Articles

Intelligent control of in-wheel motors in a vehicle with analytical determination of torque distribution

• 
• 

User Rating:  / 0

PoorBest 

Details

Category: Content №4 2026

Last Updated on 24 August 2026

Published on 30 November -0001

Hits: 1133

Authors:

O. Bazhinov, orcid.org/0000-0002-5755-8553, Kharkiv National Automobile and Highway University, Kharkiv, Ukraine

M. Arpabekov*, orcid.org/0000-0002-7998-2507, L. N. Gumilyov Eurasian National University, Astana, Kazakhstan, e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

I. Taran, orcid.org/0000-0002-3679-2519, Dnipro University of Technology, Dnipro, Ukraine

T. Bazhynova, orcid.org/0000-0003-3003-4028, Kharkiv National Automobile and Highway University, Kharkiv, Ukraine

E. Kykla, orcid.org/0009-0006-8547-2120, Kharkiv National Automobile and Highway University, Kharkiv, Ukraine

* Corresponding author e-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

повний текст / full article

Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu. 2026, (4): 068 - 076

https://doi.org/10.33271/nvngu/2026-4/068

Abstract:

Purpose. To derive a closed-form analytical solution for the optimal distribution of drive torque between the left and right sides of an all-wheel-drive vehicle equipped with in-wheel motors. The proposed solution maximizes the instantaneous efficiency of the wheel propulsion system while accounting for load asymmetry and driving conditions.

Methodology. The study employs analytical methods based on a reduced energy model of the wheel propulsion system, quadratic optimization techniques, and simulation modelling in the MATLAB/Simulink environment to verify the performance of the proposed torque distribution law.

Findings. A closed-form analytical expression was obtained for determining the optimal torque distribution coefficient between the left and right sides of the vehicle. Its application ensures the maximization of the instantaneous efficiency of the wheel propulsion system. It was demonstrated that the optimal torque distribution depends on the normal tyre-road reactions, vehicle geometric parameters, and driving conditions. Simulation results confirmed the effectiveness of the proposed control law under both traction and curvilinear driving conditions.

Originality. For the first time, the problem of torque distribution between the left and right sides of an all-wheel-drive vehicle with independently driven in-wheel motors has been formulated as the problem of maximizing the instantaneous efficiency of the wheel propulsion system. This made it possible to derive a control law suitable for real-time implementation without the need for numerical optimization.

Practical value. The proposed analytical torque distribution law can be integrated into the upper-level control system of all-wheel-drive vehicles equipped with independently driven in-wheel motors. Its implementation improves vehicle energy efficiency without increasing the complexity of the control algorithms or the associated computational burden.

Keywords: in-wheel motor, all-wheel-drive vehicle, vehicle speed, torque, regenerative braking

References.

1. Dizqah, A. M., Lenzo, B., Sorniotti, A., Gruber, P., Fallah, S., & De Smet, J. (2016). A Fast and Parametric Torque Distribution Strategy for Four-Wheel-Drive Energy-Efficient Electric Vehicles. IEEE Transactions on Industrial Electronics, 63(7), 4367-4376. https://doi.org/10.1109/tie.2016.2540584

2. De Filippis, G., Lenzo, B., Sorniotti, A., Gruber, P., & De Nijs, W. (2018). Energy-Efficient Torque-Vectoring Control of Electric Vehicles With Multiple Drivetrains. IEEE Transactions on Vehicular Technology, 67(6), 4702-4715. https://doi.org/10.1109/tvt.2018.2808186

3. Koehler, S., Viehl, A., Bringmann, O., & Rosenstiel, W. (2017). Energy-Efficiency Optimization of Torque Vectoring Control for Battery Electric Vehicles. IEEE Intelligent Transportation Systems Magazine, 9(3), 59-74. https://doi.org/10.1109/mits.2017.2709799

4. Fischer, S., Hermán, B., Sysyn, M., Kurhan, D., & Kocsis Szürke, S. (2025). Quantitative analysis and optimization of energy efficiency in electric multiple units. Facta Universitatis, Series: Mechanical Engineering, 23(2), 351-375. https://doi.org/10.22190/FUME241103001F

5. Chatzikomis, C., Zanchetta, M., Gruber, P., Sorniotti, A., ­Modic, B., Motaln, T., Blagotinsek, L., & Gotovac, G. (2019). An energy-efficient torque-vectoring algorithm for electric vehicles with multiple motors. Mechanical Systems and Signal Processing, 128, 655-673. https://doi.org/10.1016/j.ymssp.2019.03.012

6. Torinsson, J., Jonasson, M., Yang, D., & Jacobson, B. (2020). Energy reduction by power loss minimisation through wheel torque allocation in electric vehicles: a simulation-based approach. Vehicle System Dynamics, 60(5), 1488–1511. https://doi.org/10.1080/00423114.2020.1858121

7. Hu, X., Wang, P., Hu, Y., & Chen, H. (2020). A stability-guaranteed and energy-conserving torque distribution strategy for electric vehicles under extreme conditions. Applied Energy, 259, 114162. https://doi.org/10.1016/j.apenergy.2019.114162

8. Novytskyi, O., Taran, I., & Zhanbirov, Z. (2019). Increasing mine train mass by means of improved efficiency of service braking. E3S Web of Conferences, 123, 01034. https://doi.org/10.1051/e3sconf/201912301034

9. Mangia, A., Lenzo, B., & Sabbioni, E. (2021). An integrated torque-vectoring control framework for electric vehicles featuring multiple handling and energy-efficiency modes selectable by the ­driver. Meccanica, 56(5), 991-1010. https://doi.org/10.1007/s11012-021-01317-3

10.      Wu, S., Li, Y., Guan, Y., Liu, T., & Che, C. (2023). Distribution Method of Automotive Torque for Hub Motor Considering Energy Consumption Optimization. International Journal of Automotive Technology, 24(3), 913-928. https://doi.org/10.1007/s12239-023-0075-9

11.      Xu, T., Zhao, Y., Deng, H., Guo, S., Li, D., & Lin, F. (2023). Integrated optimal control of distributed in-wheel motor drive electric vehicle in consideration of the stability and economy. Energy, 282, 128990. https://doi.org/10.1016/j.energy.2023.128990

12.      Wang, J., Lv, S., Sun, N., Gao, S., Sun, W., & Zhou, Z. (2021). Torque Vectoring Control of RWID Electric Vehicle for Reducing Driving-Wheel Slippage Energy Dissipation in Cornering. Energies, 14(23), 8143. https://doi.org/10.3390/en14238143

13.      Liang, Y., Zhao, W., Wu, J., Xu, K., Zhou, X., Luan, Z., & Wang, C. (2025). Energy-efficient driving for distributed electric vehicles considering wheel loss energy: A distributed strategy based on multi-agent architecture. Applied Energy, 384, 125462. https://doi.org/10.1016/j.apenergy.2025.125462

14.      Kou, L., Sysyn, M., Liu, J., Fischer, S., Nabochenko, O., & He, W. (2023). Prediction system of rolling contact fatigue on crossing nose based on support vector regression. Measurement, 210, 112579. https://doi.org/10.1016/j.measurement.2023.112579

15.      Klein, D., Mandl, P., Plöchl, M., Klinger, F., & Edelmann, J. (2026). Power optimal torque distribution for overactuated electric vehicles: analysis and experimental validation. Automotive and Engine Technology, 11(1). https://doi.org/10.1007/s41104-025-00164-8

16.      Hua, M., Chen, G., Zhang, B., & Huang, Y. (2018). A hierarchical energy efficiency optimization control strategy for distributed drive electric vehicles. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 233(3), 605-621. https://doi.org/10.1177/0954407017751788

17.      Chen, H., Du, P., Wang, Y., Jin, D., & Lian, X. (2020). Dynamic energy-efficient torque allocation algorithm for in-wheel motor-driven vehicle. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 234(7), 1815-1825. https://doi.org/10.1177/0954407019899205

18.      Taran, I. A., & Klimenko, I. Yu. (2014). Transfer ratio of double-split transmissions in case of planetary gear input. Naukovyi Visnyk Natsionalnoho Hirnychoho Universytetu, (6), 60-66.

19.      Szántó, N., Fischer, S., & Monek, G. D. (2025). A Novel Method for Simulation Model Generation of Production Systems Using PLC Sensor and Actuator State Monitoring. Journal of Sensor and Actuator Networks, 14(3), 55. https://doi.org/10.3390/jsan14030055

20.      He, S., Fan, X., Wang, Q., Chen, X., & Zhu, S. (2022). Review on Torque Distribution Scheme of Four-Wheel In-Wheel Motor Electric Vehicle. Machines, 10(8), 619. https://doi.org/10.3390/machines10080619

21.      Zhao, K., Fan, X., Huang, Z., Yu, X., Wang, L., & Peng, J. (2024). A review of drive torque distribution control for distributed drive electric vehicles. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 239(12), 5291-5315. https://doi.org/10.1177/09544070241286016

22.      Wang, F., Feng, Y., Tan, F., Liang, J., Wang, D., Jang, S., & Li, Z. (2025). Torque allocation strategy for distributed-drive electric vehicles with synergistic optimization of energy saving and safety. Energy, 360, 3, 100022. https://doi.org/10.1016/j.energ.2025.100022

23.      Li, W., Xu, H., Liu, X., Wang, Y., Zhu, Y., Lin, X., Wang, Z., & Zhang, Y. (2024). Regenerative braking control strategy for pure electric vehicles based on fuzzy neural network. Ain Shams Engineering Journal, 15(2), 102430. https://doi.org/10.1016/j.asej.2023.102430

24.      Bazhinov, A., Bazhinova, T., Podrigalo, M., Kholodov, M., Haiek, Y., & Sierikova, I. (2022). Dynamics Hybrid Vehicle Driven with Electric Motor Driving Wheels from Batteries. SAE Technical Paper Series, 1. https://doi.org/10.4271/2022-01-0667

25.      Gu, J., Ouyang, M., Lu, D., Li, J., & Lu, L. (2013). Energy efficiency optimization of electric vehicle driven by in-wheel motors. International Journal of Automotive Technology, 14(5), 763-772. https://doi.org/10.1007/s12239-013-0084-1

26.      Puma-Benavides, D. S., Cevallos-Carvajal, A. S., Masaquiza-Yanzapanta, A. G., Quinga-Morales, M. I., Moreno-Pallares, R. R., Usca-Gomez, H. G., & Murillo, F. A. (2024). Comparative Analysis of Energy Consumption between Electric Vehicles and Combustion Engine Vehicles in High-Altitude Urban Traffic. World Electric Vehicle Journal, 15(8), 355. https://doi.org/10.3390/wevj15080355

27.      Monastyrskyi, Y., Taran, I., Kokayev, U., & Sistuk, V. (2025). Assessing the performance efficiency of haul trucks and diesel-trolley trucks when changing their technological states and parameters of traffic routes. Mining of Mineral Deposits, 19(2), 47-55. https://doi.org/10.33271/mining19.02.047

• < Prev
• Next >