Vehicle Dynamic Control for In-Wheel Electric Vehicles Via Temperature Consideration of Braking Systems

  • Jinhyun Park
  • Minho Kwon
  • Gwangil Du
  • Jeewook Huh
  • Sung-Ho Hwang


−Vehicle dynamic control (VDC) systems play an important role with regard to vehicle stability and safety when turning. VDC systems prevent vehicles from spinning or slipping when cornering sharply by controlling vehicle yaw moment, which is generated by braking forces. Thus, it is important to control braking forces depending on the driving conditions of the vehicle. The required yaw moment to stabilize a vehicle is calculated through optimal control and a combination of braking forces used to generate the calculated yaw moment. However, braking forces can change due to frictional coefficients being affected by variations in temperature. This can cause vehicles to experience stability problems due an improper yaw moment being applied to the vehicle. In this paper, a brake temperature estimator based on the finite different method (FDM) was proposed with a friction coefficient estimator in order to solve this problem. The developed braking characteristic estimation model was used to develop a VDC cooperative control algorithm using hydraulic braking and the regenerative braking of an in-wheel motor. Performance simulations of the developed cooperative control algorithm were performed through cosimulation with MATLAB/Simulink and CarSim. From the simulation results, it was verified that vehicle stability was ensured despite any changes in the braking characteristics due to brake temperatures.

Key words

In-wheel electric vehicle Vehicle dynamic control Friction braking system In-wheel motor 



vehicle velocities


vehicle longitudinal velocities


vehicle lateral velocities


vehicle yaw rate


vehicle sideslip angle

νf, νr

front and rear tire velocities, respectively

δf, δr

front and rear steering angles, respectively

αf, αr

front and rear tire slip angles, respectively

Fyf, Fyr

front and rear lateral tire forces, respectively

a, b

longitudinal distances from the C.G to the front and rear tire, respectively


tire tread


vehicle yaw moment of inertia


control yaw moment


cornering stiffness values of the front tires


cornering stiffness values of the rear tires


understeer coefficient


friction heat


braking torque


wheel velocity


disk friction heat


pad friction heat


heat distribution factor

ρd, ρp

disk and pad density, respectively

cd, cp

disk and pad specific heat, respectively

kd, kp

disk and pad thermal conductivity, respectively

Ad, Ap

pad and disk area, respectively


Fourier number


convective heat transfer coefficient


Biot number


estimated braking force


estimated friction coefficient


estimated pad temperature


disk effective radius


wheel radius


normal force applied to the disk


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Balotin, J. G., Neis, P. D. and Ferreira, N. F. (2010). Analysis of the influence of temperature on the friction coefficient of friction materials. ABCM Symp. Series in Mechatronics, 4, 898–906.Google Scholar
  2. Boada, B. L., Boada, M. J. L. and Díaz, V. (2005). Fuzzylogic applied to yaw moment control for vehicle stability. Vehicle System Dynamics: Int. J. Vehicle Mechanics and Mobility 43, 10, 753–770.CrossRefGoogle Scholar
  3. Esmailzadeh, E., Goodarzi, A. and Vossoughi, G. R. (2003). Optimal yaw moment control law for improved vehicle handling. Mechatronics 13, 7, 659–675.CrossRefGoogle Scholar
  4. Franklin, G. F., Powell, J. D. and Emami-Naeini, A. (2012). Feedback Control of Dynamic Systems. 6th edn. Pearson. New Jersey, USA.zbMATHGoogle Scholar
  5. Gao, C. H. and Lin, X. Z. (2002). Transient temperature field analysis of a brake in a non-axisymmetric threedimensional model. J. Materials Processing Technology 129, 1–3, 513-517.CrossRefGoogle Scholar
  6. Han, J. H., Park, Y. J. and Park, Y. S. (2011). Adaptive regenerative braking control in severe cornering for guaranteeing the vehicle stability of fuel cell hybrid electric vehicle. Proc. IEEE Vehicle Power and Propulsion Conf., 1–5.Google Scholar
  7. Hori, Y. (2004). Future vehicle driven by electricity and control-research on four-wheel-motored “UOT electric march II”. IEEE Trans. Industrial Electronics 51, 5, 954–962.CrossRefGoogle Scholar
  8. Incropera, F. P., Dewitt, D. P., Bergman, T. L. and Lavine, A. S. (2006). Fundamentals of Heat and Mass Transfer. 6th edn. John Wiley & Sons. New York, USA.Google Scholar
  9. Kiefer, J. R. (1996). Modeling of Road Vehicle Lateral Dynamics. M. S. Thesis. Rochester Insititute of Technology. New York, USA.Google Scholar
  10. Kim, J. M., Park, C. M., Hwang, S. H., Hori, Y. and Kim, H. S. (2010). Control algorithm for an independent motor-drive vehicle. IEEE Trans. Vehicular Technology 59, 7, 3213–3222.CrossRefGoogle Scholar
  11. Kwon, M. H. (2015). Brake System Control for Electric Vehicle considering Temperature and Dynamics. M. S. Thesis. Sungkyunkwan University. Gyeonggi, Korea.Google Scholar
  12. Kwon, M. H., Park, J. H., Gwak, G. S., Huh, J. W., Choi, H. K. and Hwang, S. H. (2016). Cooperative control for friction and regenerative braking systems considering charactreristic and temperature condition. Int. J. Automotive Technology 17, 3, 437–446.CrossRefGoogle Scholar
  13. Limpert, R. (1999). Brake Design and Safety. 2nd edn. SAE International. Warrendale, Pennsylvania, USA.Google Scholar
  14. Piyabongkarn, D. N., Rajamani, R., Grogg, J. A. and Lew, J. Y. (2009). Development and experimental evaluation of a slip angle estimator for vehicle stability control. IEEE Trans. Control Systems Technology 17, 1, 78–88.CrossRefGoogle Scholar
  15. Rajamani, R. (2012). Vehicle Dynamics and Control. 2nd edn. Springer. New York, USA.CrossRefzbMATHGoogle Scholar
  16. Yu, F., Li, D. F. and Crolla, D. A. (2008). Integrated vehicle dynamics control-state-of-the art review. Proc. IEEE Vehicle Power and Propulsion Conf., 1–6.Google Scholar
  17. Zhang, S., Zhou, S. and Sun, J. (2009). Vehicle dynamics control based on sliding mode control technology. Proc. IEEE Control and Decision Conf., 2435–2439.Google Scholar
  18. Zheng, S., Tang, H., Han, Z. and Zhang, Y. (2006). Controller design for vehicle stability enhancement. Control Engineering Practice 14, 12, 1413–1421.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Automotive Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Jinhyun Park
    • 1
  • Minho Kwon
    • 1
  • Gwangil Du
    • 2
  • Jeewook Huh
    • 2
  • Sung-Ho Hwang
    • 1
  1. 1.Department of Mechanical EngineeringSungkyunkwan UniversityGyeonggiKorea
  2. 2.HEV Performance Development TeamHyundai Motor CompanyGyeonggiKorea

Personalised recommendations