基于非合作博弈的四轮独立电动汽车轮毂电机群稳定性裕度与能效优化管理

丁月恒; 王禹棋; 花为; 许德智; 吴中泽

doi:10.16383/j.aas.c250629

基于非合作博弈的四轮独立电动汽车轮毂电机群稳定性裕度与能效优化管理

doi: 10.16383/j.aas.c250629 cstr: 32138.14.j.aas.c250629

丁月恒^{1, 2,},
王禹棋^{1, 2,},
花为^{1, 2,},
许德智^{1, 2,},
吴中泽^{1, 2,}

1.
东南大学电气工程学院南京 210096
2.
电动载运技术教育部工程研究中心南京 210096

基金项目: 江苏省前沿技术研发计划 (BF2025021), 国家自然科学基金 (62222307, U24A20146)资助

详细信息

作者简介:
丁月恒：东南大学电气工程学院助理研究员. 2024年获得英国肯特大学博士学位. 主要研究方向为电动汽车用轮毂电机系统及其控制, 控制理论与应用. E-mail: ingyueheng@seu.edu.cn

王禹棋：东南大学电气工程学院硕士研究生. 2023年获得苏州大学学士学位. 主要研究方向为四轮独立驱动电动汽车的能效优化策略与稳定性控制. E-mail: 220242995@seu.edu.cn

花为：东南大学电气工程学院教授. 2007年获得东南大学博士学位. 主要研究方向为电机驱动系统, 新型永磁电机本体设计与控制. E-mail:huawei1978@seu.edu.cn

许德智：东南大学电气工程学院教授. 2013年获得南京航空航天大学博士学位. 主要研究方向为储能系统, 运动系统与电机控制, 故障诊断与容错技术. 本文通信作者. E-mail: xudezhi@seu.edu.cn

吴中泽：东南大学电气工程学院教授. 2017年获得英国谢菲尔德大学博士学位. 主要研究方向为电动汽车驱动电机系统, 高速电机系统与扁线电机. E-mail: zzwu@seu.edu.cn

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- 被引次数: 0
出版历程
- 收稿日期: 2025-11-13
- 录用日期: 2026-01-20
- 网络出版日期: 2026-03-02

Non-cooperative Game-based Optimization Management of Stability Margin and Energy Efficiency for an In-Wheel Motor Group on Four-wheel Independently Driven Electric Vehicles

DING Yue-Heng^{1, 2
,},
WANG Yu-Qi^{1, 2
,},
HUA Wei^{1, 2
,},
XU De-Zhi^{1, 2
,},
WU Zhong-Ze^{1, 2
,}

1.
School of Electrical Engineering, Southeast University, Nanjing 210096
2.
Engineering Research Center of Electrical Transport Technology, Ministry of Education, Nanjing 210096

Funds: Supported by Jiangsu Provincial Frontier Technology Research and Development Program (BF2025021) and National Natural Science Foundation of China (62222307, U24A20146)

More Information

Author Bio:
DING Yue-Heng　Assistant researcher at the School of Electrical Engineering, Southeast University. He received his Ph.D. degree from University of Kent, United Kingdom in 2024. His research interests include in-wheel motor systems for electric vehicles and their control, control theory and applications

WANG Yu-Qi　Master student at the School of Electrical Engineering, Southeast University. He received his bachelor degree from Soochow University in 2023. His research interests include energy efficiency optimization strategies and stability control for four-wheel independently driven electric vehicles

HUA Wei　Professor at the School of Electrical Engineering, Southeast University. He received his Ph.D. degree from Southeast University in 2007. His research interests include motor drive systems, design and control of novel permanent magnet motors

XU De-Zhi　Professor at the School of Electrical Engineering, Southeast University. He received his Ph.D. degree from Nanjing University of Aeronautics and Astronautics in 2013. His research interests include energy storage systems; motion systems and motor control; fault diagnosis and fault tolerance. Corresponding author of this paper

WU Zhong-Ze　Professor at the School of Electrical Engineering, Southeast University. He received his Ph.D. degree from University of Sheffield, United Kingdom in 2017. His research interests include drive motor system for electric vehicles, high-speed motor systems and hairpin motors

摘要

摘要: 针对四轮独立驱动电动汽车轮毂电机转矩矢量控制中稳定性与经济性相冲突的问题, 提出一种基于稳定裕度博弈与分层优化的协同控制策略. 首先建立车辆动力学模型与高保真能耗模型; 进而设计分层控制器: 上层基于线性二次调节器计算广义横摆力矩, 中层通过模型预测控制在相平面稳定裕度约束下以系统损耗最小为目标优化横摆力矩与分配权重, 下层利用二次规划算法求解最优轮端转矩. 基于~dSPACE~平台的硬件在环仿真结果表明, 在双移线工况下, 所提策略在保证稳定性的同时能耗降低5.7%, 具有优良的综合性能与鲁棒性.
- 四轮独立驱动电动汽车 /
- 轮毂电机群 /
- 稳定性 /
- 能效优化 /
- 博弈论 /
- 转矩矢量分配 /
- 分层控制
Abstract: Aiming at the conflict between stability and economy in torque vectoring control of in-wheel motors for four-wheel independently driven electric vehicles, a coordinated control strategy based on stability margin game and hierarchical optimization is proposed. First, a vehicle dynamics model and a high-fidelity energy consumption model are established. Then, a hierarchical controller is designed: The upper layer calculates the generalized yaw moment based on a linear quadratic regulator, the middle layer employs model predictive control to optimize the yaw moment and distribution weights with the objective of minimizing system losses, subject to stability margin constraints in the phase plane, and the lower layer solves for the optimal wheel torque using a quadratic programming algorithm. Hardware-in-the-loop simulation results on a dSPACE platform show that under double lane-change conditions, the proposed strategy reduces energy consumption by 5.7% while ensuring stability, demonstrating excellent comprehensive performance and robustness.
- four-wheel independently driven electric vehicles /
- in-wheel motor group /
- stability /
- energy efficiency optimization /
- game theory /
- torque vectoring allocation /
- hierarchical control

HTML全文

图 1 四轮独立驱动电动汽车拓扑图

Fig. 1 Topology diagram of four-wheel independently driven electric vehicles

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图 2 车辆稳定性状态模型

Fig. 2 Vehicle stability state model

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图 3 四轮车辆模型结构

Fig. 3 Four-wheel vehicle modeling structure

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图 4 分层博弈控制器框图

Fig. 4 Block diagram of hierarchical game-based controller

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图 5 车辆稳定裕度相平面示意图

Fig. 5 Phase plane diagram of vehicle stability margin

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图 6 博弈权衡函数$ \alpha(\rho) $

Fig. 6 Gamed-based weight function $ \alpha(\rho) $

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图 7 基于dSPACE的硬件在环仿真平台

Fig. 7 dSPACE-based hardware-in-the-loop (HIL) simulation platform

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图 8 双移线工况说明

Fig. 8 Double lane-change maneuver description

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图 9 基于质心侧偏角($ \beta $和$ \beta_d $)的车辆稳定性能对比

Fig. 9 Comparison of vehicle stability performance based on sideslip angle $ \beta $ and $ \beta_d $

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图 10 车辆相平面能效与稳定博弈轨迹

Fig. 10 Vehicle phase-plane trajectory of energy-efficiency and stability gaming

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图 11 汽车驱动系统总能耗对比 (60 km/h)

Fig. 11 Total energy consumption comparison of the vehicle propulsion system (60 km/h)

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图 12 低速下的四轮转矩分配

Fig. 12 Torque distribution for four wheels at low speed

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图 13 低速下的车辆路径跟踪性能

Fig. 13 Vehicle path-tracking performance at low speed

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图 14 基于质心侧偏角($ \beta $和$ \beta_d $)的车辆稳定性能对比

Fig. 14 Comparison of vehicle stability performance based on sideslip angle $ \beta $ and $ \beta_d $

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图 15 车辆相平面能效与稳定博弈轨迹

Fig. 15 Vehicle phase-plane trajectory of energy-efficiency and stability gaming

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图 16 汽车驱动系统总能耗对比 (90 km/h)

Fig. 16 Total energy consumption comparison of the vehicle propulsion system (90 km/h)

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图 17 高速下的四轮转矩分配

Fig. 17 Torque distribution for four wheels at high speed

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图 18 高速下的车辆路径跟踪性能

Fig. 18 Vehicle path-tracking performance at high speed

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