基于NFTSMC的分布式驱动电动汽车稳定性控制

doi:10.3969/j.issn.1674-8484.2023.02.008

汽车安全与节能学报 ›› 2023, Vol. 14 ›› Issue (2): 212-223.DOI: 10.3969/j.issn.1674-8484.2023.02.008

基于NFTSMC的分布式驱动电动汽车稳定性控制

张一西¹(), 赵轩²^,³^,^*(), 马建²^,³, 王兴路¹, 胡月琦¹

1.西安航空学院车辆工程学院，西安 710077，中国
2.长安大学汽车运输安全保障技术交通运输行业重点实验室，西安 710064，中国
3.长安大学汽车学院，西安 710064，中国

收稿日期:2022-09-04 修回日期:2022-12-13 出版日期:2023-04-30 发布日期:2023-04-27
通讯作者: 赵轩
作者简介:*赵轩(1983—)，男(汉)，陕西，教授。E-mail：zhaoxuan@chd.edu.cn。
张一西(1993—)，女(汉)，陕西，讲师。E-mail：zyixixixi@163.com。
基金资助:
汽车运输安全保障技术交通运输行业重点实验室（长安大学）开放基金资助项目(300102223507);西安航空学院校级科研基金项目(2021KY0207);陕西省自然科学基础研究计划项目(2023-JC-YB-483)

Stability control of distributed drive electric vehicles based on the nonsingular fast terminal sliding mode control (NFTSMC)

ZHANG Yixi¹(), ZHAO Xuan²^,³^,^*(), MA Jian²^,³, WANG Xinglu¹, HU Yueqi¹

1. School of Vehicle Engineering, Xi’an Aeronautical Institute, Xi’an 710077, China
2. Key Laboratory of Transportation Industry of Automotive Transportation Safety Enhancement Technology, Chang’an University, Xi’an 710064, China
3. School of Automobile, Chang’an University, Xi’an 710064, China

Received:2022-09-04 Revised:2022-12-13 Online:2023-04-30 Published:2023-04-27
Contact: ZHAO Xuan

摘要/Abstract

摘要：

为提高分布式驱动电动汽车在极限行驶工况下的稳定性，提出了一种具有三层结构的直接横摆力矩控制策略。顶层控制器解析驾驶人期望行驶状态值；上层控制器采用非奇异快速终端滑模控制（NFTSMC），决策维持车辆稳定行驶所需附加横摆力矩；下层控制器以车辆稳定裕度最大为目标，以电机输出极限、路面附着极限、轮胎纵/侧向力耦合关系为约束，基于加权最小二乘法实现4轮力矩动态优化分配。基于MATLAB/Simulink和Carsim仿真平台开展仿真试验。结果表明：相比滑模控制，车速为70 km/h时，双移线和正弦迟滞工况下，质心侧偏角最大跟踪误差分别减小66.7%、45.8%，均方根误差分别减小64.8%、56.4%，可见该策略能够提高期望状态跟踪精确性，改善车辆在极限行驶工况下的稳定性。

关键词: 分布式驱动电动汽车, 直接横摆力矩控制, 非奇异快速终端滑模（NFTSMC）, 转矩优化分配

Abstract:

A direct yaw moment control strategy with a three-layers structure was proposed to improve the stability of distributed drive electric vehicles for extreme conditions. The top controller was designed to resolve the desired driving state value of the driver. The additional yaw moment required of the vehicle was determined in the upper controller by utilizing the nonsingular fast terminal sliding mode control (NFTSMC). To maximize the vehicle stability margin, the low controller was designed to optimal assign torque to four wheels by using the weighted least square method, which synchronously considered the motor output capability, road adhesion limitation, and the coupling relationship between the longitudinal and lateral tire forces. The simulation experiments were carried out on the MATLAB/Simulink and Carsim platform. The results show that when the vehicle speed is 70 km/h, the maximum tracking error of side slip angle decreases by 66.7% and 45.8%, and the root mean square error decreases by 64.8% and 56.4%, respectively, compared with the sliding mode control, Which shows that this strategy can improve the expected state tracking accuracy and improve the stability of the vehicle in the extreme conditions.

Key words: distributed drive electric vehicle, direct yaw moment control, nonsingular fast terminal sliding mode control(NFTSMC), torque optimization distribution

中图分类号:

U461.6

张一西, 赵轩, 马建, 王兴路, 胡月琦. 基于NFTSMC的分布式驱动电动汽车稳定性控制[J]. 汽车安全与节能学报, 2023, 14(2): 212-223.

ZHANG Yixi, ZHAO Xuan, MA Jian, WANG Xinglu, HU Yueqi. Stability control of distributed drive electric vehicles based on the nonsingular fast terminal sliding mode control (NFTSMC)[J]. Journal of Automotive Safety and Energy, 2023, 14(2): 212-223.

图/表 12

参考文献 28

[1]	王震坡, 陈辛波, 张雷, 等. 分布式驱动电动汽车关键技术及产业化展望[J]. 科技导报, 2020, 38(8): 99-100.
	WANG Zhenpo, CHEN Xinbo, ZHANG Lei, et al. Key technologies and industrialization prospect of distributed drive electric vehicle[J]. Sci Tech Rev 2020, 38(8): 99-100. (in Chinese)
[2]	ZHAI Li, WANG Chengping, HOU Yuhan, et al. Two-level optimal torque distribution for handling stability control of a four hub-motor independent-drive electric vehicle under various adhesion conditions[J]. Proc Inst Mech Eng Part D: J Automob Eng, 2022, 237(2-3): 544-559. doi: 10.1177/09544070221075508 URL
[3]	赵又群, 李宇昊, 邓汇凡, 等. 基于Popov超稳定性的分布式电动汽车稳定性控制[J]. 吉林大学学报 (工学版), 2022, 52(10): 2225-2233.
	ZHAO Youqun, LI Yuhao, DENG Huifan, et al. Stability control of distributed electric vehicle based on Popov hyperstability[J]. J Jilin Univ(Engi Tech Ed), 2022, 52(10): 2225-2233. (in Chinese)
[4]	漆星, 王群京, 陈龙, 等. 前后轴双电机电动汽车转矩分配优化策略[J]. 电机与控制学报, 2020, 24(3): 62-78.
	QI Xing, WANG Qunjing, CHEN Long, et al. Optimization strategies of torque distribution for front and rear dual motor driven electric vehicles[J]. Elect Mach Contr, 2020, 24(3): 62-78. (in Chinese)
[5]	GUO Lie, GE Pingshu, SUN Dachuan. Torque distribution algorithm for stability control of electric vehicle driven by four in-wheel motors under emergency conditions[J]. IEEE Access, 2019, 7: 104737-104748. doi: 10.1109/ACCESS.2019.2931505
[6]	WANG Junnian, GAO Shoulin, WANG Kai, et al. Wheel torque distribution optimization of four-wheel independent-drive electric vehicle for energy efficient driving[J]. Contr Eng Pract, 2021, 110: 1-14.
[7]	WANG Hongbo, SUN Youding, TAN Hongliang, et al. Stability control of in-wheel motor driven vehicle based on extension pattern recognition[J]. Sci Prog, 2020, 103(4): 1-24.
[8]	ZHAO Youqun, DENG Huifan, LI Yong, et al. Coordinated control of stability and economy based on torque distribution of distributed drive electric vehicle[J]. Proc Inst Mech Eng Part D: J Automob Eng, 2019, 234(6): 1792-1806. doi: 10.1177/0954407019880427 URL
[9]	林程, 曹放, 梁晟, 等. 双电机后驱车辆操纵稳定性分层混杂模型预测控制[J]. 机械工程学报, 2019, 55(22): 123-130. doi: 10.3901/JME.2019.22.123
	LIN Cheng, CAO Fang, LIANG Sheng, et al. Yaw stability control of distributed drive electric vehicle based on hierarchical hybrid model predictive control[J]. J Mech Engi, 2019, 55(22): 123-130. (in Chinese)
[10]	张雷, 赵宪华, 王震坡. 四轮轮毂电机独立驱动电动汽车轨迹跟踪与横摆稳定性协调控制研究[J]. 汽车工程, 2022, 42(11): 1513-1521.
	ZHANG Lei, ZHAO Xianhua, WANG Zhenpo. Study on coordinated control of trajectory tracking and yaw stability for autonomous four-wheel-independent-driving electric vehicles[J]. Autom Engineering, 2022, 42(11): 1513-1521. (in Chinese)
[11]	GUO Ningyuan, Lenzo B, ZHANG Xudong, et al. A real-time nonlinear model predictive controller for yaw motion optimization of distributed drive electric vehicles[J]. IEEE Trans Veh Tech, 2020, 69(5): 4935-4946. doi: 10.1109/TVT.25 URL
[12]	ZHANG Houzhong, LIANG Jiasheng, JIANG Haobin, et al. Stability research of distributed drive electric vehicle by adaptive direct yaw moment control[J]. IEEE Access, 2019, 7: 106225-106237. doi: 10.1109/ACCESS.2019.2933016
[13]	Chae M, Hyun Y, Yi K, et al. Dynamic handling characteristics control of an in-wheel-motor driven electric vehicle based on multiple sliding mode control approach[J]. IEEE Access, 2019, 7: 132448-132458. doi: 10.1109/Access.6287639 URL
[14]	ZHAI Li, WANG Chengping, ZHANG Xueying, et al. Handling stability control strategy for four-wheel hub motor-driven vehicle based on adaptive control for road adhesion[J]. IET Intell Transport Syst, 2022, 16: 586-601.
[15]	DING Shihong, LIU Lu, ZHENG Weixing. Sliding mode direct yaw-moment control design for in-wheel electric vehicles[J]. IEEE Trans Ind Electron, 2017, 64(8): 6752-6762. doi: 10.1109/TIE.2017.2682024 URL
[16]	Asiabar A N, Kazemi R. A direct yaw moment controller for a four in-wheel motor drive electric vehicle using adaptive sliding mode control[J]. Proc Inst Mech Eng Pt K: J Multi-Body Dyn, 2019, 233(3): 549-567.
[17]	姚来鹏, 侯保林, 刘曦. 采用摩擦补偿的弹药传输机械臂自适应终端滑模控制[J]. 上海交通大学学报, 2020, 54(2): 144-151.
	YAO Lai Peng, HOU Baolin, LIU Xi. Adaptive terminal sliding mode control of a howitzer shell transfer arm with friction compensation[J]. J Shanghai Jiaotong Univ, 2020, 54(2): 144-151. (in Chinese)
[18]	CHEN Mou, WU Qingxian, CUI Rongxin. Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems[J]. ISA Trans, 2013, 52(2): 198-206. doi: 10.1016/j.isatra.2012.09.009 URL
[19]	WANG Jianmin, WU Yunjie, DONG Xiaomeng. Recursive terminal sliding mode control for hypersonic flight vehicle with sliding mode disturbance observer[J]. Nonlinear Dyn, 2015, 81(3): 1489-1510. doi: 10.1007/s11071-015-2083-4 URL
[20]	WANG Yaoyao, LI Shizhen, WANG Dan, et al. Adaptive time-delay control for cable-driven manipulators with enhanced nonsingular fast terminal sliding mode[J]. IEEE Trans Ind Elect, 2021, 68(3): 2356-2367. doi: 10.1109/TIE.41 URL
[21]	Rangel M A G, Manzanilla A, Suarez A E Z, et al. Adaptive non-singular terminal sliding mode control for an unmanned underwater vehicle: Real-time experiment[J]. Int J Control Autom Syst, 2022, 18(3): 615-628. doi: 10.1007/s12555-019-0674-4
[22]	Pacejka H B, Besselink I J M. Magic formula tyre model with transient properties[J]. Vehi Syst Dyn, 1997, 27: 234-249.
[23]	LIN Jiming, ZOU Teng, ZHANG Feng, et al. Yaw stability research of the distributed drive electric bus by adaptive fuzzy sliding mode control[J]. Energies, 2022, 15(1280): 1-16. doi: 10.3390/en15010001 URL
[24]	YIN Dejun, WANG Junjie, DU Jinjian, et al. A new torque distribution control for four-wheel independent-drive electric vehicles[J]. Actuators, 2021, 10(6): 1-15. doi: 10.3390/act10010001 URL
[25]	李春善. 四轮独立线控电动汽车驱动系统主动容错控制策略研究[D]. 长春: 吉林大学, 2018.
	LI Chunshan. Research on active fault tolerant control strategy for electric drive system of X-by-wire electric vehicle with four wheels independent control[D]. Changchun: Jilin University, 2018. (in Chinese)
[26]	Ono E, Hattori Y, Muragishi Y, et al. Vehicle dynamics integrated control for four-wheel-distributed steering and four-wheel-distributed traction/braking systems[J]. Vehi Syst Dyn, 2006, 44(2): 139-151.
[27]	Markovsky I, Van Huffel S. Overview of total least-squares methods[J]. Sign Process, 87(10): 2283-2302. doi: 10.1016/j.sigpro.2007.04.004 URL
[28]	Nocedal J, Wright S. Numerical Optimization(2nd Edit)[M]. New York: Springer, 2006: 467-478.

侧向力	a₀	a₁	a₂	a₃	a₄	a₅	a₆	a₇	a₈
取值	1.30	-22.1	1 011	1 078	1.82	0.208	0	-0.354	0.707
纵向力	b₀	b₁	b₂	b₃	b₄	b₅	b₆	b₇	b₈
取值	1.65	-21.3	1 144	49.6	226	0.069	-0.006	0.056	0.486

侧向力	a₀	a₁	a₂	a₃	a₄	a₅	a₆	a₇	a₈
取值	1.30	-22.1	1 011	1 078	1.82	0.208	0	-0.354	0.707
纵向力	b₀	b₁	b₂	b₃	b₄	b₅	b₆	b₇	b₈
取值	1.65	-21.3	1 144	49.6	226	0.069	-0.006	0.056	0.486

整车质量, m	1.350 t
绕z轴的转动惯量, I_z	1 343 kg·m²
车轮转动惯量, J_ω	0.6 kg·m²
质心高度, h_g	0.54 m
质心到前轴的距离, a	1.04 m
质心到后轴的距离, b	1.56 m
轴距, l	2.6 m
轮胎有效滚动半径, R_e	29.8 cm
轮距, B_w	1.48 m
轮胎型号	185/65 R15
前轮侧偏刚度, C_f	58.07 kN·rad^-1
后轮侧偏刚度, C_r	58.07 kN·rad^-1

整车质量, m	1.350 t
绕z轴的转动惯量, I_z	1 343 kg·m²
车轮转动惯量, J_ω	0.6 kg·m²
质心高度, h_g	0.54 m
质心到前轴的距离, a	1.04 m
质心到后轴的距离, b	1.56 m
轴距, l	2.6 m
轮胎有效滚动半径, R_e	29.8 cm
轮距, B_w	1.48 m
轮胎型号	185/65 R15
前轮侧偏刚度, C_f	58.07 kN·rad^-1
后轮侧偏刚度, C_r	58.07 kN·rad^-1

r₁_β	5/3	ε_β	1 000
r₂_β	7/5	k_β	100
ξ₁_β	0.5	?	0.5
ξ₂_β	0.5	D_β	0.3

基于NFTSMC的分布式驱动电动汽车稳定性控制

Stability control of distributed drive electric vehicles based on the nonsingular fast terminal sliding mode control (NFTSMC)

RichHTML

PDF

可视化

摘要/Abstract

引用本文

使用本文

图/表 12

参考文献 28

相关文章 2

编辑推荐

Metrics

本文评价

期刊信息

在线期刊

作者中心

审稿中心

联系我们

控制策略	E_max,_β / (?)		E_RMSE,_β / (?)
控制策略	70 km/h	90 km/h	70 km/h	90 km/h
SMC	0.371 2	0.657 6	0.115 3	0.150 6
NFTSMC	0.123 6	0.304 4	0.040 6	0.066 6

[1]	裴晓飞，刘志厅，陈祯福，陈可际，杨波 . 分布式驱动电动汽车的差速转向控制及其适用性[J]. JASE, 2019, 10(4): 423-432.
[2]	赵树恩，张雄，唐俊涛. 重型半挂汽车列车防侧翻分层递阶控制[J]. JASE, 2019, 10(4): 474-482.