Skip to main content

Electric-hydraulic Compound Control Anti-lock Braking System


An anti-lock control strategy for electric-hydraulic compound braking is proposed to improve the emergency braking safety of a hub motor electric vehicle. Based on the half-vehicle braking longitudinal dynamics model, the optimal control is solved to obtain the total braking torque corresponding to each wheel. A fuzzy algorithm is used to determine the proportion coefficient of the motor based on the battery state of charge coefficient (SOC) and the motor speed constraints on the motor braking, and the total braking torque is distributed. The hydraulic and motor braking torques obtained from the allocation are input as reference values to the electric-hydraulic compound braking system, and the output braking torque is fed back into the CarSim vehicle model. The proposed electric-hydraulic compound ABS control strategy is also validated in the co-simulation of CarSim and MATLAB/Simulink on high, medium and low adhesion road surfaces.

This is a preview of subscription content, access via your institution.


m :

half-vehicle mass, kg

F xf :

front wheel longitudinal braking force, N

F xr :

rear wheel longitudinal braking force, N

J :

wheel rotational inertia, kgm2

ω i :

wheel angular velocity, r/s

F xi :

longitudinal wheel force, N

R :

wheel radius, m

T bi :

braking moment, N·m


front wheel road adhesion coefficient


rear wheel road adhesion coefficient

F zf :

front wheel vertical load, N

F zr :

rear wheel vertical load, N

i=f,r :

front and rear wheels

a :

longitudinal acceleration, m/s2

g :

gravitational acceleration, m/s2

L r :

distance from the centre of mass of the car to the centre line of the rear axle, m

L f :

distance from the centre of mass of the car to the centre line of the front axle, m

L :

axle distance, m

h g :

height of the centre of mass of the car, m

c 1, c 2, c 3 :

the condition characteristic parameters related to the pavement condition

μ p :

peak adhesion coefficient

λ p :

slip rate corresponding to the peak adhesion coefficient

μ s :

adhesion coefficient

ξ :

pressure regulation signal

p m :

brake master cylinder pressure, Pa

c :

energy reservoir equivalent constant fluid pressure, Pa

c e :

hydraulic system equivalent fluid volume

R e1 :

equivalent fluid resistance when increasing pressure, N

R e2 :

equivalent fluid resistance when increasing pressure, N

u 1, u 2 :

solenoid valve control commands

k b :

braking torque constant, N·m

τ :

hydraulic system hysteresis time, s

R s :

stator resistance, N

Ld :

d-axis inductances, H

Lq :

q-axis inductances, H

p :

number of pole pairs of the motor

ω s :

mechanical angular velocity of the motor, r/s

φ f :

magnetic flux, Wb

φ d, φ q :

components of the magnetic flux on the d and q axes, Wb

k t :

motor torque constant, N·m

J e :

rotational inertia of the rotating part of the motor, kg·m

B :

damping factor

T L :

motor load torque, N·m

u* :

wheel speed corresponding to the optimal slip rate

u :

real wheel speed, r/s

Q :

weighting matrix of the state variables

R :

weighting matrix of the control variables

v a :

instantaneous vehicle speed, r/s

i g, i 0 :

transmission mechanism transmission ratio

F xbi,max :

maximum ground braking force corresponding to the front and rear wheels, N

T hi :

hydraulic braking torque required for the front and rear wheels, N·m

T eregi :

full effective braking torque of the motor under the current operating conditions, N·m

n mn :

rated speed

P mn :

rated power of the motor

T e,max :

effective braking torque of the motor


  • Aksjonov, A., Vodovozov, V., Augsburg, K. and Petlenkov, E. (2018). Design of regenerative anti-lock braking system controller for 4 in-wheel-motor drive electric vehicle with road surface estimation. Int. J. Automotive Technology 19, 4, 727–742.

    Article  Google Scholar 

  • Basrah, M. S., Siampis, E., Velenis, E., Cao, D. and Longo, S. (2017). Wheel slip control with torque blending using linear and nonlinear model predictive control. Vehicle System Dynamics 55, 11, 1665–1685.

    Article  Google Scholar 

  • Cao, Y. (2017). Design of ABS braking system with sliding mode variable structure. J. Yancheng University of Technology (Natural Science Edition) 30, 3, 26–29.

    Google Scholar 

  • Chen, C. P. and Chiang, M. H. (2018). Mathematical simulations and analyses of proportional electrohydraulic brakes and anti-lock braking systems in motorcycles. Actuators 7, 3, 34.

    Article  Google Scholar 

  • Filipozzi, L., Assadian, F., Kuang, M., Johri, R. and Alcantar, J. V. (2020). An investigation into the traction and anti-lock braking system control design. SAE Paper No. 2020-01-0997.

  • Gu, Y., He, R. and Wang, J. C. (2020). Coordinated control strategy of regenerative hydraulic composite braking system for an in-wheel motors driven electric vehicle. J. Chongqing University of Technology (Natural Science) 34, 6, 32–40.

    Google Scholar 

  • He, L., Ye, W., He, Z., Song, K. and Shi, Q. (2020). A combining sliding mode control approach for electric motor anti-lock braking system of battery electric vehicle. Control Engineering Practice, 102, 104520.

    Article  Google Scholar 

  • Li, C. C. (2018). Research on the Integrated Control of Regenerative Braking and Anti-lock Braking for an Electric Vehicle. Hefei University of Technology.

  • Li, K. Q., Luo, Y. G. and Guo, J. H. (2021). Advanced Vehicle System Dynamics and Control. Huazhong University of Science and Technology, 91.

  • Limpert, R. (1976). Analysis and design of automotive brake systems. US Army Material Development and Readiness Command Engineering Design Handbook, DARCOM-P-706-358.

  • Liu, B. (2004). Modern Control Theory. 2nd edn. China Machinery Industry Press. Beijing, China.

    Google Scholar 

  • Pan, N., Yu, L. Y., Zhang, L., Song, J. and Zhang, Y. H. (2017). Anti-lock braking control in coordinated braking system considering braking comfort. J. Zhejiang University (Engineering Science) 51, 1, 9–16.

    Google Scholar 

  • Rafatnia, S. and Mirzaei, M. (2021). Adaptive estimation of vehicle velocity from updated dynamic model for control of anti-lock braking system. IEEE Trans. Intelligent Transportation Systems, 1–10.

  • Sun, J., Xue, X. and Cheng, K. W. E. (2019). Fuzzy sliding mode wheel slip ratio control for smart vehicle anti-lock braking system. Energies 12, 13, 2501.

    Article  Google Scholar 

  • Wachter, E., Ngu, T. Q. and Alirand, M. (2019). Virtual simulation of an electro-hydraulic braking system. ATZ Worldwide 121, 7, 54–59.

    Article  Google Scholar 

  • Wang, G. W. and Yin, A. D. (2020). Research on electric vehicle ABS control based on neural network road recognition. J. Hefei University of Technology (Natural Science Edition) 43, 7, 878–883.

    Google Scholar 

  • Wang, J. C. and He, R. (2019). Hydraulic anti-lock braking control strategy of a vehicle based on a modified optimal sliding mode control method. Proc. Institution of Mechanical Engineers, Part D: J. Automobile Engineering 233, 12, 3185–3198.

    Google Scholar 

  • Wu, M. X. (2019). Research on optimal tracking control for ABS slip ratio of high speed vehicle in complex road conditions. J. Shanghai Normal University: Natural Science, 4, 375–382.

    Google Scholar 

  • Yao, Y., Zhao, Y. and Yamazaki, M. (2020). Integrated regenerative braking system and anti-lock braking system for hybrid electric vehicles & battery electric vehicles. SAE Int. J. Advances and Current Practices in Mobility 2, 2020-01-0846, 1592–1601.

    Google Scholar 

  • Yu, Z. (2009). Automobile Theory. 5th edn. China Machinery Industry Press. Beijing, China.

    Google Scholar 

  • Yuan, L., Zhao, H., Chen, H. and Ren, B. (2016). Nonlinear MPC-based slip control for electric vehicles with vehicle safety constraints. Mechatronics, 38, 1–15.

    Article  Google Scholar 

  • Zhang, J., Kong, X. D., Yao, J., Wang, J. and Chang, L. Y. (2016). Modeling and simulation of ABS HCU. China Mechanical Engineering 27, 21, 2967–2974.

    Google Scholar 

  • Zhang, X. Z. (2007). Fundamentals of Vehicle Control Theory and Applications (pp. 149–166). Chemical Industry Press. Beijing, China.

    Google Scholar 

  • Zhang, Y., Gong, G., Yang, H. and Peng, X. (2018a). Modeling and adaptive control of the electro-hydraulic braking system of low-floor vehicle. Proc. Institution of Mechanical Engineers, Part C: J. Mechanical Engineering Science 232, 20, 3639–3651.

    Google Scholar 

  • Zhang, Z., Ma, R., Wang, L. and Zhang, J. (2018b). Novel PMSM control for anti-lock braking considering transmission properties of the electric vehicle. IEEE Trans. Vehicular Technology 67, 11, 10378–10386.

    Article  Google Scholar 

  • Zheng, C. H., Park, Y. I., Lim, W. S. and Cha, S. W. (2012). Fuel economy evaluation of fuel cell hybrid vehicles based on optimal control. Int. J. Automotive Technology 13, 3, 517–522.

    Article  Google Scholar 

Download references


This paper is supported by the Hubei Key R&D Program Project Fund (Grant No. 2020BAA005), Industrial Internet Innovation and Development Project of the Ministry of Industry and Information Technology (Grant No. TC200802C, Grant No. TC200A00W).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Mingmao Hu.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Yang, F., Chen, X., Guo, D. et al. Electric-hydraulic Compound Control Anti-lock Braking System. Int.J Automot. Technol. 23, 1593–1608 (2022).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key Words

  • Wheel motors
  • Electric-hydraulic ABS
  • Optimal control
  • Brake torque distribution
  • Fuzzy control