电工技术学报  2024, Vol. 39 Issue (4): 1059-1073    DOI: 10.19595/j.cnki.1000-6753.tces.222202
电机及其系统 |
基于几何约束优化的重复控制器及PMSM电流谐波抑制应用
朱元, 朱醴亭, 肖明康, 孟令
同济大学汽车学院 上海 201804
Repetitive Controller Based on Geometric Constraint Optimization and Its Application to Current Harmonic Suppression of PMSM
Zhu Yuan, Zhu Liting, Xiao Mingkang, Meng Ling
School of Automotive Studies Tongji University Shanghai 201804 China
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摘要 重复控制器凭借其具有多个谐振峰而广泛应用于电流谐波抑制领域,然而在实际电机控制系统中,由于系统采样频率固定而电流谐波频率随电机转速而变化,会导致重复控制器中出现分数阶延时环节,而该环节在实际控制器中无法实现。对此,该文针对现有分数阶处理方法进行讨论,分析了插值逼近方法中插值系数对重复控制器整体频率特性的作用,据此提出基于几何约束优化的分数阶重复控制器,通过优化各插值系数,电机在全转速范围内都可以保证谐振频率和电流谐波频率相吻合,并且谐振峰值更符合电机谐波组成规律;还分析了滤波器所处反馈回路位置对频率特性的影响,作为组合滤波器设计依据;为保证系统稳定,对包含PI、重复控制器以及离散电机模型的电流控制系统进行稳定性分析,并作为控制参数选取依据。最后,通过台架实验验证了该文所提出的方法的谐波抑制性能是更优的。
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关键词 分数阶延时环节重复控制器控制稳定性谐波抑制永磁同步电机(PMSM)    
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.
Key wordsFractional order delay    repetitive controller    control stability    harmonic suppression    permanent magnet synchronous motor (PMSM)   
收稿日期: 2022-11-23     
PACS: TM351  
基金资助:江西省重点研发计划-产业链科技创新联合体资助项目(20224BBE52003)
通讯作者: 朱 元 男,1976年生,博士,副教授,研究方向为汽车电子嵌入式软件、车用永磁同步电机控制。E-mail: yuan.zhu@tongji.edu.cn   
作者简介: 朱醴亭 男,1999年生,硕士研究生,研究方向为车用永磁同步电机控制。E-mail: 2131592@tongji.edu.cn
引用本文:   
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.
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