悬架馈能作动器力学特性测试及非线性主动控制器设计

陈士安; 管毓亮; 任洁雨; 姚明; 蒋栋

doi:10.19818/j.cnki.1671-1637.2022.04.018

悬架馈能作动器力学特性测试及非线性主动控制器设计

doi: 10.19818/j.cnki.1671-1637.2022.04.018

1.
江苏大学汽车与交通工程学院，江苏镇江 212013
2.
浙江万向马瑞利减震器有限公司，浙江杭州 311215

基金项目:

国家自然科学基金项目 52575239

国家自然科学基金项目 52072158

详细信息

作者简介:
陈士安(1973-)，男，湖北荆州人，江苏大学教授，工学博士，从事汽车悬架控制研究

中图分类号: U461
计量
- 文章访问数: 326
- HTML全文浏览量: 86
- PDF下载量: 43
- 被引次数: 0
出版历程
- 收稿日期: 2022-02-02
- 网络出版日期: 2022-10-08
- 刊出日期: 2022-08-25

Mechanical characteristics test and nonlinear active controller design of energy-regenerative actuator for suspension

1.
School of Automotive and Traffic Engineering, Jiangsu University, Zhenjiang 212013, Jiangsu, China
2.
Zhejiang Wanxiang Marelli Shock Absorbers Co., Ltd., Hangzhou 311215, Zhejiang, China

Funds:

National Natural Science Foundation of China 52575239

National Natural Science Foundation of China 52072158

More Information

Author Bio:
CHEN Shi-an(1973-), male, professor, PhD, chenshian73@ujs.edu.cn

摘要

摘要: 为提高车辆的乘坐舒适性并兼具回收振动能量的功能，对试制PMSM-滚珠丝杠式馈能作动器进行了力学特性测试，对库仑阻尼和作动器等效惯性质量进行识别，根据识别结果设计了馈能型主动悬架非线性控制器；结合电磁动力学建模、电气参数校核，采用分级变压充电试验方法对作动器样机进行三角波及正弦波位移输入下的力学特性测试，利用参数拟合使建模仿真力学特性曲线逼近实测曲线，完成库仑阻尼识别和等效惯性质量验证；对含有库仑阻尼及作动器等效惯性质量的主动悬架力学模型中的非线性项进行前馈反馈线性化处理，并对簧载质量/非簧载质量加速度项正则化处理，在此基础上根据作动器最大输出力设计了双约束H₂/H_∞控制器；利用数值仿真对被动悬架、理想主动悬架、常规H₂/H_∞控制主动悬架和双约束H₂/H_∞控制主动悬架进行悬架综合性能对比验证及馈能性能分析。分析结果表明：双约束H₂/H_∞控制主动悬架的簧载质量加速度均方根和综合性能指标较被动悬架分别降低47.05%和51.67%，仅比理想主动悬架分别差1.86%和1.34%，且比常规H₂/H_∞控制主动悬架分别优19.28%和11.21%；库仑阻尼和电机定子电阻分别消耗掉了作动器总吸收功率的18.99%和20.19%，相比之下，流向蓄电池的回收平均功率高达60.82%。
- 车辆工程 /
- 主动悬架 /
- 馈能作动器 /
- 力学特性测试 /
- 参数识别 /
- 非线性双约束H₂/H_∞控制
Abstract: In order to improve the riding comfort and recover the vibration energy, the mechanical characteristics of a prototyped PMSM-ball screw energy-regenerative actuator were tested. The Coulomb damping and equivalent inertial mass of the actuator were identified, and the nonlinear controller for the corresponding energy-regenerative active suspension was designed. With electromagnetic dynamic modeling and electrical parameter calibration, the mechanical characteristic test on the actuator prototype with the triangle-wave and sine-wave displacement inputs was conducted by the experimental method of stepwise variable voltage charging. The Coulomb damping identification and equivalent inertial mass verification were carried out by the parameter fitting to make the modeling simulation curves of mechanical characteristics approximate the measured ones. For the mechanical active suspension model involving the Coulomb damping and equivalent inertial mass of the actuator, the nonlinear term was processed by the feedforward and feedback linearization, and the acceleration terms of the sprung mass or unsprung mass were normalized. On this basis, a dual-constraints-based H₂/H_∞ controller was developed according to the maximum output force of the actuator. A comprehensive performance comparison among the passive suspension, ideal active suspension, conventional active suspension with H₂/H_∞ control, and active suspension with dual-constraints-based H₂/H_∞ control was made through the numerical simulations for verification and energy-regenerative performance analysis. Analysis results show that compared with the passive suspension, the root mean square of sprung mass acceleration and the comprehensive performance index of the active suspension with dual-constraints-based H₂/H_∞ control reduce by 47.05% and 51.67%, respectively, which are just 1.86% and 1.34% inferior to those of the ideal active suspension, and 19.28% and 11.21% superior to those of the conventional active suspension with H₂/H_∞ control. The total absorption power of the actuator is consumed by the Coulomb damping and motor stator resistance by 18.99% and 20.19%, respectively. By contrast, the average power reclaimed to batteries is as high as 60.82%. 7 tabs, 11 figs, 35 refs.
- vehicle engineering /
- active suspension /
- energy-regenerative actuator /
- mechanical characteristic test /
- parameter identification /
- nonlinear dual constraints based H₂/H_∞ control

HTML全文

图 1 PMSM-滚珠丝杠式作动器及结构

Figure 1. PMSM-ballscrew actuator and structure

下载: 全尺寸图片幻灯片

图 2 作动器样机台架试验布置

Figure 2. Bench test layout of actuator prototype

下载: 全尺寸图片幻灯片

图 3 充电开路状态三角波激励下台架检测力的试验和仿真结果

Figure 3. Test and simulation results of bench measuring force under open-circuit state of charging with triangle wave excitations

下载: 全尺寸图片幻灯片

图 4 充电开路状态正弦波激励下台架检测力的试验和仿真结果

Figure 4. Test and simulation results of bench measuring force under open-circuit state of charging with sine wave excitations

下载: 全尺寸图片幻灯片

图 5 1.00 Hz正弦波激励不同充电电压下作动器力学特性的试验和仿真结果

Figure 5. Test and simulation results of actuator mechanical characteristics under 1.00 Hz sine wave excitation and different charging voltages

下载: 全尺寸图片幻灯片

图 6 1/4车主动悬架模型

Figure 6. 1/4 vehicle active suspension model

下载: 全尺寸图片幻灯片

图 7 馈能型主动悬架非线性双约束H₂/H_∞控制原理

Figure 7. Principle of nonlinear dual constraints based H₂/H_∞ control for energy-regenerative active suspension

下载: 全尺寸图片幻灯片

图 8 三种悬架的主动控制力对比

Figure 8. Active control force comparison among 3 types of suspensions

下载: 全尺寸图片幻灯片

图 9 四种悬架的性能指标对比

Figure 9. Performance index comparison among four types of suspensions

下载: 全尺寸图片幻灯片

图 10 双约束H₂/H_∞控制馈能型主动悬架功率和能量仿真结果

Figure 10. Dual constraints based H₂/H_∞ control energy-regenerative active suspension power and energy simulation results

下载: 全尺寸图片幻灯片

图 11 两种变工况下的悬架综合性能指标对比

Figure 11. Suspension comprehensive performance index comparison under two different driving conditions

下载: 全尺寸图片幻灯片

表 1 LCMT-10L02NB-80M04025B型PMSM标定参数

Table 1. Marked parameters of LCMT-10L02NB-80M04025B PMSM

参数名称	数值
额定功率/W	1 000
额定力矩/(N·m)	4
峰值力矩/(N·m)	12
额定线电流/A	4.4
峰值电流/A	13.2
线间电阻/Ω	1.83
线间电感/mH	4.72
反电势常数/[V·(r·min^-1)^-1]	56 000
转子惯量/(kg·m²)	2.97×10^-4
极对数	4

下载: 导出CSV

表 2 SFY-2040-3.6滚珠丝杠标定参数

Table 2. Marked parameters of SFY-2040-3.6 ballscrew

参数名称	数值
直径/m	0.02
螺距/m	0.02
导程/m	0.04
动载荷/N	13 110

下载: 导出CSV

表 3 作动器力学特性试验设置

Table 3. Actuator mechanical characteristic test setup

参数名称	数值
幅值/m	0.05
频率/Hz	0.25、0.50、0.75、1.00、1.25、1.50
充电电压/V	开路，3.2、6.4、9.6、12.8、16.0

下载: 导出CSV

表 4 作动器识别力学特性参数

Table 4. Identified actuator mechanical characteristic parameters

参数	G_g/N	f/N	m_t/kg	m_e/kg
数值	297.47	82.05	15.84	10.97

下载: 导出CSV

表 5 作动器输出力试验和仿真数据分析

Table 5. Test and simulation data analysis of actuator output force

频率/Hz	充电电压/V	均方根误差/N	决定系数
0.50	3.2	24.68	0.993 5
0.50	6.4	28.51	0.980 4
0.50	9.6	30.19	0.940 5
1.00	3.2	29.45	0.997 0
1.00	9.6	35.67	0.993 0
1.00	16.0	36.32	0.983 0

下载: 导出CSV

表 6 研究所需参数

Table 6. Required parameters in research

参数	数值	参数	数值
m₁/kg	32	n₀/m^-1	0.1
m₂/kg	450	u/(km·h^-1)	72
m_e/kg	10.97	F_Emax /N	1 885
k₁/(N·m^-1)	270 000	S_smax/m	0.08
k₂/(N·m^-1)	45 500	δ₁	1
c₀/(N·s·m^-1)	2 985	δ₂	34 639
f/N	82.05	δ₃	4 438.6
G_q(n₀)/m³	2.56×10^-4	κ₁	6.6×10^-4
n_min/m^-1	0.011	κ₂	1
n_max/m^-1	2.83	κ₂₀	500

下载: 导出CSV

表 7 四种悬架的性能指标统计数据

Table 7. Statistics data of performance indexes for four types of suspensions

指标	被动悬架	主动悬架1	主动悬架2	主动悬架3
a/(m·s^-2)	1.641 8	0.853 5	1.077 0	0.869 4
(z₁-q)/m	0.003 3	0.003 8	0.003 6	0.003 9
(z₂-z₁)/m	0.009 1	0.009 5	0.007 8	0.009 3
J	3.443	1.642	1.874	1.664

下载: 导出CSV

参考文献(35)

[1]	BOLTON T, IVANOV A, MARAVIN Y, et al. Energy, ride comfort, and road handling of regenerative vehicle suspensions[J]. Anta, 2014, 135(1): 48-65.
[2]	ZHANG Yu-xin, GUO Kong-hui, WANG Dai, et al. Energy conversion mechanism and regenerative potential of vehicle suspensions[J]. Energy, 2017, 119: 961-970. doi: 10.1016/j.energy.2016.11.045
[3]	WEI Chong-feng, JING Xing-jian. A comprehensive review on vibration energy harvesting: modelling and realization[J]. Renewable and Sustainable Energy Reviews, 2017, 74: 1-18. doi: 10.1016/j.rser.2017.01.073
[4]	GAO Ze-peng, CHEN Si-zhong, ZHAO Yu-zhuang, et al. Numerical evaluation of compatibility between comfort and energy recovery based on energy flow mechanism inside electromagnetic active suspension[J]. Energy, 2019, 170: 521-536. doi: 10.1016/j.energy.2018.12.193
[5]	WANG Jia-bin, WANG Wei-ya, ATALLAH K, et al. A linear permanent-magnet motor for active vehicle suspension[J]. IEEE Transactions on Vehicular Technology, 2011, 60(1): 55-63. doi: 10.1109/TVT.2010.2089546
[6]	JASTRZEBSKI L, SAPIŃSKI B. Electrical interface for a self-powered MR damper-based vibration reduction system[J]. Acta Mechanica et Automatica, 2016, 10(3): 165-172. doi: 10.1515/ama-2016-0025
[7]	寇发荣, 任全, 方涛, 等. 直线电机式悬架作动器性能分析及参数优化[J]. 机械设计, 2017(12): 37-42. doi: 10.3969/j.issn.2095-509X.2017.12.009 KOU Fa-rong, REN Quan, FANG Tao, et al. Performance analysis and parameter optimization of the suspension actuator with a linear motor[J]. Journal of Machine Design, 2017(12): 37-42. (in Chinese) doi: 10.3969/j.issn.2095-509X.2017.12.009
[8]	KAWAMOTO Y, SUDA Y, INOUE H, et al. Modeling of electromagnetic damper for automobile suspension[J]. Journal of System Design and Dynamics, 2007, 1(3): 524-535. doi: 10.1299/jsdd.1.524
[9]	LIU Yi-lun, XU Lin, ZUO Lei. Design, modeling, lab, and field tests of a mechanical-motion-rectifier-based energy harvester using a ball-screw mechanism[J]. IEEE/ASME Transactions on Mechatronics, 2017, 22(5): 1933-1943. doi: 10.1109/TMECH.2017.2700485
[10]	XIE Long-han, LI Jie-hong, LI Xiao-dong, et al. Damping-tunable energy-harvesting vehicle damper with multiple controlled generators: design, modeling and experiments[J]. Mechanical Systems and Signal Processing, 2018, 99: 859-872. doi: 10.1016/j.ymssp.2017.07.005
[11]	BENO J H, WEEKS D A, BRESIE D A, et al. Experimental comparison of losses for conventional passive and energy efficient active suspension systems[J]. SAE International, 2002, DOI: 10.4271/2002-01-0282.
[12]	CHOI S B, SEONG M S, KIM K S. Vibration control of an electrorheological fluid-based suspension system with an energy regenerative mechanism[J]. Noise and Vibration Worldwide, 2009, 223(4): 459-469.
[13]	LI Zhong-jie, ZUO Lei, KUANG Jian, et al. Energy-harvesting shock absorber with a mechanical motion rectifier[J]. Smart Material Structures, 2013, 22(2): 025008. doi: 10.1088/0964-1726/22/2/025008
[14]	MARAVANDI A, MOALLEM M. Regenerative shock absorber using a two-leg motion conversion mechanism[J]. IEEE/ASME Transactions on Mechatronics, 2015, 20(6): 2853-2861. doi: 10.1109/TMECH.2015.2395437
[15]	GU Cheng, YIN Jun, LUO Jie, et al. Performance-oriented controls of a novel rocker-pushrod electromagnetic active vehicle suspension[J]. Mechanical Systems and Signal Processing, 2018, 109: 1-14. doi: 10.1016/j.ymssp.2018.02.019
[16]	LI Chuan, TSE P W. Fabrication and testing of an energy- harvesting hydraulic damper[J]. Smart Materials and Structures, 2013, 22(6): 065024. doi: 10.1088/0964-1726/22/6/065024
[17]	WANG Rui-chen, GU Feng-shou, CATTLEY R, et al. Modelling, testing and analysis of a regenerative hydraulic shock absorber system[J]. Energies, 2016, DOI: 10.3390/en9050386.
[18]	ZOU Jun-yi, GUO Xue-xun, XU Lin, et al. Design, modeling, and analysis of a novel hydraulic energy-regenerative shock absorber for vehicle suspension[J]. Shock and Vibration, 2017, DOI: 10.1155/2017/3186584
[19]	ABDELKAREEM M A A, XU Lin, ALI M K A, et al. Vibration energy harvesting in automotive suspension system: a detailed review[J]. Applied Energy, 2018, 229: 672-699. doi: 10.1016/j.apenergy.2018.08.030
[20]	JONASSON M, ROOS F. Design and evaluation of an active electromechanical wheel suspension system[J]. Mechatronics, 2008, 18(4): 218-230. doi: 10.1016/j.mechatronics.2007.11.003
[21]	HUANG C N, CHEN K H, LIN D T W. Development of an novel adaptive suspension system based on ball-screw mechanism[J]. Applied Mechanics and Materials, 2013, 477: 128-131.
[22]	YIN Jun, CHEN Xin-bo, LI Jian-qin, et al. Investigation of equivalent unsprung mass and nonlinear features of electromagnetic actuated active suspension[J]. Shock and Vibration, 2015, DOI: 10.1155/2015/624712.
[23]	ZHENG Xue-chun, YU Fan. Study on the potential benefits of an energy-regenerative active suspension for vehicles[J]. SAE transactions, 2005, DOI: 10.4271/2005-01-3564.
[24]	许广灿, 徐俊, 李士盈, 等. 电动汽车振动能量回收悬架及其特性优化[J]. 西安交通大学学报, 2016, 50(8): 90-95. https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT201608015.htm XU Guang-can, XU Jun, LI Shi-ying, et al. Energy regenerative suspension and its performance optimization for electric vehicle[J]. Journal of Xian Jiaotong University, 2016, 50(8): 90-95. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT201608015.htm
[25]	KAWAMOTO Y, SUDA Y, INOUE H, et al. Modeling of electromagnetic damper for automobile suspension[J]. Journal of System Design and Dynamics, 2007, 1(3): 524-535. doi: 10.1299/jsdd.1.524
[26]	王庆年, 刘松山, 王伟华, 等. 滚珠丝杠式馈能型减振器的结构设计及参数匹配[J]. 吉林大学学报(工学版), 2012, 42(5): 1100-1106. https://www.cnki.com.cn/Article/CJFDTOTAL-JLGY201205006.htm WANG Qing-nian, LIU Song-shan, WANG Wei-hua, et al. Structure design and parameter matching of ball-screw regenerative damper[J]. Journal of Jilin University (Engineering and Technology Edition), 2012, 42(5): 1100-1106. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JLGY201205006.htm
[27]	CHEN Shi-an, JIANG Xu-dong, YAO Ming, et al. A dual vibration reduction structure-based self-powered active suspension system with PMSM-ball screw actuator via an improved H₂/H_∞ control[J]. Energy, 2020, DOI: 10.1016/j.energy.2020.117590.
[28]	ROCKHILL A A, LIPO T A. A generalized transformation methodology for polyphase electric machines and networks[C]// IEEE. 2015 IEEE International Electric Machines and Drives Conference. New York: IEEE, 2016: 27-34.
[29]	TIAN Bing, AN Qun-tao, DUAN Jian-dong, et al. Cancellation of torque ripples with FOC strategy under two-phase failures of the five-phase PM motor[J]. IEEE Transactions on Power Electronics, 2017, 32(7): 5459-5472. doi: 10.1109/TPEL.2016.2598778
[30]	陈士安, 孙文强, 王健, 等. 基于变压充电方法的直线电机式馈能型半主动悬架控制[J]. 交通运输工程学报, 2018, 18(2): 90-100. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC201802013.htm CHEN Shi-an, SUN Wen-qiang, WANG Jian, et al. Control of energy-reclaiming semi-active suspension with linear motor based on varying charge voltage method[J]. Journal of Traffic and Transportation Engineering, 2018, 18(2): 90-100. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC201802013.htm
[31]	ZHANG Yu-xin, CHEN Hong, GUO Kong-hui, et al. Electro-hydraulic damper for energy harvesting suspension: modeling, prototyping and experimental validation[J]. Applied energy, 2017, 199: 1-12. doi: 10.1016/j.apenergy.2017.04.085
[32]	SALMAN W, QI Ling-fei, ZHU Xin, et al. A high-efficiency energy regenerative shock absorber using helical gears for powering low-wattage electrical device of electric vehicles[J]. Energy, 2018, 159: 361-372. doi: 10.1016/j.energy.2018.06.152
[33]	陈士安, 仝嘉成, 蒋旭东, 等. 基于调制白噪声与查表法的非平稳路面不平度建模方法[J]. 交通运输工程学报, 2020, 20(6): 171-179. https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202006018.htm CHEN Shi-an, TONG Jia-cheng, JIANG Xu-dong, et al. Modeling method for non-stationary road irregularity based on modulated white noise and lookup table method[J]. Journal of Traffic and Transportation Engineering, 2020, 20(6): 171-179. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JYGC202006018.htm
[34]	CHEN Shi-an, WANG Jun-cheng, YAO Ming, et al. Improved optimal sliding mode control for a non-linear vehicle active suspension system[J]. Journal of Sound and Vibration, 2017, DOI: 10.1016/j.jsv.2017.02.017.
[35]	陈士安, 邱峰, 何仁, 等. 一种确定车辆悬架LQG控制加权系数的方法[J]. 振动与冲击, 2008(2): 65-68, 176. https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200802013.htm CHEN Shi-an, QIU Feng, HE Ren, et al. A method for choosing weights in a suspension LQG control[J]. Vibration and shock, 2008(2): 65-68, 176. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZDCJ200802013.htm