Skip to main content

Advertisement

SpringerLink
Log in

A homogeneous domination output feedback control method for active suspension of intelligent electric vehicle

  • Original paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

An active suspension of an intelligent electric vehicle driven by four in-wheel motors (IEV-DFIM) is a strong nonlinear system because of time-varying parameters in practice, which causes difficult controllability. For addressing this issue, the paper proposes a novel homogeneous output feedback control method. Firstly, an active suspension dynamic model which considers the time-varying sprung mass, stiffness coefficients and damping coefficients is built. Secondly, an active suspension control system is constructed based on the dynamic model whose uncertain and nonlinear terms do not meet the linear or high-order growing. Thirdly, the homogeneous output feedback method is developed to relax the growth condition imposed on the uncertain and nonlinear terms for the active suspension. Finally, the simulation and test are carried out to verify the effectiveness of the designed controller compared with the sliding mode control method and passive suspension.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Attia, T., Vamvoudakis, K.G., Kochersberger, K., Bird, J., Furukawa, T.: Simultaneous dynamic system estimation and optimal control of vehicle active suspension. Veh. Syst. Dyn. 57(10), 1467–1493 (2019). https://doi.org/10.1080/00423114.2018.1521000

    Article  Google Scholar 

  2. Bernuau, E., Moulay, E., Coirault, P., Isfoula, F.: Practical consensus of homogeneous sampled-data multiagent systems. IEEE Trans. Autom. Control 64(11), 4691–4697 (2019). https://doi.org/10.1109/TAC.2019.2904442

    Article  MathSciNet  MATH  Google Scholar 

  3. Casavola, A., Di Iorio, F., Tedesco, F.: A multiobjective H-infinity control strategy for energy harvesting in regenerative vehicle suspension systems. Int. J. Control 91(4), 741–754 (2018). https://doi.org/10.1080/00207179.2017.1293298

    Article  Google Scholar 

  4. Chai, L., Wang, P., Fei, S.: Global state control for a class of inherently higher-order parameterized nonlinear time-delay systems based on homogeneous domination approach. Int. J. Robust Nonlinear Control 29(4), 829–848 (2019). https://doi.org/10.1002/rnc.4405

    Article  MathSciNet  MATH  Google Scholar 

  5. Chen, C.C., Qian, C., Liang, Y.W., Li, S.: Interval homogeneous domination approach for global stabilization of nonlinear systems with time-varying powers. In: 2016 IEEE 55th (CDC), pp. 7258–7263. IEEE (2016). http://doi.org/10.1109/CDC.2016.7799389

  6. Cseko, L.H., Kvasnica, M., Lantos, B.: Explicit MPC-based RBF neural network controller design with discrete-time actual kalman filter for semiactive suspension. IEEE Trans. Control Syst. Technol. 23(5), 1736–1753 (2015). https://doi.org/10.1109/TCST.2014.2382571

    Article  Google Scholar 

  7. Ding, S., Lu, L., Wei, X.Z.: Sliding mode direct yaw-moment control design for in-wheel electric vehicles. IEEE Trans. Ind. Electron. 64(8), 6752–6762 (2017). https://doi.org/10.1109/TIE.2017.2682024

    Article  Google Scholar 

  8. Ding, S., Mei, K., Li, S.: A new second-order sliding mode and its application to nonlinear constrained systems. IEEE Trans. Autom. Control 64(6), 2545–2552 (2019). https://doi.org/10.1109/TAC.2018.2867163

    Article  MathSciNet  MATH  Google Scholar 

  9. Ding, S., Qian, C., Li, S.: Global stabilization of a class of feedforward systems with lower-order nonlinearities. IEEE Trans. Autom. Control 55(3), 691–696 (2010). https://doi.org/10.1109/TAC.2009.2037455

    Article  MathSciNet  MATH  Google Scholar 

  10. Ding, S., Zheng, W.X.: Global stabilisation of a class of generalised cascaded systems by homogeneous method. Int. J. Control 89(4), 815–832 (2016). https://doi.org/10.1080/00207179.2015.1101787

    Article  MathSciNet  MATH  Google Scholar 

  11. Du, H., Qian, C., Li, S., Chu, Z.: Global sampled-data output feedback stabilization for a class of uncertain nonlinear systems. Automatica 99, 403–411 (2019). https://doi.org/10.1016/j.automatica.2018.11.002

    Article  MathSciNet  MATH  Google Scholar 

  12. Du, M., Zhao, D., Yang, M., Chen, H.: Nonlinear extended state observer-based output feedback stabilization control for uncertain nonlinear half-car active suspension systems. Nonlinear Dyn. 100(3), 2483–2503 (2020). https://doi.org/10.1007/s11071-020-05638-y

    Article  Google Scholar 

  13. Guo, J., Luo, Y., Hu, C., Tao, C., Li, K.: Robust combined lane keeping and direct yaw moment control for intelligent electric vehicles with time delay. Int. J. Autom. Technol. 20(2), 289–296 (2019). https://doi.org/10.1007/s12239-019-0028-5

    Article  Google Scholar 

  14. Guo, X., Yan, W., Cui, R.: Neural network-based nonlinear sliding-mode control for an AUV without velocity measurements. Int. J. Control 92(3), 677–692 (2019). https://doi.org/10.1080/00207179.2017.1366669

    Article  MathSciNet  MATH  Google Scholar 

  15. Hardy, G., Littlewood, J., Polya, G.: Ainequalities. Cambridge University Press, Cambridge (1952)

    Google Scholar 

  16. Harmouche, M., Laghrouche, S., Chitour, Y., Hamerlain, M.: Stabilisation of perturbed chains of integrators using Lyapunov-based homogeneous controllers. Int. J. Control 90(12), 2631–2640 (2017). https://doi.org/10.1080/00207179.2016.1262967

    Article  MathSciNet  MATH  Google Scholar 

  17. Hermes, H.: Homogeneous coordinates and continuous asymptotically stabilizing feedback controls. Diff. Equ. Stab. Control 109(1), 249–260 (1991)

    MathSciNet  Google Scholar 

  18. Hsiao, W.Y., Chiang, H.H., Lee, T.T.: Sliding-mode-based filtered feedback control design for active suspension system. In: IEEE International Conference on Systems (2011). http://doi.org/10.1109/ICSMC.2011.6083969

  19. Hu, C., Wang, Z., Qin, Y., Huang, Y., Wang, J., Wang, R.: Lane keeping control of autonomous vehicles with prescribed performance considering the rollover prevention and input saturation. IEEE Trans. Intell. Transp. Syst. (2019). https://doi.org/10.1109/TITS.2019.2924937

    Article  Google Scholar 

  20. Hu, C., Wang, Z., Taghavifar, H., Na, J., Qin, Y., Guo, J., Wei, C.: Mme-ekf-based path-tracking control of autonomous vehicles considering input saturation. IEEE Trans. Veh. Technol. (2019). https://doi.org/10.1109/TVT.2019.2907696

    Article  Google Scholar 

  21. Li, H., Zhang, Z., Yan, H., Xie, X.: Adaptive event-triggered fuzzy control for uncertain active suspension systems. IEEE Trans. Cybern. 49(12), 4388–4397 (2019). https://doi.org/10.1109/TCYB.2018.2864776

    Article  Google Scholar 

  22. Li, W., Xie, Z., Wong, P., Gao, J.: Improved adaptive event-triggered robust control for networked T-S fuzzy systems with asynchronous constraints. IEEE Trans. Cybern. Publ. Online (2020). https://doi.org/10.1109/TCYB.2020.2989404

    Article  Google Scholar 

  23. Li, W., Xie, Z., Wong, P., Mei, X., Zhao, J.: Adaptive-event-triggered-based fuzzy nonlinear lateral dynamic control for autonomous electric vehicles under insecure communication networks. IEEE Trans. Ind. Electron. Publ. Online (2020). https://doi.org/10.1109/TIE.2020.2970680

    Article  Google Scholar 

  24. Liang, Z., Zhao, J., Dong, Z., Wang, Y., Ding, Z.: Torque vectoring and rear-wheel-steering control for vehicle’s uncertain slips on soft and slope terrain using sliding mode algorithm. IEEE Trans. Veh. Technol. 69(4), 3805–3815 (2020). https://doi.org/10.1109/TVT.2020.2974107

    Article  Google Scholar 

  25. Liu, F., Xiang, C., Liu, H., Han, L., Wu, Y., Wang, X., Gao, P.: Asymmetric effect of static radial eccentricity on the vibration characteristics of the rotor system of permanent magnet synchronous motors in electric vehicles. Nonlinear Dyn. 96(4), 2581–2600 (2019). https://doi.org/10.1007/s11071-019-04942-6

    Article  Google Scholar 

  26. Liu, S., Zhou, H., Luo, X., Xiao, J.: Adaptive sliding fault tolerant control for nonlinear uncertain active suspension systems. J. Franklin Inst.-Eng. Appl. Math. 353(1), 180–199 (2016). https://doi.org/10.1016/j.jfranklin.2015.11.002

    Article  MathSciNet  MATH  Google Scholar 

  27. Liu, Y.J., Zeng, Q., Tong, S., Chen, C.L.P., Liu, L.: Adaptive neural network control for active suspension systems with time-varying vertical displacement and speed constraints. IEEE Trans. Ind. Electron. 66(12), 9458–9466 (2019). https://doi.org/10.1109/TIE.2019.2893847

    Article  Google Scholar 

  28. Meng, Q., Chen, C.C., Wang, P., Sun, Z.Y., Li, B.: Study on vehicle active suspension system control method based on homogeneous domination approach. Asian J. Control (2019). https://doi.org/10.1002/asjc.2242

    Article  Google Scholar 

  29. Meng, Q., Qian, C., Liu, R.: Dual-rate sampled-data stabilization for active suspension system of electric vehicle. Int. J. Robust Nonlinear Control 28(5), 1610–1623 (2018). https://doi.org/10.1002/rnc.3974

    Article  MathSciNet  MATH  Google Scholar 

  30. Meng, Q., Sun, Z.Y., Shu, Y., Liu, T.: Lateral motion stability control of electric vehicle via sampled-data state feedback by almost disturbance decoupling. Int. J. Control 92(4), 734–744 (2019). https://doi.org/10.1080/00207179.2017.1367104

    Article  MathSciNet  MATH  Google Scholar 

  31. Meng, Q., Zhao, T., Qian, C., Sun, Z., Ge, P.: Integrated stability control of afs and dyc for electric vehicle based on non-smooth control. Int. J. Syst. Sci. 49, 1–11 (2018). https://doi.org/10.1080/00207721.2018.1460410

    Article  MathSciNet  Google Scholar 

  32. Nakamura, N., Nakamura, H., Yamashita, Y., Nishitani, H.: Homogeneous stabilization for input affine homogeneous systems. IEEE Trans. Autom. Control 54(9), 2271–2275 (2009). https://doi.org/10.1109/TAC.2009.2026865

    Article  MathSciNet  MATH  Google Scholar 

  33. Nemeth, B., Fenyes, D., Gaspar, P., Bokor, J.: Coordination of independent steering and torque vectoring in a variable-geometry suspension system. IEEE Trans. Control Syst. Technol. 27(5), 2209–2220 (2019). https://doi.org/10.1109/TCST.2018.2867369

    Article  Google Scholar 

  34. Nguyen, S.D., Lam, B.D., Ngo, V.H.: Fractional-order sliding-mode controller for semi-active vehicle MRD suspensions. Nonlinear Dyn. Publ. Online (2020). https://doi.org/10.1007/s11071-020-05818-w

    Article  Google Scholar 

  35. Pan, H., Jing, X., Sun, W., Gao, H.: A bioinspired dynamics-based adaptive tracking control for nonlinear suspension systems. IEEE Trans. Control Syst. Technol. 26(3), 903–914 (2018). https://doi.org/10.1109/TCST.2017.2699158

    Article  Google Scholar 

  36. Parra, A., Zubizarreta, A., Perez, J., Dendaluce, M.: Intelligent torque vectoring approach for electric vehicles with per-wheel motors. Complexity (2018). https://doi.org/10.1155/2018/7030184

    Article  Google Scholar 

  37. Polyakov, A., Coron, J.M., Rosier, L.: On homogeneous finite-time control for linear evolution equation in hilbert space. IEEE Trans. Autom. Control 63(9), 3143–3150 (2018). https://doi.org/10.1109/TAC.2018.2797838

    Article  MathSciNet  MATH  Google Scholar 

  38. Qian, C.: A homogeneous domination approach for global output feedback stabilization of a class of nonlinear systems. In: Proceedings of the 2005 American Control Conference, pp. 4708–4715. IEEE (2005)

  39. Qian, C., Du, H., Li, S.: Global stabilization via sampled-data output feedback for a class of linearly uncontrollable and unobservable systems. IEEE Trans. Autom. Control 61(12), 4088–4093 (2016). https://doi.org/10.1109/TAC.2016.2542238

    Article  MathSciNet  MATH  Google Scholar 

  40. Qian, C., Lin, W.: A continuous feedback approach to global strong stabilization of nonlinear systems. IEEE Trans. Autom. Control 46(7), 1061–1079 (2001)

    Article  MathSciNet  Google Scholar 

  41. Qian, C., Lin, W., Zha, W.: Generalized homogeneous systems with applications to nonlinear control: a survey. Math. Control Relat. Fields 5(3), 585–611 (2015). https://doi.org/10.3934/mcrf.2015.5.585

    Article  MathSciNet  MATH  Google Scholar 

  42. Rath, J.J., Defoort, M., Karimi, H.R., Veluvolu, K.C.: Output feedback active suspension control with higher order terminal sliding mode. IEEE Trans. Ind. Electron. 64(2), 1392–1403 (2017). https://doi.org/10.1109/TIE.2016.2611587

    Article  Google Scholar 

  43. Rosolia, U., De Bruyne, S., Alleyne, A.G.: Autonomous vehicle control: a nonconvex approach for obstacle avoidance. IEEE Trans. Control Syst. Technol. 25(2), 469–484 (2017). https://doi.org/10.1109/TCST.2016.2569468

    Article  Google Scholar 

  44. van der Sande, T.P.J., Besselink, I.J.M., Nijmeijer, H.: Rule-based control of a semi-active suspension for minimal sprung mass acceleration: design and measurement. Veh. Syst. Dyn. 54(3), 281–300 (2016). https://doi.org/10.1080/00423114.2015.1135970

    Article  Google Scholar 

  45. Shao, X., Naghdy, F., Du, H., Li, H.: Output feedback H-infinity, control for active suspension of in-wheel motor driven electric vehicle with control faults and input delay. ISA Trans. 92, 94–108 (2019). https://doi.org/10.1016/j.isatra.2019.02.016

    Article  Google Scholar 

  46. Sun, X., Zhang, H., Cai, Y., Wang, S., Chen, L.: Hybrid modeling and predictive control of intelligent vehicle longitudinal velocity considering nonlinear tire dynamics. Nonlinear Dyn. 97(2), 1051–1066 (2019). https://doi.org/10.1007/s11071-019-05030-5

    Article  MATH  Google Scholar 

  47. Sun, Z.Y., Shao, Y., Chen, C.C., Meng, Q.: Global output-feedback stabilization for stochastic nonlinear systems: a double-domination approach. Int. J. Robust Nonlinear Control 28(15), 4635–4646 (2018). https://doi.org/10.1002/rnc.4242

    Article  MathSciNet  MATH  Google Scholar 

  48. Sun, Z.Y., Yang, S.H., Li, T.: Global adaptive stabilization for high-order uncertain time-varying nonlinear systems with time-delays. Int. J. Robust Nonlinear Control 27(13), 2198–2217 (2017). https://doi.org/10.1002/rnc.3678

    Article  MathSciNet  MATH  Google Scholar 

  49. Wang, R., Jing, H., Karimi, H.R., Chen, N.: Robust fault-tolerant H-infinity control of active suspension systems with finite-frequency constraint. Mech. Syst. Signal Process. 62–63, 341–355 (2015). https://doi.org/10.1016/j.ymssp.2015.01.015

    Article  Google Scholar 

  50. Wu, D., Du, H., Wen, G., Lu, J.: Fixed-time synchronization control for a class of master-slave systems based on homogeneous method. IEEE Trans. Circuits Syst. ii-Express Briefs 66(9), 1547–1551 (2019). https://doi.org/10.1109/TCSII.2018.2886574

    Article  Google Scholar 

  51. Xing, Y., Lv, C., Wang, H., Cao, D., Velenis, E., Wang, F.Y.: Driver activity recognition for intelligent vehicles: a deep learning approach. IEEE Trans. Veh. Technol. 68(6), 5379–5390 (2019). https://doi.org/10.1109/TVT.2019.2908425

    Article  Google Scholar 

  52. Xu, X., Zhang, C., Liu, Q., Cao, J., Alsaedi, A.: Adaptive stabilization for a class of uncertain -normal nonlinear systems via a generalized homogeneous domination technique. Nonlinear Dyn. 93(2), 847–862 (2018). https://doi.org/10.1007/s11071-018-4231-0

    Article  MATH  Google Scholar 

  53. Yang, C., Xia, J., Park, J.H., Shen, H., Wang, J.: Sliding mode control for uncertain active vehicle suspension systems: an event-triggered H-infinity control scheme. Nonlinear Dyn. Publ. Online (2020). https://doi.org/10.1007/s11071-020-05742-z

    Article  Google Scholar 

  54. Yang, S.H., Sun, Z.Y., Wang, Z., Li, T.: A new approach to global stabilization of high-order time-delay uncertain nonlinear systems via time-varying feedback and homogeneous domination. J. Franklin Inst.-Eng. Appl. Math. 355(14), 6469–6492 (2018). https://doi.org/10.1016/j.jfranklin.2018.05.063

  55. Zhai, J., Qian, C.: Global control of nonlinear systems with uncertain output function using homogeneous domination approach. Int. J. Robust Nonlinear Control 22(14), 1543–1561 (2012). https://doi.org/10.1002/rnc.1765

    Article  MathSciNet  MATH  Google Scholar 

  56. Zhai, J.Y., Song, Z.B.: Adaptive sliding mode trajectory tracking control for wheeled mobile robots. Int. J. Control 92(10), 2255–2262 (2019). https://doi.org/10.1080/00207179.2018.1436194

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

This research was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No. LZ21E050002, National Natural Science Foundation of China under Grant No. 61773237.

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Hangzhou Dianzi University, Hangzhou, China

    Qinghua Meng

  2. College of Engineering, University of Texas at San Antonio, San Antonio, USA

    Chunjiang Qian

  3. Institute of Automation, Qufu Normal University, Qufu, China

    Zong-Yao Sun

  4. Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan

    Chih-Chiang Chen

Authors
  1. Qinghua Meng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chunjiang Qian
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zong-Yao Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chih-Chiang Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qinghua Meng.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

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

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Meng, Q., Qian, C., Sun, ZY. et al. A homogeneous domination output feedback control method for active suspension of intelligent electric vehicle. Nonlinear Dyn 103, 1627–1644 (2021). https://doi.org/10.1007/s11071-020-06188-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-06188-z

Keywords

Search

Navigation