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Sideslip Angle Control of Electronic-four-wheel Drive Vehicle Using Backstepping Controller

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Abstract

This paper presents our investigation into creating a sideslip angle control system for an electronic-four-wheel drive (e-4WD) vehicle. In keeping with the growing demand for fun-to-drive vehicles, our e-4WD vehicle, which is equipped with in-wheel motor systems (IWMs) on the front wheels and an active differential on the rear axle, is mainly aimed at improving cornering performance. The vehicle system in this paper is based on a bicycle model, which has a recursive structure in terms of the sideslip angle and yaw moment, a backstepping controller is utilized as they have proven to be effective for this kind of structure. The backstepping controller generates the desired yaw moment while its feed-forward control term actively reflects the sideslip angle reference, improving both the convergence rate and responsiveness of control actions. Then, the desired yaw moment is distributed through the IWM torques on the front wheels and shaft torques on the rear axle. A Daisy-chaining method is utilized for distribution of the IWM torques while taking into consideration practical issues. Using the simulation software CarSim, it was found that some cornering performance evaluation factors are improved in this proposed controller when compared to conventional feedback controllers.

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Abbreviations

β :

vehicle sideslip angle, deg

α f :

tire slip angle of front axle, deg

α r :

tire slip angle of rear axle, deg

C f :

tire cornering stiffness of front axle, N/rad

C r :

tire cornering stiffness of rear axle, N/rad

r :

vehicle yaw rate, deg/s

δ f :

front steering angle, deg

v x :

vehicle longitudinal velocity, km/h

I z :

vehicle yaw moment of inertia, kg·m2

M z :

yaw moment, N·m

R e :

tire effective rolling radius, mm

t :

track width, mm

h :

height of vehicle center of gravity (CG), mm

m :

total mass of vehicle, kg

l f :

distance between the CG and the front axle, mm

l r :

distance between the CG and the rear axle, mm Tm: in-wheel motor (IWM) torque, N·m

T shaft :

shaft torque of active differential, N·m

T cl :

maximum clutch torque of active differential, N·m

w :

wheel speed, km/h

a x :

vehicle longitudinal acceleration, g

a y :

vehicle lateral acceleration, g

q :

distribution ratio of active differential, -

μ :

tire-road friction coefficient

FL, FR, RL, RR:

front left, front right, rear left, rear right f, r: front and rear axles

References

  • Buffington, J. M. and Enns, D. F. (1996). Lyapunov stability analysis of daisy chain control allocation. J. Guidance, Control, and Dynamics 50, 3, 1226–1230.

    Article  Google Scholar 

  • Chen, Y., Li, X., Wiet, C. and Wang, J. (2013). Energy management and driving strategy for in-wheel motor electric ground vehicles with terrain profile preview. IEEE Trans. Industrial Informatics 50, 3, 1938–1947.

    Article  Google Scholar 

  • De Novellis, L., Sorniotti, A. and Gruber, P. (2013). Wheel torque distribution criteria for electric vehicles with torque-vectoring differentials. IEEE Trans. Vehicular Technology 50, 3, 1593–1602.

    Google Scholar 

  • Fallah, S., Khajepour, A., Fidan, B., Chen, S. K. and Litkouhi, B. (2012). Vehicle optimal torque vectoring using state-derivative feedback and linear matrix inequality. IEEE Trans. Vehicular Technology 50, 3, 1540–1552.

    Google Scholar 

  • Goggia, T., Sorniotti, A., De Novellis, L., Ferrara, A., Gruber, P., Theunissen, J., Steenbeke, D., Knauder, B. and Zehetner, J. (2014). Integral sliding mode for the torque-vectoring control of fully electric vehicles: Theoretical design and experimental assessment. IEEE Trans. Vehicular Technology 50, 3, 1701–1715.

    Google Scholar 

  • Guo, N., Zhang, X., Zou, Y., Lenzo, B., Zhang, T. and Göhlich, D. (2020). A fast model predictive control allocation of distributed drive electric vehicles for tire slip energy saving with stability constraints. Control Engineering Practice, 102, 104554.

    Article  Google Scholar 

  • Han, K., Park, G., Sankar, G. S., Nam, K. and Choi, S. B. (2020). Model predictive control framework for improving vehicle cornering performance using handling characteristics. IEEE Trans. Intelligent Transportation Systems 50, 3, 3014–3024.

    Google Scholar 

  • Kasinathan, D., Kasaiezadeh, A., Wong, A., Khajepour, A., Chen, S. K. and Litkouhi, B. (2015). An optimal torque vectoring control for vehicle applications via real-time constraints. IEEE Trans. Vehicular Technology 50, 3, 4368–4378.

    Google Scholar 

  • Khalil H. K. and Grizzle J. (1996). Nonlinear Systems. 3rd edn. Prentice Hall. Hoboken, New Jersey, USA.

    Google Scholar 

  • Khosravani, S., Kasaiezadeh, A., Khajepour, A., Fidan, B., Chen, S. and Litkouhi, B. (2014). Torque-vectoring-based vehicle control robust to driver uncertainties. IEEE Trans. Vehicular Technology 50, 3, 3359–3367.

    Google Scholar 

  • Lu, Q., Gentile, P., Tota, A., Sorniotti, A., Gruber, P., Costamagna, F. and De Smet, J. (2016). Enhancing vehicle cornering limit through sideslip and yaw rate control. Mechanical System and Signal Processing, 75, 455–472.

    Article  Google Scholar 

  • Murata, S. (2012). Innovation by in-wheel-motor drive unit. Vehicle System Dynamics 50, 3, 807–830.

    Article  Google Scholar 

  • Nam, K., Fujimoto, H. and Hori, Y. (2012). Lateral stability control of in-wheel-motor-driven electric vehicles based on sideslip angle estimation using lateral tire force sensors. IEEE Trans. Vehicular Technology 50, 3, 1972–1985.

    Google Scholar 

  • Pacejka, H. (2005). Tire and Vehicle Dynamics. Elsevier. Oxford, UK.

    Google Scholar 

  • Park, G. and Choi, S. B. (2019). Development of a torque vectoring system in hybrid 4WD vehicles to improve vehicle safety and agility. American Control Conf (ACC), Philadelphia, Pennsylvania, USA.

  • Park, G., Choi, S. B., Hyun, D. and Lee, J. (2018). Integrated observer approach using in-vehicle sensors and GPS for vehicle state estimation. Mechatronics, 50, 134–147.

    Article  Google Scholar 

  • Park, G., Han, K., Nam, K., Kim, H. and Choi, S. B. (2020). Torque vectoring algorithm of electronic-four-wheel drive vehicles for enhancement of cornering performance. IEEE Trans. Vehicular Technology 50, 3, 3668–3679.

    Article  Google Scholar 

  • Rajamani, R. (2006). Vehicle Dynamics and Control. Springer. New York, NY, USA.

    MATH  Google Scholar 

  • Voser, C., Hindiyeh, R. Y. and Gerdes, J. C. (2010). Analysis and control of high sideslip manoeuvres. Vehicle System Dynamics 48, S1, 317–336.

    Article  Google Scholar 

  • Yin, D., Wang, J., Du, J., Chen, G. and Hu, J. S. (2021). A new torque distribution control for four-wheel independent-drive electric vehicles. Actuators 50, 3, 122.

    Article  Google Scholar 

  • Yoon, J. H., Li, S. E. and Ahn, C. (2016). Estimation of vehicle sideslip angle and tire-road friction coefficient based on magnetometer with GPS. Int. J. Automotive Technology 50, 3, 427–435.

    Article  Google Scholar 

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Acknowledgement

This research was supported by the 2021 Research Fund of University of Ulsan.

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  1. School of Mechanical Engineering, University of Ulsan, Ulsan, 44610, Korea

    Giseo Park

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Park, G. Sideslip Angle Control of Electronic-four-wheel Drive Vehicle Using Backstepping Controller. Int.J Automot. Technol. 23, 729–739 (2022). https://doi.org/10.1007/s12239-022-0066-2

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