Torque distribution for distributed drive of three-module virtual track trains
Article Text (Baidu Translation)
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摘要: 为优化分布式驱动虚拟轨道胶轮列车的稳定性，结合列车动力分配特性构建了驱动力分配模型，该分配模型先进行总驱动力模块间分配，再实现模块中车轮间驱动力分配；一次分配根据加速度一致原则将总驱动力按比例分配给每模块车辆；二次分配则是利用分层控制方法进行各模块车辆单元中4个车轮动力分配，上层期望横摆力矩控制器输出车辆在运行时该模块的期望横摆力矩和总驱动力，下层设计稳定性目标函数，利用二次规划法以驱动力不超过路面附着力为不等式约束、以四轮驱动力之和等于单车总驱动力以及四轮驱动横摆力矩之和等于车辆期望横摆力矩为等式约束求解目标函数，根据求解结果得到了各车轮在运行时所需驱动力矩；通过建立三模块虚拟轨道列车动力学模型，搭建联合仿真平台，验证该策略的可行性，对比分析了该策略与驱动力矩平均分配的分配情况。研究结果表明：所建立的驱动力矩分配模型能有效实现驱动力矩的分配，首次分配前铰接点纵向、横向铰接力分别为6.4 kN和7.7 kN，相较第2个铰接点的铰接力偏大，表明该分配策略对车间铰接系统的力学平衡无影响；曲线行驶状态下，靠近曲线侧车轮分配到的驱动力矩高于远离曲线侧车轮分配到的驱动力矩，首车、中间车、尾车在曲线内、外侧驱动力矩差值依次相校于内侧驱动力矩增加了6.6%、16.6%和24.9%，说明尾车有足够的附加横摆力矩通过曲线，更易于通过曲线；对比驱动力矩平均分配，该策略可在弯道处实现内外车轮转矩差，保证附加的横摆力矩通过弯道。该策略为多轴铰接型的驱动力矩分配研究提供新的研究思路，并为虚拟轨道列车向更高运能、更长编组方向发展提供理论支撑。Abstract: To optimize the stability of distributed-drive virtual rail rubber-tired trains, a driving force distribution model was constructed based on the train's power distribution characteristics. This distribution model first allocated the total driving force among the modules and then distributed the driving force among the wheels within each module. The first allocation distributed the total driving force proportionally to each module vehicle according to the acceleration consistency principle. The second allocation used a hierarchical control method to distribute the driving force among the four wheels of each vehicle unit within each module. The upper-layer expected yaw moment controller output the expected yaw moment and total driving force of the module during vehicle operation. The lower layer designed a stability objective function and used quadratic programming method to solve the objective function with the inequality constraint that the driving force did not exceed the road surface adhesion, as well as the equality constraints that the sum of the driving forces of the four wheels was equal to the total driving force of a single vehicle, and the sum of the driving yaw moments of the four wheels was equal to the expected yaw moment of the vehicle. The driving torque required by each wheel during vehicle operation was obtained based on the solution results. By establishing a dynamic model of a three-module virtual rail train and building a joint simulation platform, the feasibility of this strategy was verified, and a comparative analysis was conducted on the distribution performance between this strategy and the average driving torque distribution method. The research results show that the established driving torque distribution model can effectively achieve the distribution of driving torque. Before the first allocation, the longitudinal and lateral hinge forces at the hinge point are 6.4 kN and 7.7 kN, respectively, which are larger than those at the second hinge point, indicating that this distribution strategy has no effect on the mechanical balance of the inter-vehicle hinge system. During curve driving, the driving torques allocated to the wheels on the curve side is higher than that allocated to the wheels on the outer side of the curve. The ratio of the driving torque between the inner and outer sides of the curve for the head car, middle car, and tail car is 6.6%, 16.6%, and 24.9%, respectively, indicating that the tail car has sufficient additional yaw moment to pass through the curve and is easier to pass through the curve. Compared with the average driving torque distribution method, this strategy can achieve the torque difference between the inner and outer wheels at the curve, ensuring additional yaw moment to pass through the curve. This strategy provides a new research idea for the study of driving torque distribution in multi-axle articulated vehicles and offers theoretical support for the development of virtual rail trains towards higher transportation capacity and longer marshalling.
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图 1 车辆稳定性导向多模块转矩优化分配控制流程
Figure 1. Flow of multi-module torque optimization and distribution control strategy oriented to vehicle stability
图 4 基于模糊逻辑的期望横摆力矩动态调节控制器
Figure 4. Dynamic regulating controller for desired yaw moment based on fuzzy logic
图 11 平均分配策略时首车驱动力矩-时间历程曲线
Figure 11. Driving torque-time curves of lead vehicle under equal distribution strategy
图 12 最优分配策略时各车的驱动力矩-时间曲线
Figure 12. Driving torque-time curves of each vehicle under optimal distribution strategy
表 1 模糊控制器的输入与输出模糊论域
Table 1. Input and output fuzzy universe of fuzzy controller
横摆角速度误差 质心侧偏角误差 期望横摆力矩 NB NB NB NS NS NM ZE ZE NS PS PS ZE PB PB PS PM PB 
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表 2 横摆角速度误差的模糊隶属度函数坐标点
Table 2. Coordinate points of fuzzy membership function for lateral angular velocity error
子集 点1 点2 点3 点4 点5 NB (-1, 1) (-1, 1) (-0.8, 1) (-0.2, 0) (1, 0) NS (-1, 0) (-0.5, 0) (-0.25, 1) (0, 0) (1, 0) ZE (-1, 0) (-0.2, 0) (0, 1) (0.2, 0) (1, 0) PS (-1, 0) (0, 0) (0.25, 1) (0.5, 0) (1, 0) PB (-1, 0) (0.2, 0) (0.8, 1) (1, 1) (1, 1)
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表 3 质心侧偏角误差的模糊隶属度函数坐标点
Table 3. Coordinate point of fuzzy membership function of centroid lateral deviation angle error
子集 点1 点2 点3 点4 点5 NB (-1, 1) (-1, 1) (-0.8, 1) (-0.2, 0) (1, 0) NS (-1, 0) (-0.7, 0) (-0.3, 1) (0, 0) (1, 0) ZE (-1, 0) (-0.2, 0) (0, 1) (0.2, 0) (1, 0) PS (-1, 0) (0, 0) (0.3, 1) (0.7, 0) (1, 0) PB (-1, 0) (0.2, 0) (0.8, 1) (1, 1) (1, 1)
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表 4 期望横摆力矩误差的模糊隶属度函数坐标点
Table 4. Coordinate point of fuzzy membership function of expected yaw moment error
子集 点1 点2 点3 点4 点5 NB (-1, 1) (-1, 1) (-0.75, 1) (-0.5, 0) (1, 0) NM (-1, 0) (-0.8, 0) (-0.5, 1) (-0.25, 0) (1, 0) NS (-1, 0) (-0.5, 0) (-0.1, 1) (0, 0) (1, 0) ZE (-1, 0) (-0.1, 0) (0, 1) (0.1, 0) (1, 0) PS (-1, 0) (0, 0) (0.1, 1) (0.5, 0) (1, 0) PM (-1, 0) (0.25, 0) (0.5, 1) (0.75, 0) (1, 0) PB (-1, 0) (0.2, 0) (0.8, 1) (1, 1) (1, 1)
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表 5 期望横摆力矩控制器模糊控制规则推理
Table 5. Inference of fuzzy control rules for expected yaw moment controller
参数 eβ(NB) eβ(NS) eβ(ZE) eβ(PS) eβ(PB) eω(NB) NB NB NB NM NM eω(NS) NB NM NM NS NS eω(ZE) NS NS ZE PS PS eω(PS) PS PS PM PM PB eω(PB) PM PM PB PB PB
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表 6 虚拟轨道列车参数
Table 6. Virtual rail train parameters
参数 数值 首/尾车质量m0/t 10.0 中间车质量m1/t 9.6 质心高度hg/m 0.45 质心到前轴的距离a/m 2.7 质心到后轴的距离b/m 2.7 轮距W/m 2.2 轴距L/m 5.4 车轮半径R/m 0.496 前轮轮胎侧偏刚度Kf/(kN·rad-1) -75 后轮轮胎侧偏刚度Kr/(kN·rad-1) -75 车轮纵向刚度Kc/(MN·m-1) 6.9
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[1] 陆海英, 丁铁成, 杨岗. 智能轨道列车综述[J]. 电子世界, 2021(3): 166-167.LU Hai-ying, DING Tie-cheng, YANG Gang. Summary of intelligent track trains[J]. Electronics World, 2021(3): 166-167. [2] 张弛, 朱涛, 张卫华, 等. 虚拟轨道车辆关键技术研究现状与挑战[J]. 铁道车辆, 2024, 62(5): 1-9.ZHANG Chi, ZHU Tao, ZHANG Wei-hua, et al. Research status and challenges of key technologies of virtual rail vehicles[J]. Rolling Stock, 2024, 62(5): 1-9. [3] 任利惠, 李稳, 冷涵, 等. 轮胎式轨道交通车辆动力学研究现状与挑战[J]. 交通运输工程学报, 2021, 21(6): 8-30. doi: 10.19818/j.cnki.1671-1637.2021.06.002REN Li-hui, LI Wen, LENG Han, et al. Research on dynamics of rail transit vehicle with tire running gears: State-of-arts and challenges[J]. Journal of Traffic and Transportation Engineering, 2021, 21(6): 8-30. doi: 10.19818/j.cnki.1671-1637.2021.06.002 [4] 崔涛, 王淇, 刘学刚, 等. 虚拟轨道列车多轴协同预瞄循迹控制方法[J]. 北京交通大学学报, 2022, 46(1): 139-146.CUI Tao, WANG Qi, LIU Xue-gang, et al. Multi-axle coordination-based pre-targeting path-tracking control method for virtual railway vehicles[J]. Journal of Beijing Jiaotong University, 2022, 46(1): 139-146. [5] 李中奇, 衷玲玉, 杨辉. 虚拟编组列车的分布式协同预测控制[J]. 交通运输工程学报, 2024, 24(5): 362-378. doi: 10.19818/j.cnki.1671-1637.2024.05.023LI Zhong-qi, ZHONG Ling-yu, YANG Hui. Distributed cooperative predictive control of virtual coupled trains[J]. Journal of Traffic and Transportation Engineering, 2024, 24(5): 362-378. doi: 10.19818/j.cnki.1671-1637.2024.05.023 [6] 张众华, 杨蔡进, 张卫华. 虚拟轨道列车超螺旋滑模自适应导向控制[J]. 交通运输工程学报, 2023, 23(5): 163-182. doi: 10.19818/j.cnki.1671-1637.2023.05.011ZHANG Zhong-hua, YANG Cai-jin, ZHANG Wei-hua. Adaptive guidance control of super-twisting sliding mode for virtual track train[J]. Journal of Traffic and Transportation Engineering, 2023, 23(5): 163-182. doi: 10.19818/j.cnki.1671-1637.2023.05.011 [7] 胡云卿, 冯江华, 龙腾, 等. 智轨电车多源环境感知系统[J]. 控制与信息技术, 2020(1): 13-18, 26.HU Yun-qing, FENG Jiang-hua, LONG Teng, et al. Multi-source environment perception system for autonomous-rail rapid tram[J]. Control and Information Technology, 2020(1): 13-18, 26. [8] 石阳阳, 刘光勇, 吴金勇. 智能轨道快运系统地面防护及路口优先系统设计[J]. 控制与信息技术, 2022(3): 112-116.SHI Yang-yang, LIU Guang-yong, WU Jin-yong. Design of the field protection and signal priority at intersection system for autonomous-rail rapid transit[J]. Control and Information Technology, 2022(3): 112-116. [9] 吴梦阳. 电动智轨列车纵向速度规划研究[D]. 南京: 东南大学, 2021.WU Meng-yang. Research on the velocity trajectory planning of the autonomous-rail rapid tram[D]. Nanjing: Southeast University, 2021. [10] 宋强, 王冠峰, 商赫, 等. 基于多参数控制的分布式驱动电动汽车操纵稳定性控制策略研究[J]. 汽车工程, 2023, 45(11): 2104-2112, 2138.SONG Qiang, WANG Guan-feng, SHANG He, et al. Research on handling stability control strategy for distributed drive electric vehicle based on multi-parameter control[J]. Automotive Engineering, 2023, 45(11): 2104-2112, 2138. [11] XU T, ZHAO Y Q, DENG H F, et al. Integrated optimal control of distributed in-wheel motor drive electric vehicle in consideration of the stability and economy[J]. Energy, 2023, 282: 128990. doi: 10.1016/j.energy.2023.128990 [12] 刘晓童, 赵红, 路来伟, 等. 分布式驱动电动汽车车轮转矩分配控制策略[J]. 内燃机与动力装置, 2023, 40(2): 50-55.LIU Xiao-tong, ZHAO Hong, LU Lai-wei, et al. Control strategy of wheel torque distribution for distributed drive electric vehicle[J]. Internal Combustion Engine & Powerplant, 2023, 40(2): 50-55. [13] 曲大义, 李奥迪, 张智, 等. 多车响应的网联自动驾驶纵横向协同控制方法[J]. 交通运输工程学报, 2025, 25(4): 281-295. doi: 10.19818/j.cnki.1671-1637.2025.04.020QU Da-yi, LI Ao-di, ZHANG Zhi, et al. A longitudinal and lateral cooperative control method for connected autonomous vehicles with multi-vehicle response[J]. Journal of Traffic and Transportation Engineering, 2025, 25(4): 281-295. doi: 10.19818/j.cnki.1671-1637.2025.04.020 [14] TENG F, WANG J N, JIN L Q, et al. Cooperative control strategy of trajectory tracking and driving stability for distributed-drive vehicles under extreme conditions[J]. Control Engineering Practice, 2024, 147: 105905. doi: 10.1016/j.conengprac.2024.105905 [15] LI L Q, WANG H L, PI D W, et al. Research on torque distribution control of high-performance distributed drive multi-axle special vehicle[C]//IEEE. 2022 6th CAA International Conference on Vehicular Control and Intelligence (CVCI). New York: IEEE, 2022: 1-8. [16] 李军, 唐爽, 黄志祥, 等. 融合稳定性的高速无人驾驶车辆纵横向协调控制方法[J]. 交通运输工程学报, 2020, 20(2): 205-218. doi: 10.19818/j.cnki.1671-1637.2020.02.017LI Jun, TANG Shuang, HUANG Zhi-xiang, et al. A longitudinal and lateral coordinated control method for high-speed autonomous vehicles incorporating stability[J]. Journal of Traffic and Transportation Engineering, 2020, 20(2): 205-218. doi: 10.19818/j.cnki.1671-1637.2020.02.017 [17] KIM D H, KIM C J, KIM S H, et al. Development of adaptive direct yaw-moment control method for electric vehicle based on identification of yaw-rate model[C]//IEEE. 2011 IEEE Intelligent Vehicles Symposium (Ⅳ). New York: IEEE, 2011: 1098-1103. [18] 左昊, 葛平淑, 王阳, 等. 分布式驱动独立转向电动汽车四轮转向与直接横摆力矩集成控制研究[J]. 重庆理工大学学报(自然科学), 2025, 39(1): 12-18.ZUO Hao, GE Ping-shu, WANG Yang, et al. Research on four-wheel steering and direct transverse torque integration control for distributed-drive independent-steering electric vehicles[J]. Journal of Chongqing University of Technology (Natural Science), 2025, 39(1): 12-18. [19] 田泽玺. 分布式驱动电动汽车稳定性控制策略研究[D]. 长春: 吉林大学, 2023.TIAN Ze-xi. Research on stability control strategy of distributed drive electric vehicles[D]. Changchun: Jilin University, 2023. [20] WEI H Q, ZHANG N, LIANG J, et al. Deep reinforcement learning based direct torque control strategy for distributed drive electric vehicles considering active safety and energy saving performance[J]. Energy, 2022, 238: 121725. doi: 10.1016/j.energy.2021.121725 [21] MEDINA A, BISTUE G, RUBIO A. Comparison of typical controllers for direct yaw moment control applied on an electric race car[J]. Vehicles, 2021, 3(1): 127-144. doi: 10.3390/vehicles3010008 [22] 户燕会, 任燕, 户东亮, 等. 电驱铰接车横摆贝叶斯滤波模糊控制及状态估计[J]. 机械设计与制造, 2025(4): 32-35.HU Yan-hui, REN Yan, HU Dong-liang, et al. Fuzzy yaw control and state estimation of electric drive articulated vehicle based on Bayesian filtering[J]. Machinery Design & Manufacture, 2025(4): 32-35. [23] 王文伟, 赵一凡, 张伟, 等. 多轴轮边驱动铰接客车的横摆稳定性控制策略[J]. 机械工程学报, 2020, 56(14): 161-172.WANG Wen-wei, ZHAO Yi-fan, ZHANG Wei, et al. Yaw stability control strategy of multi-wheel independent electric articulated bus[J]. Journal of Mechanical Engineering, 2020, 56(14): 161-172. [24] KONG X X, DENG Z W, GAO W, et al. Lateral stability control of distributed electric-drive articulated heavy vehicles[J]. International Journal of Vehicle Performance, 2023, 9(2): 184. doi: 10.1504/IJVP.2023.130050 [25] 任志勇, 石琴, 赵远, 等. 矿用双电机双轴驱动铰接车辆转矩协调控制[J]. 工程科学与技术, 2021, 53(3): 173-179.REN Zhi-yong, SHI Qin, ZHAO Yuan, et al. Torque coordinated control for mine articulated vehicles driven by twin motors and twin shafts[J]. Advanced Engineering Sciences, 2021, 53(3): 173-179. [26] RINI G, MAZZILLI V, BOTTIGLIONE F, et al. On nonlinear model predictive vehicle dynamics control for multi-actuated car-semitrailer configurations[J]. IEEE Access, 2024, 12: 165928-165947. doi: 10.1109/ACCESS.2024.3473303 [27] GAO W, LIAO Y, DENG Z W, et al. Study on lateral stability of distributed drive electric tractor semi-trailers under low adhesion road conditions[J]. Transactions of the Canadian Society for Mechanical Engineering, 2024, 48(4): 592-604. doi: 10.1139/tcsme-2023-0220 [28] 余志生. 汽车理论[M]. 6版. 北京: 机械工业出版社, 2019.YU Zhi-sheng. Automobile theory[M]. 6th ed. Beijing: China Machine Press, 2019. [29] 诸静. 模糊控制理论与系统原理[M]. 北京: 机械工业出版社, 2005.ZHU Jing. Fuzzy control theory and system principle[M]. Beijing: China Machine Press, 2005. [30] BOYD S, VANDENBERGHE L. Convex optimization[M]. Cambridge: Cambridge University Press, 2004. [31] 田秋艳. 一种双横臂式独立悬架转向传动系统的设计[J]. 重型汽车, 2021(1): 21-23.TIAN Qiu-yan. Design of a double wishbone independent suspension steering transmission system[J]. Heavy Truck, 2021(1): 21-23. [32] PACEJKA H B, BESSELINK I J M. Magic formula tyre model with transient properties[J]. Vehicle System Dynamics, 1997, 27(S1): 234-249. [33] 田端洋. 多轴轮毂电机驱动汽车转向行驶转矩优化控制[D]. 长春: 吉林大学, 2019.TIAN Duan-yang. Optimal torque control for steering of multi-axle vehicle with in-wheel motors[D]. Changchun: Jilin University, 2019. -
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