International Journal of Automotive Technology

, Volume 20, Issue 6, pp 1221–1236 | Cite as

Modeling and Control of A High Speed On/Off Valve Actuator

  • Jigen Fang
  • Xifeng Wang
  • Jinjun Wu
  • Shuai Yang
  • Liang LiEmail author
  • Xiang Gao
  • Yue Tian


Accurate electromagnetic force control in a high speed on/off valve actuator (HSVA) can improve the performance of a vehicle braking system, and an accurate theoretical model is the key to smoothly controlling the high speed on/off valve. Therefore, a nonlinear model of an HSVA is proposed in this paper. Three subsystems are modeled as a spring/mass/damper system, a nonlinear resistor/inductor system and a multiwall heat transfer system, respectively. Then, a sliding-model controller combined with a sliding-model observer is designed to adjust the electromagnetic force for an accurate HSVA state control, taking the effect of the coil heating into account. The feasibility of the three submodels and the sliding-model controller are verified by comparing the simulation results with the experimental results obtained on a test bench. Our study shows that the three subsystems are coupled to one another through resistance, displacement, and temperature. When the excitation voltage exceeds 9 V, the coil temperature can reach more than 150 degrees Celsius within 300 s, and the electromagnetic force decreases by approximately 30 %. However, by applying the above control strategy, the electromagnetic force can also be stable, fluctuating within 5 % even if the temperature of the coil rises to the thermal equilibrium temperature.

High speed on/off valve actuator Spring/mass/damper system Resistor/inductor system Multiwall heat transfer system Sliding-model controller 



section area of the air gap


magnetic flux density


coulomb friction term


specific heat capacity of the copper wire


specific heat capacity of the nylon frame


specific heat capacity of the shell


differential thickness


is the estimation error


electromagnetic force


spring force


preload of the return spring


magnetic field


current through the coil


desired current


measured current


eddy current density


return spring


proportional gain


integral gain


inductance of the coil


mass of the copper wire


mass of the nylon frame


mass of the shell


number of turns on solenoid coil

nx, ny, nz

direction cosines of the exterior normal to the boundary


copper loss


iron loss


heat conduction rate


heat flow


heat flux of heat conduction


heat flux of thermal convection


heat generation ratio


resistance of the coil


inner radius of a heat transfer layer


outer radius of a heat transfer layer




supply voltage


voltage of the equivalent resistance


voltage of the equivalent inductor


viscous damping term


armature/spool displacement


desired armature position


thermal conductivity

λx, λy, λ

heat conductivity coefficients in the x-, y- and z-directions


black body coefficient


electrical conductivity


flux linkage


temperature coefficient of resistance


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



This work was supported by the National Natural Science Foundation of China (grant number 51475197 and 51422505). The authors would like to thank Tianjin Trinova Automobile Technology Co. Ltd. for providing technical and experimental support for this research.


  1. Alberti, L. and Bianchi, N. (2008). A coupled thermal-electromagnetic analysis for a rapid and accurate prediction of IM performance. IEEE Trans. Industrial Electronics 55 10, 3575–3582.CrossRefGoogle Scholar
  2. Boada, B. L., Boada, M. J. L., Gauchia, A., Olmeda, E. and Diaz, V. (2015). Sideslip angle estimator based on ANFIS for vehicle handling and stability. J. Mechanical Science and Technology 29 4, 1473–1481.CrossRefGoogle Scholar
  3. Chladny, R. R., Koch, C. R. and Lynch, A. F. (2005). Modeling automotive gas-exchange solenoid valve actuators. IEEE Trans. Magnetics 41 3, 1155–1162.CrossRefGoogle Scholar
  4. De Castro, R., Araujo, R. E. and Freitas, D. (2013). Wheel slip control of EVs based on sliding mode technique with conditional integrators. IEEE Trans. Industrial Electronics 60 8, 3256–3271.CrossRefGoogle Scholar
  5. Imine, H., Benallegue, A., Madani, T. and Srairi, S. (2014). Rollover risk prediction of heavy vehicle using high-order sliding-mode observer: Experimental results. IEEE Trans. Vehicular Technology 63 6, 2533–2543.CrossRefGoogle Scholar
  6. Jiang, W. Y. and Jahns, T. M. (2015). Coupled electromagnetic — Thermal analysis of electric machines including transient operation based on finite-element techniques. IEEE Trans. Industry Applications 51 2, 1880–1889.CrossRefGoogle Scholar
  7. Jiles, D. C. (1994). Frequency dependence of hysteresis curves in conducting magnetic materials. J. Applied Physics 76 10, 5849–5855.CrossRefGoogle Scholar
  8. Khatun, P., Bingham, C. M., Schofield, N. and Mellor, P. H. (2003). Application of fuzzy control algorithms for electric vehicle antilock braking/traction control systems. IEEE Trans. Vehicular Technology 52 5, 1356–1364.CrossRefGoogle Scholar
  9. Li, L., Li, X. J., Wang, X. Y., Liu, Y. H., Song, J. and Ran, X. (2016). Transient switching control strategy from regenerative braking to anti-lock braking with a semi-brake-by-wire system. Vehicle System Dynamics: Int. J. Vehicle Mechanics and Mobility 54 2, 231–257.CrossRefGoogle Scholar
  10. Lin, F., Zuo, S., Deng, W and Wu, S. (2016). Modeling and analysis of electromagnetic force, vibration, and noise in permanent-magnet synchronous motor considering current harmonics. IEEE Trans. Industrial Electronics 63 12, 7455–7466.CrossRefGoogle Scholar
  11. Liu, P., Fan, L. Y., Hayat, Q., Xu, D., Ma, X. Z. and Song, E. Z. (2014). Research on key factors and their interaction effects of electromagnetic force of high-speed solenoid valve. The Scientific World J., 2014, Article ID 567242.Google Scholar
  12. Liu, Y., Wu, Z., Wang, X., Duan, Z., Gao, X. and Qu, J. (2013). Design and performance analysis based on high-speed switching valve of magnetorheological plug-mounted. Advanced Materials Research, 630, 106–109.CrossRefGoogle Scholar
  13. Liu, Z., Liu, W.-P and He, Q. (2009). Simimulation analysis and study on transient property of high speed switch electromagnetic valve. J. Natural Science of Hunan Normal University 32 3, 53–57.Google Scholar
  14. Ma, J., Zhu, G. G. and Schock, H. (2010). A dynamic model of an electropneumatic valve actuator for internal combustion engines. J. Dynamic Systems, Measurement, and Control 132 2, 021007–1–021007–10.CrossRefGoogle Scholar
  15. Mach, F., Kaminský, T. and Doležel, I. (2017). Monostable electromagnetic actuator for high-speed and fail-safe valve operation. Electrical Engineering 99 4, 1317–1324.CrossRefGoogle Scholar
  16. Mezani, S., Takorabet, N. and Laporte, B. (2005). A combined electromagnetic and thermal analysis of induction motors. IEEE Trans. Magnetics 41 5, 1572–1575.CrossRefGoogle Scholar
  17. Miller, J. I., Flack, T. J. and Cebon, D. (2014). Modeling the magnetic performance of a fast pneumatic brake actuator. J. Dynamic Systems, Measurement, and Control 136 2, 021022–1–021022–12.CrossRefGoogle Scholar
  18. Parlikar, T. A., Chang, W. S., Qiu, Y. H., Seeman, M. D., Perreault, D. J., Kassakian, J. G. and Keim, T. A. (2005). Design and experimental implementation of an electromagnetic engine valve drive. IEEE/ASME Trans. Mechatronics 10 5, 482–494.CrossRefGoogle Scholar
  19. Ran, X., Zhao, X., Chen, J., Yang, C. and Yang, C. (2016). Novel coordinated algorithm for Traction Control System on split friction and slope road. Int. J. Automotive Technology 17 5, 817–827.CrossRefGoogle Scholar
  20. Shin, Y., Lee, S., Choi, C. and Kim, J. (2015). Shape optimization to minimize the response time of direct-acting solenoid valve. J. Magnetics 20 2, 193–200.CrossRefGoogle Scholar
  21. Subudhi, B. and Ge, S. S. (2012). Sliding-mode-observer-based adaptive slip ratio control for electric and hybrid vehicles. IEEE Trans. Intelligent Transportation Systems 13 4, 1617–1626.CrossRefGoogle Scholar
  22. Szczyglowski, J. (2001). Influence of eddy currents on magnetic hysteresis loops in soft magnetic materials. J. Magnetism and Magnetic Materials 223 1, 97–102.CrossRefGoogle Scholar
  23. Tziouvaras, D. A., Mclaren, P., Alexander, G., Dawson, D., Esztergalyos, J., Fromen, C., Glinkowski, M., Hasenwinkle, I., Kezunovic, M., Kojovic, L., Kotheimer, B., Kuffel, R., Nordstrom, J., Zocholl, S. and Working Grp, C. S. P. S. (2000). Mathematical models for current, voltage, and coupling capacitor voltage transformers. IEEE Trans. Power Delivery 15 1, 62–72.CrossRefGoogle Scholar
  24. Vaughan, N. D. and Gamble, J. B. (1996). The modeling and simulation of a proportional solenoid valve. J. Dynamic Systems, Measurement, and Control 118 1, 120–125.CrossRefGoogle Scholar
  25. Wang, H., Kong, H. F., Man, Z. H., Tuan, D. M., Cao, Z. W. and Shen, W. X. (2014). Sliding Mode Control for Steer-by-Wire Systems With AC Motors in Road Vehicles. IEEE Trans. Industrial Electronics 61 3, 1596–1611.CrossRefGoogle Scholar
  26. Wang, L., Li, G.-X., Xu, C.-L., Xi, X., Wu, X.-J. and Sun, S.-P. (2016). Effect of characteristic parameters on the magnetic properties of solenoid valve for high-pressure common rail diesel engine. Energy Conversion and Management, 127, 656–666.CrossRefGoogle Scholar
  27. Wu, M. C. and Shih, M. C. (2003). Simulated and experimental study of hydraulic anti-lock braking system using sliding-mode PWM control. Mechatronics 13 4, 331–351.CrossRefGoogle Scholar
  28. Yim, S., Jeon, K. and Yi, K. (2012). An investigation into vehicle rollover prevention by coordinated control of active anti-roll bar and electronic stability program. Int. J. Control, Automation and Systems 10 2, 275–287.CrossRefGoogle Scholar
  29. Zhao, J., Fan, L., Liu, P., Grekhov, L., Ma, X. and Song, E. (2017). Investigation on electromagnetic models of high-speed solenoid valve for common rail injector. Mathematical Problems in Engineering, 2017, Article ID 9078598.Google Scholar

Copyright information

© KSAE/ 111-14 2019

Authors and Affiliations

  • Jigen Fang
    • 1
  • Xifeng Wang
    • 1
  • Jinjun Wu
    • 1
  • Shuai Yang
    • 3
  • Liang Li
    • 2
    Email author
  • Xiang Gao
    • 2
  • Yue Tian
    • 3
  1. 1.China Productivity Center for MachineryChina Academy of Machinery Science and TechnologyBeijingChina
  2. 2.State Key Laboratory of Automotive Safety and EnergyTsinghua UniversityBeijingChina
  3. 3.School of Mechanical EngineeringYanshan UniversityHebeiChina

Personalised recommendations