approximation method is mapped to compound circular motion, combined with the amplitude-frequency characteristic surface of the proposed repetitive controller. The effects of the interpolation coefficient on the resonant frequency and harmonic peak value of the repetitive controller are analyzed, and a fractional-order repetitive controller based on geometric constraint optimization is proposed. The resonance frequency and current harmonic frequency of the motor can be guaranteed to coincide in a broader range of speeds. Moreover, the resonance peak value is consistent with the harmonic composition of the motor, thus achieving a better harmonic suppression effect. The repetitive controller with a large resonance peak in the high-frequency part will cause system instability. This paper also introduces the combined filter, and discusses the influence of the feedback loop position of the filter on the resonance frequency and peak. This paper introduces the sensitivity function and combines the Nyquist curve to analyze the stability of the current control system, including PI, repetitive controller, and discrete motor model. First, the influence of PI controller gain K on the system’s stability without a repetitive controller is analyzed. After determining the value of K, the influence of repetitive controller gain Krc and internal model coefficient Q on the stability of the system is discussed, and the values of Krc and Q are determined. After all parameters are determined, the stability of the current control system at different motor speeds is also discussed. Finally, the experiments of no repetitive controller, rounding, Lagrange interpolation, and the improved repetitive controller proposed in this paper are carried out on the motor bench at different speeds. The current waveform and FFT analysis verify that the harmonic suppression performance of the proposed method is good.
朱元, 朱醴亭, 肖明康, 孟令. 基于几何约束优化的重复控制器及PMSM电流谐波抑制应用[J]. 电工技术学报, 2024, 39(4): 1059-1073.
Zhu Yuan, Zhu Liting, Xiao Mingkang, Meng Ling. Repetitive Controller Based on Geometric Constraint Optimization and Its Application to Current Harmonic Suppression of PMSM. Transactions of China Electrotechnical Society, 2024, 39(4): 1059-1073.
[1] 赵文祥, 刘桓, 陶涛, 等. 基于虚拟信号和高频脉振信号注入的无位置传感器内置式永磁同步电机MTPA控制[J]. 电工技术学报, 2021, 36(24): 5092-5100. Zhao Wengxiang, Liu Huan, Tao Tao, et al.MTPA control of sensorless IPMSM based on virtual signal and high-frequency pulsating signal injection[J]. Transactions of China Electrotechnical Society, 2021, 36(24): 5092-5100. [2] Sun Tongze, Liu Xiping, Zou Yongling, et al.Design and optimization of a mechanical variable-leakage- flux interior permanent magnet machine with auxiliary rotatable magnetic poles[J]. CES Transa- ctions on Electrical Machines and Systems, 2021, 5(1): 21-29. [3] 黄科元, 周佳新, 刘思美, 等. 考虑逆变器非线性永磁同步电机高频注入电感辨识方法[J]. 电工技术学报, 2021, 36(8): 1607-1616. Huang Keyuan, Zhou Jiaxin, Liu Simei, et al.Inductance identification method of permanent magnet synchronous motor considering inverter nonlinearity based on high-frequency injection[J]. Transactions of China Electrotechnical Society, 2021, 36(8): 1607-1616. [4] Zhang Guoqiang, Wang Gaolin, Xu Dianguo, et al.ADALINE-network-based PLL for position sensorless interior permanent magnet synchronous motor drives[J]. IEEE Transactions on Power Electronics, 2016, 31(2): 1450-1460. [5] Zhou Min, Zhang Xinxing, Zhao Wenxiang, et al.Influence of magnet shape on the cogging torque of a surface-mounted permanent magnet motor[J]. Chinese Journal of Electrical Engineering, 2019, 5(4): 40-50. [6] Wu D, Zhu Z Q.Design tradeoff between cogging torque and torque ripple in fractional slot surface- mounted permanent magnet machines[J]. IEEE Transactions on Magnetics, 2015, 51(11): 1-4. [7] 谭广军. 高速永磁同步电机驱动控制关键技术研究[D]. 哈尔滨: 哈尔滨工业大学, 2013. [8] 杜鹏程. 高速永磁同步电机电流谐波抑制技术[D]. 哈尔滨: 哈尔滨工业大学, 2020. [9] 陈杰, 章新颖, 闫震宇, 等. 基于虚拟阻抗的逆变器死区补偿及谐波电流抑制分析[J]. 电工技术学报, 2021, 36(8): 1671-1680. Chen Jie, Zhang Xinying, Yan Zhenyu, et al.Dead- time effect and background grid-voltage harmonic suppression methods for inverters with virtual impedance control[J]. Transactions of China Elec- trotechnical Society, 2021, 36(8): 1671-1680. [10] 廖勇, 甄帅, 刘刃, 等. 用谐波注入抑制永磁同步电机转矩脉动[J]. 中国电机工程学报, 2011, 31(21): 119-127. Liao Yong, Zhen Shuai, Liu Ren, et al.Torque ripple suppression of permanent magnet synchronous motor by the harmonic injection[J]. Proceedings of the CSEE, 2011, 31(21): 119-127. [11] 李思毅, 苏健勇, 杨贵杰. 基于自抗扰控制的永磁同步电机弱磁控制策略[J]. 电工技术学报, 2022, 37(23): 6135-6144. Li Siyi, Su Jianyong, Yang Guijie.Flux weakening control strategy of permanent magnet synchronous motor based on active disturbance rejection control[J]. Transactions of China Electrotechnical Society, 2022, 37(23): 6135-6144. [12] 黄仁志, 全相军, 吴在军, 等. 基于多重谐振控制器的参考值前馈自适应控制[J]. 电工技术学报, 2022, 37(16): 4212-4224. Huang Renzhi, Quan Xiangjun, Wu Zaijun, et al.A multiple resonant based on reference feedforward adaptive voltage control of three-phase inverter[J]. Transactions of China Electrotechnical Society, 2022, 37(16): 4212-4224. [13] 夏薇, 王凯, 张建亚, 等. 基于谐振控制器的谐波削极型永磁同步电机转矩脉动抑制策略[J]. 中国电机工程学报, 2019, 39(18): 5499-5508, 5598. Xia Wei, Wang Kai, Zhang Jianya, et al.Torque ripple suppression of permanent magnet synchronous motor with harmonic shaped rotors based on resonance controllers[J]. Proceedings of the CSEE, 2019, 39(18): 5499-5508, 5598. [14] Tian Minghe, Wang Bo, Yu Yong, et al.Discrete-time repetitive control-based ADRC for current loop disturbances suppression of PMSM drives[J]. IEEE Transactions on Industrial Informatics, 2022, 18(5): 3138-3149. [15] Tang Mi, Gaeta A, Formentini A, et al.A fractional delay variable frequency repetitive control for torque ripple reduction in PMSMs[J]. IEEE Transactions on Industry Applications, 2017, 53(6): 5553-5562. [16] 武永燎, 李红, 宋欣达, 等. 基于改进型重复控制器的永磁同步电机电流谐波抑制方法研究[J]. 电工技术学报, 2019, 34(11): 2277-2286. Wu Yongliao, Li Hong, Song Xinda, et al.Suppression of harmonic current in permanent magnet synchronous motors using improved repetitive controller[J]. Transactions of China Electrotechnical Society, 2019, 34(11): 2277-2286. [17] 陈东, 张军明, 钱照明. 一种具有频率变化适应性的并网逆变器改进型重复控制方法[J]. 电工技术学报, 2014, 29(6): 64-70. Chen Dong, Zhang Junming, Qian Zhaoming.An improved repetitive control scheme for grid- con- nected inverter with frequency-varying adaptability[J]. Transactions of China Electrotechnical Society, 2014, 29(6): 64-70. [18] 徐群伟, 吴俊, 吕文韬, 等. 基于双分数阶快速重复控制的有源电力滤波器电流控制策略[J]. 电工技术学报, 2019, 34(增刊1): 300-311. Xu Qunwei, Wu Jun, Lü Wentao, et al.Current control strategy of active power filter based on double fractional-order rapid repetitive control[J]. Transa- ctions of China Electrotechnical Society, 2019, 34(S1): 300-311. [19] 刘兴亚. 永磁同步电机电流谐波抑制策略的研究[D]. 哈尔滨: 哈尔滨工业大学, 2018. [20] Yepes A G, Freijedo F D, Lopez Ó, et al.Analysis and design of resonant current controllers for voltage-source converters by means of Nyquist diagrams and sensitivity function[J]. IEEE Transa- ctions on Industrial Electronics, 2011, 58(11): 5231-5250.
2024, Vol. 39 
