基于几何约束优化的重复控制器及PMSM电流谐波抑制应用  

Repetitive Controller Based on Geometric Constraint Optimization and Its Application to Current Harmonic Suppression of PMSM

作　　者：朱元[1] 朱醴亭 肖明康 孟令 Zhu Yuan;Zhu Liting;Xiao Mingkang;Meng Ling(School of Automotive Studies Tongji University,Shanghai 201804 China)

机构地区：[1]同济大学汽车学院,上海201804

出　　处：《电工技术学报》2024年第4期1059-1073,共15页Transactions of China Electrotechnical Society

基　　金：江西省重点研发计划-产业链科技创新联合体资助项目(20224BBE52003)。

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。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 harmo

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) 

分 类 号：TM351[电气工程—电机]