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Article(id=1244336754744999996, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, articleNumber=null, orderNo=null, doi=10.16450/j.cnki.issn.1004-6801.2025.05.010, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1692633600000, receivedDateStr=2023-08-22, revisedDate=1696608000000, revisedDateStr=2023-10-07, acceptedDate=null, acceptedDateStr=null, onlineDate=1774602600990, onlineDateStr=2026-03-27, pubDate=1759248000000, pubDateStr=2025-10-01, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1774602600990, onlineIssueDateStr=2026-03-27, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1774602600990, creator=13701087609, updateTime=1774602600990, updator=13701087609, issue=Issue{id=1244336743298740932, tenantId=1146029695717560320, journalId=1244311425741537314, year='2025', volume='45', issue='5', pageStart='855', pageEnd='1056', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1774602598261, creator=13701087609, updateTime=1774603435030, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1244340253042000577, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1244340253042000578, tenantId=1146029695717560320, journalId=1244311425741537314, issueId=1244336743298740932, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=929, endPage=936, ext={EN=ArticleExt(id=1244336756535967831, articleId=1244336754744999996, tenantId=1146029695717560320, journalId=1244311425741537314, language=EN, title=Design and Parameter Optimization of LLCC Resonant Network for Linear Ultrasonic Motors, columnId=1244336744728998604, journalTitle=Journal of Vibration,Measurement and Diagnosis, columnName=PAPER, runingTitle=null, highlight=null, articleAbstract=

Aiming to address the operation stability affected by the parameter time-variation of the ultrasonic motor and the harmonic effect of the drive voltage，this paper focuses on the design and optimization of LLCC resonant network topology as well as total harmonic distortion （THD） of the output voltage for driving linear ultrasonic motors （LUMs）. Such method can effectively overcome the issue on the variations of the driving voltages caused by the parameter time-variation to improve their operation stability. Firstly，the calculation method for the LLCC matching parameters is derived by using a contact-based equivalent circuit of LUMs considering the stator/mover contact boundary conditions，and a compensation capacitor is added to improve the elasticity margin and the stability of impedance matching. Furthermore，the filtering characteristics of the LLCC resonant network near the resonant frequency is discussed in depth，and the mathematical relationships are derived between the THD of the output voltage and the parameters of the LLCC resonant network are derived. Furthermore，the influence of the parasitic parameters of the transformer on the LLCC resonant network is also analyzed. On this basis，the design optimization methodology for the LLCC resonant network is proposed while acting the THD of the sinusoidal output voltage as the main target. Finally，a LLCC resonant driver is designed for a V-shape LUM，and the corresponding experiments are conducted. The results indicated that the gain and the THD of the output voltage as well as the peak amplitude of the series capacitor voltage itself are determined by the ratio of the series capacitor and the parallel capacitor in the resonant network. The series inductor is the dominating factor for the soft switching characteristics. The THD of the output voltage is controlled below 3%，which is improved more than 70% compared to the unoptimized LLCC resonant driver.

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针对直线超声电机参数时变性以及驱动电压谐波影响其运行稳定性的问题，通过设计两电感⁃两电容（简称LLCC）谐振网络拓扑及优化其输出电压总谐波畸变率（total harmonic distortion，简称THD）的方法，提升了电机运行稳定性。首先，采用考虑定/动子接触状态下的等效电路模型，推导出LLCC阻抗匹配的计算公式，引入补偿电容改善阻抗匹配的弹性裕度与稳定性；其次，探讨了谐振点附近的LLCC匹配电路滤波特性，推导出输出电压THD与LLCC谐振电路参数的数学关系，分析了变压器寄生参数对LLCC谐振电路的影响，并提出以正弦输出电压THD 值为主要指标的LLCC 谐振电路优化设计方法；最后，设计了V型直线超声电机的LLCC谐振驱动器。实验结果表明：谐振网络中串、并联电容的比值决定输出电压幅值增益水平、THD和串联电容两端电压峰值，且前两者相互制衡；并联电感值为软开关特性的主要决定因素；驱动电压THD值控制在3%以内，相比优化前提升了70%以上。

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李响，男，1986年12月生，博士、副教授。主要研究方向为超声电机动力学建模与驱动控制技术。 E-mail：
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郭鹏涛，男，1999年5月生，硕士生。主要研究方向为超声电机驱动技术。曾发表《A generalized electromechanical coupled model of standing-wave linear ultrasonic motors and its nonlinear version》（《Mechanical Systems and Signal Processing》2023，Vol.186）等论文。 E-mail：

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郭鹏涛，男，1999年5月生，硕士生。主要研究方向为超声电机驱动技术。曾发表《A generalized electromechanical coupled model of standing-wave linear ultrasonic motors and its nonlinear version》（《Mechanical Systems and Signal Processing》2023，Vol.186）等论文。 E-mail：

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郭鹏涛，男，1999年5月生，硕士生。主要研究方向为超声电机驱动技术。曾发表《A generalized electromechanical coupled model of standing-wave linear ultrasonic motors and its nonlinear version》（《Mechanical Systems and Signal Processing》2023，Vol.186）等论文。 E-mail：

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inductive and capacitive load switch tubes, figureFileSmall=rNF6P/lLAPHMg6hhGriHlg==, figureFileBig=WTQ29YBZ2KNsS4tqJCWPQA==, tableContent=null), ArticleFig(id=1244351830528995898, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754744999996, language=CN, label=图14, caption=感性与容性负载开关管温升实验对比图, figureFileSmall=rNF6P/lLAPHMg6hhGriHlg==, figureFileBig=WTQ29YBZ2KNsS4tqJCWPQA==, tableContent=null), ArticleFig(id=1244351830600299071, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754744999996, language=EN, label=Tab.1, caption=

Parameters of V⁃shaped linear ultrasonic motor

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参数A相B相
R0/Ω636.775411.229
L0/mH365.658293.248
C0/pF44.51955.872
Cd/nF2.0752.001
fr/kHz39.44739.319
), ArticleFig(id=1244351830684185158, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754744999996, language=CN, label=表1, caption=

V型直线超声电机参数

, figureFileSmall=null, figureFileBig=null, tableContent=
参数A相B相
R0/Ω636.775411.229
L0/mH365.658293.248
C0/pF44.51955.872
Cd/nF2.0752.001
fr/kHz39.44739.319
), ArticleFig(id=1244351830759682635, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754744999996, language=EN, label=Tab.2, caption=

Simulation of A⁃phase stator matching（a=0.5）

, figureFileSmall=null, figureFileBig=null, tableContent=
f/kHzLs/mHTHD/%Qs
39.012.5710.033
53.5520.167
84.9590.267
39.312.4850.181
53.4320.907
84.8271.632
39.512.4250.341
53.3661.705
84.6862.728
39.812.2740.053
53.1850.265
84.4900.424
), ArticleFig(id=1244351830847763027, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754744999996, language=CN, label=表2, caption=

A相定子匹配仿真（a=0.5）

, figureFileSmall=null, figureFileBig=null, tableContent=
f/kHzLs/mHTHD/%Qs
39.012.5710.033
53.5520.167
84.9590.267
39.312.4850.181
53.4320.907
84.8271.632
39.512.4250.341
53.3661.705
84.6862.728
39.812.2740.053
53.1850.265
84.4900.424
), ArticleFig(id=1244351830948426328, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754744999996, language=EN, label=Tab.3, caption=

Design parameters and calculated parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数数值计算参数数值
Udc/V12Ls/mH3.000
Po/W15Cs/nF5.440
k10∶1Lr=Lm3/mH2.000
f/kHz38.5~40.5CcA/nF6.850
a0.5CcB/nF13.520
fr/kHz39.4QsA1.043
THD/%<3QsB1.195
), ArticleFig(id=1244351831028118108, tenantId=1146029695717560320, journalId=1244311425741537314, articleId=1244336754744999996, language=CN, label=表3, caption=

设计参数与计算参数

, figureFileSmall=null, figureFileBig=null, tableContent=
设计参数数值计算参数数值
Udc/V12Ls/mH3.000
Po/W15Cs/nF5.440
k10∶1Lr=Lm3/mH2.000
f/kHz38.5~40.5CcA/nF6.850
a0.5CcB/nF13.520
fr/kHz39.4QsA1.043
THD/%<3QsB1.195
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直线超声电机LLCC谐振网络设计与参数优化方法
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郭鹏涛 1 , 李响 1 , 周利锋 2 , 姚志远 3
振动、测试与诊断 | 论文 2025,45(5): 929-936
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振动、测试与诊断 | 论文 2025, 45(5): 929-936
直线超声电机LLCC谐振网络设计与参数优化方法
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郭鹏涛1 , 李响1 , 周利锋2, 姚志远3
作者信息
  • 1合肥工业大学电气与自动化工程学院　合肥，230009
  • 2南京工程学院工业中心/创新创业学院　南京，211167
  • 3南京航空航天大学航空学院　南京，210016

    • 郭鹏涛，男，1999年5月生，硕士生。主要研究方向为超声电机驱动技术。曾发表《A generalized electromechanical coupled model of standing-wave linear ultrasonic motors and its nonlinear version》（《Mechanical Systems and Signal Processing》2023，Vol.186）等论文。 E-mail：

通讯作者:

李响，男，1986年12月生，博士、副教授。主要研究方向为超声电机动力学建模与驱动控制技术。 E-mail：
Design and Parameter Optimization of LLCC Resonant Network for Linear Ultrasonic Motors
Pengtao GUO1 , Xiang LI1 , Lifeng ZHOU2, Zhiyuan YAO3
Affiliations
  • 1.School of Electrical Engineering and Automation，Hefei University of Technology　Hefei，230009，China
  • 2.Industrial Center/School of Innovation and Entrepreneurship，Nanjing Institute of Technology　Nanjing，211167，China
  • 3.College of Aerospace Engineering，Nanjing University of Aeronautics and Astronautics　Nanjing，210016，China
出版时间: 2025-10-01 doi: 10.16450/j.cnki.issn.1004-6801.2025.05.010
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摘要
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针对直线超声电机参数时变性以及驱动电压谐波影响其运行稳定性的问题，通过设计两电感⁃两电容（简称LLCC）谐振网络拓扑及优化其输出电压总谐波畸变率（total harmonic distortion，简称THD）的方法，提升了电机运行稳定性。首先，采用考虑定/动子接触状态下的等效电路模型，推导出LLCC阻抗匹配的计算公式，引入补偿电容改善阻抗匹配的弹性裕度与稳定性；其次，探讨了谐振点附近的LLCC匹配电路滤波特性，推导出输出电压THD与LLCC谐振电路参数的数学关系，分析了变压器寄生参数对LLCC谐振电路的影响，并提出以正弦输出电压THD 值为主要指标的LLCC 谐振电路优化设计方法；最后，设计了V型直线超声电机的LLCC谐振驱动器。实验结果表明：谐振网络中串、并联电容的比值决定输出电压幅值增益水平、THD和串联电容两端电压峰值，且前两者相互制衡；并联电感值为软开关特性的主要决定因素；驱动电压THD值控制在3%以内，相比优化前提升了70%以上。

直线超声电机  /  LLCC谐振网络  /  阻抗匹配  /  谐波抑制

Aiming to address the operation stability affected by the parameter time-variation of the ultrasonic motor and the harmonic effect of the drive voltage，this paper focuses on the design and optimization of LLCC resonant network topology as well as total harmonic distortion （THD） of the output voltage for driving linear ultrasonic motors （LUMs）. Such method can effectively overcome the issue on the variations of the driving voltages caused by the parameter time-variation to improve their operation stability. Firstly，the calculation method for the LLCC matching parameters is derived by using a contact-based equivalent circuit of LUMs considering the stator/mover contact boundary conditions，and a compensation capacitor is added to improve the elasticity margin and the stability of impedance matching. Furthermore，the filtering characteristics of the LLCC resonant network near the resonant frequency is discussed in depth，and the mathematical relationships are derived between the THD of the output voltage and the parameters of the LLCC resonant network are derived. Furthermore，the influence of the parasitic parameters of the transformer on the LLCC resonant network is also analyzed. On this basis，the design optimization methodology for the LLCC resonant network is proposed while acting the THD of the sinusoidal output voltage as the main target. Finally，a LLCC resonant driver is designed for a V-shape LUM，and the corresponding experiments are conducted. The results indicated that the gain and the THD of the output voltage as well as the peak amplitude of the series capacitor voltage itself are determined by the ratio of the series capacitor and the parallel capacitor in the resonant network. The series inductor is the dominating factor for the soft switching characteristics. The THD of the output voltage is controlled below 3%，which is improved more than 70% compared to the unoptimized LLCC resonant driver.

linear ultrasonic motor  /  LLCC resonant network  /  impedance matching  /  harmonic suppression
郭鹏涛, 李响, 周利锋, 姚志远. 直线超声电机LLCC谐振网络设计与参数优化方法. 振动、测试与诊断, 2025 , 45 (5) : 929 -936 . DOI: 10.16450/j.cnki.issn.1004-6801.2025.05.010
Pengtao GUO, Xiang LI, Lifeng ZHOU, Zhiyuan YAO. Design and Parameter Optimization of LLCC Resonant Network for Linear Ultrasonic Motors[J]. Journal of Vibration,Measurement and Diagnosis, 2025 , 45 (5) : 929 -936 . DOI: 10.16450/j.cnki.issn.1004-6801.2025.05.010
正文
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引言
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直线超声电机（linear ultrasonic motor，简称LUM）为新型微特直线电机，其利用压电陶瓷的逆压电效应激发出定子的超声频机械共振，进而在定子驱动足处产生微观椭圆运动，通过定动子的摩擦传动机制转换为动子的宏观直线运动［1‑2］。与传统电磁电机相比，直线超声电机具有结构简单、功率密度高、响应快、抗电磁干扰能力强及可直接驱动负载等优点，在航天器、精密定位平台及微型机器人等领域具有重要的应用前景［3⁃5］。
超声电机虽具有上述优点，但其内部机械阻抗有很强的非线性和时变特性，在定动子接触过程中随边界条件、温度等因素变化发生较大改变［6⁃9］。此外，超声电机所需驱动电压大多由低压直流电（DC12~24 V）逆变为高压（AC100~200 V）方波，经滤波网络输出高压正弦波。驱动电压的峰值、相移及THD等均对电机运行效果有很大影响［10‑11］，这就要求驱动电路充分考虑在动态边界条件下的阻抗匹配问题，得到幅值和相位不随负载（电机）阻抗的变化而变化的输出电压，同时具有良好的THD，以实现电机的最优驱动效果。
一般由2个谐振电感和2个谐振电容经不同的组合方式组成的4阶谐振电路，统称为 LLCC 谐振滤波器。傅平［12］应用LLCC谐振匹配，实现了输出两相高频正弦电压来驱动超声电机。Lin等［13］将LLCC匹配网络应用在模糊控制中，设计出电压、相移稳定性较高的自适应控制系统。卢其威等［14］基于移相全桥逆变拓扑结构，建立功率器件的损耗模型，实现固定频率下低损耗、低THD的大功率正弦逆变输出。Zhang等［15］利用LLCC匹配实现了低温漂驱动电源。Li等［16］提出一种用于驱动超声高功率压电致动器的新型逆变器，减少电机电压的总谐波失真，并局部补偿压电致动器的无功功率。Shafiei等［17］利用LCLC谐振匹配实现了高压软开关输出，提高了逆变器的效率。俞浦等［18］设计的旋转超声电机的LLCC匹配网络，满足电压幅值和相角不随负载和驱动频率变化而改变，仅以主电路实现软开关、电压幅值和相移为目标。如果要实现电机的高性能驱动，必须考虑高次谐波对其非目标振动模态的影响，且因为构成特定频率范围内LLCC谐振网络的电容、电感选取有多种方案，还需进一步分析各元件参数的限制条件与最佳匹配组合。
针对上述问题，笔者采用接触状态下的直线超声电机定子等效电路［19］，以稳定幅值和相移为基本限制条件，以低THD的输出电压为优化目标，对超声电机的LLCC阻抗匹配网络进行分析。
1　主电路分析
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单相LLCC谐振电路如图1所示。其中，半桥逆变电路由电力场效应管与高频变压器组成，匹配电路由外加无源电感Lr、Ls及无源电容Cs、Cc组成。电机的等效电路由电气支路、机械支路和接触支路组成，其中压电陶瓷的静态电容Cd构成电气支路。在定动子未接触状态下，电机质量效应的等效电感Lm0、弹性效应的等效电容Cm0、定子内机械损耗的等效电阻Rm0串联构成动态机械支路，其决定电机机电耦合特性；在定动子接触状态下，电阻RF等效为定动子在摩擦传动过程中的能量损耗，电容CF等效为定子传递至动子的能量。
电机的等效电路参数受边界条件的改变而动态变化，所以在静态电容两端并联补偿电容Cc，以降低因夹持电容在运行过程中的变化对匹配电路干扰的权重，同时也使LLCC匹配电路的参数选择弹性化。
将推挽变压器T视为理想变压器，可把图1上方的匹配电路和超声电机等效电路分两步简化为如图1左下方电路，其中：Ls、Cs为串联匹配电感和电容；Lr、Cr为并联电感和电容，其共同组成LLCC谐振阻抗匹配网络。简化后的等效电容Cr和电阻R也具有时变特性，随电机不同的边界条件呈非线性变化。各参数变换关系为
其中：为过渡变量；Cc为补偿电容。
谐振网络电压增益及其相位为
其中：Z1为超声电机与补偿电容Cc的总阻抗；Z2为变压器副边侧除Lr的阻抗。
当式（2）分母虚部为0、实部为1时，电压增益为1，此时谐振网络的相位，在谐振频率附近有
谐振网络与超声电机的总阻抗为
由式（4）可知，在谐振频率附近，Z的分子虚部近似为0，若使总阻抗为阻性，仅需分母虚部为0，即
本次仿真及实验所用电机为一款自研的额定功率为12 W的V型直线超声电机，利用阻抗分析仪可对考虑定、动子接触的定子等效电路进行参数识别［19］。识别后的V型直线超声电机参数见表1，其中施加给定子的预压力为80 N。
2　LLCC电路的滤波特性分析
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匹配电路输入电压与基波电压如图2所示。其中：实线部分为推挽逆变电路输入至匹配电路的方波电压uin；虚线部分为基波分量uin1。对uin进行傅里叶分析，得到
uin（t）包含了3，5，7，…等高次谐波成分，会激发压电陶瓷组的非目标振动模态，影响电机运行效果。同时，仅满足式（4）和式（6）的Lr、Ls、Cr及Cs有无数种组合，因此需要研究这些元件在不同取值时对输出电压的影响及其选型的限制条件。
和分别为匹配电路输出正弦电压和输入方波电压的向量表示，其关系为
其中：A=ω2Cs（Ls+Lr）；B=ωLr（1-ω2LsCs）；C=ωLr（ω2LsCrCs-Cr-Cs）。
为了分析LLCC谐振电路在谐振频率ωr附近的滤波特性，定义
其中：Qs为品质因数。
将式（9）代入式（8），可得
将式（10）乘以式（7）中的各次谐波电压的幅值，可以得到
其中：为输出电压的各次谐波。
的波形畸变率可表示为
由式（11）可以看出，各次谐波输出幅值大小与a、品质因数Qs有关。根据式（12），利用Matlab绘出a、Qs与高次谐波含量的三维关系曲线，a和Qs对THD的影响如图3所示。可以看出，9次及以上谐波含量占总THD含量不足0.1%，因此本研究中THD计算仅考虑抑制3，5，7次谐波。
选取不同的a和Ls代入式（9），分别得到Lr、Cs和Cr。根据式（2）、式（3）得到Ls与输出电压增益和相移的关系，如图4所示。可以看出：输出电压增益会随着频率的增大而线性增大，随着a减小，将造成电压增益在驱动频域内的幅值波动增大；输出电压的相移主要由Ls决定，在谐振频率附近波动相对剧烈，但总体仍处于较低水平。因此，为了使输出电压增益、相移在不同频段变化尽量小，一般选择a>0.3和Ls<5 mH。由于装配工艺问题，超声电机的两相参数不完全相同，可大致取两相机械谐振频率的中间值fr=39.4 kHz为参考谐振频率，也作为进行LLCC匹配的目标频率和电机初始驱动频率。
考虑到超声电机可以调频调速，且运行过程中会发生频率漂移现象，需闭环频率跟踪，因而要对不同频率匹配电路输出性能进行分析。根据式（1）、式（4）、式（6）及表1，在fr附近频率下对LLCC匹配电路进行Matlab/Simulink仿真分析，得到频率和串联电感的关系。A相定子匹配仿真如表2所示。由表可知，当a确定时，不同驱动频率下THD均随Ls的增大而线性增大。由于Qs的大小随频率波动较大，不能以不同频段的Qs来进行匹配电路的选型，故仅对fr下的Qs进行分析。
选取不同a与Qs进行Matlab/Simulink仿真，得到不同Qs时的THD与a的关系曲线，如图5所示。不同a时的THD、电容Cs的端电压与Qs的关系曲线如图6所示。与图3相比，图5、图6的仿真结果进一步验证了Qs的变化对于LLCC匹配电路输出电压的THD影响很小，且随着Qs的增大，THD呈减小趋势。对比图4与图6发现，a增大会造成输出电压总谐波畸变率的线性增大，但也会使增益曲线的斜率减小，两者相互制衡，在实际电源制作过程中需根据目标电机的特点综合考虑选取。由图6还可看出，串联谐振电容Cs上的电压会随着a的减小而近似线性增大，因此需要先确定a，再根据峰值上限与安全裕度选取滤波电容Cs的型号。
为避免补偿电容Cc为负数，应满足
其中：Crmin为最小并联电容；fmax为最大驱动频率。
3　推挽变压器对 LLCC 电路的影响
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变压器等效及其简化电路如图7所示。图7（a）中：Lm1，2、C1，2ʹ、L1，2和R1，2ʹ分别为变压器原边两绕组的励磁电感、匝间电容、漏感和串并联等效电阻；Lm3、L3分别为变压器副边的励磁电感和漏感。推挽变压器一般采用多股导线并绕的方式，原边2个绕组的对应参数大致相等。由于电路负载阻抗相对较大，因此实际变压器的寄生参数C1，2ʹ≈0，且R1，2ʹ远小于电机电阻，即C1，2ʹ和R1，2ʹ对输出电压的影响可以忽略不计，图7（a）可简化为图7（b）。图7（b）中的Lm1，2对开关管零电压导通有积极影响，但会严重降低输出电压幅值和引起尖峰电压。综合考虑下，笔者没有利用原边漏感实现软开关，所以在制作变压器时尽可能使原边漏感与励磁电感达到最小。同时，实际测量的ωL1，2远小于超声电机等效电阻，其对于理论计算影响很小。
根据式（4）和式（6）可将变压器副边侧整体匹配为阻性，使开关管处于损耗较大硬开关状态，且驱动频率在一定范围内调整，整体电路阻抗性质时变性大。工作在感性负载相较于容性负载工况下可以实现软开关零电压开通，且能够避免容性负载下出现几倍于正常电流的开关尖峰电流［20］。在确定匹配电路中的各参数后，由式（8）得到Lr与总阻抗Z的相位关系，如图8所示。由图可知，若要满足在驱动频率带宽内系统总阻抗为感性状态，则需要在式（6）的基础上进一步结合图8对Lr重新选型。在本研究中，当Lr<3 mH时总阻抗呈感性，为了避免Lr消耗过多的无功电流，一般将其选择为略小于临界电感，使总阻抗在谐振频率处呈弱感性即可。
从电压的角度看，变压器副边侧可以视为高压方波与副边励磁电感Lm3并联，再与副边漏感L3串联，如图7（c）所示。此时，最理想的匹配状态是L3完全代替LLCC匹配电路的串联谐振电感Ls，Lm3完全代替Lr，这样可以减小电路元件数量和电路体积。本实验通过改变绕组线圈相对位置设计推挽变压器的副边漏感，改变各绕组的气隙设计推挽变压器的励磁电感。
4　设计步骤和实验验证
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当设计超声电机电源时，应当从提高输出电压幅值和相移稳定性、减小输出电压THD、提高电源效率及减小元器件过大的电压电流应力方面综合考虑，其中a的大小对增益脉动、总谐波畸变率和串联谐振电容Cs上的电压有着关键影响。LLCC匹配电路设计步骤如图9所示。笔者基于此方法，针对V型直线超声电机设计了输出 f=39.4 kHz和THD<3%的正弦波、功率为15 W的驱动电源。设计参数与计算参数如表3所示。
基于ARM控制器的V型直线超声电机驱动实验平台见图10。其中：可编程直流电源用于提供驱动电路的能量；示波器用于测量电机输入电压（匹配电路输出电压）与开关管漏源极电流；电流探头用于辅助示波器测量开关管漏源极电流；热成像仪用于测量匹配至感性与容性条件下的开关管温升图。
两相电压输出及THD分析如图11所示。图11（a）为fr=39.4 kHz时带载的两相输出电压经LLCC匹配前后仿真波形，可以看出，仅考虑增益和相移等因素的优化前仿真波形已出现明显的正弦波形的畸变。图11（b）为匹配后实际输出的波形，与输入方波的基波幅值152.793 V及90°的目标相位差偏差较小，偏差主要来源于：①两相定子参数不完全相同；②温度上升导致谐振频率值下降；③示波器在大刻度下显示不精准。图11（c）为仿真与实际输出波形的THD对比，可以发现，LLCC匹配经优化后高次谐波得到大幅度抑制，由于电机在运行过程中温度上升，导致静态电容Cd的容值增大，进而a小幅度减小，这可能是实际输出电压低于仿真输出电压的THD水平的主要原因。
不同频率下输出电压的理论值与测量值如图12所示。电压增益会随着频率的增加出现小幅度上升趋势，因为实际的超声电机精密控制下的驱动频率漂移一般在谐振点附近100~200 Hz左右，所以施加在电机上的峰值电压最大偏移仅为±1~4 V，实际产生的位移误差很小，并很容易通过算法实现补偿。在同等条件下，使用LC、LLCC匹配对电机分别进行堵转测试，前者堵转力为13.5 N，后者为21.9 N，堵转力提升了62.2%。
开关管漏极电流ids和漏源极电压uds实测波形如图13所示。可以看到：开关管导通前其反向并联二极管先导通，将开关管漏源极两端电压箝位为0，当续流过程结束后，开关管漏源极电流从0线性增加，成功实现零电压导通；当开关管关断时，原边电流给开关管结电容充电，漏源极电压从0开始增加，关断过程中在漏源极内部并未同时产生较大的电压电流汇聚，仅有相对很小的能量损耗。在图13中ids左右两侧，开关管漏极电流在开关瞬间都没有出现尖峰电流，相对容性负载大大减小了开关损耗和器件应力，提高了驱动效率和可靠性。
感性与容性负载开关管温升实验对比如图14所示。可以看到，在室温为22 ℃条件下，感性负载相较于容性负载的开关管有明显的温度下降，进一步验证了感性负载下开关管损耗较小。从图14（b）可以发现，由于容性负载存在尖峰电流，在电源输入端口出现严重发热，会对周围器件产生不良影响，降低了电源稳定性，且不利于驱动器的小型化。
5　结论
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1） 采用推挽拓扑电路，考虑基于定、动子接触的直线超声电机定子等效电路，得到LLCC谐振匹配拓扑并加以简化。根据简化模型，推导出LLCC参数与输出电压幅值和相移的代数关系，并以此作为THD优化的基本限制条件。
2） 对LLCC谐振匹配进行理论分析，发现串联电容与并联电容的比值对输出电压幅值的增益、THD和串联电容两端电压峰值大小起决定性作用，且为相互制衡关系；并联电感的值为软开关和输出电压相移的主要决定因素。结合变压器对LLCC网络进行优化设计，给出了带补偿电容的谐振网络参数设计方法。
3） 设计了一款用于直线超声电机的V型LLCC谐振驱动器，并进行了参数优化。将驱动电压THD值控制在3%以内，比未经优化的LLCC匹配提升了70%以上，且相对于传统的LC谐振匹配电路，电机堵转力提升了60%以上，对直线超声电机驱动器的谐振匹配电路设计与优化具有参考价值。
基金
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  • 国家自然科学基金资助项目(52105092; 52075261)
文献
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2025年第45卷第5期
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doi: 10.16450/j.cnki.issn.1004-6801.2025.05.010
  • 接收时间：2023-08-22
  • 首发时间：2026-03-27
  • 出版时间：2025-10-01
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  • 收稿日期：2023-08-22
  • 修回日期：2023-10-07
基金
国家自然科学基金资助项目(52105092; 52075261)
作者信息
    1合肥工业大学电气与自动化工程学院　合肥，230009
    2南京工程学院工业中心/创新创业学院　南京，211167
    3南京航空航天大学航空学院　南京，210016

通讯作者:

李响，男，1986年12月生，博士、副教授。主要研究方向为超声电机动力学建模与驱动控制技术。 E-mail：
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