Skip to main content
SpringerLink
Log in

Modeling and Simulation of Active Half-vehicle Suspension Based on a New Output-feedback H∞ Controller

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

The excellent performance of the controller and its insensitivity to time-delay are very important for active suspension. In this paper, a novel output-feedback H∞ optimal controller is designed for half-vehicle suspension system and it performs better than the common output-feedback H∞ optimal controller. To further study the effect of time-delay on the performance of the controller, a visual modeling and simulation method is proposed, and the detailed modeling process is given. The influence of time-delay on the vertical acceleration and pitching acceleration of vehicle body is simulated under bump road excitation and C-class pavement excitation, respectively. The results show that when the time-delay is less than 25 ms, the performance of the controller is little affected under the bump road, and under the C-level road excitation, even if the time-delay reaches 50 ms, the performance of the controller will not be affected.

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

Similar content being viewed by others

References

  1. M. Du, D. Zhao, B. Yang, and L. Wang, “Terminal sliding mode control for full vehicle active suspension systems,” Journal of Mechanical Science and Technology, vol. 32, no. 6, pp. 2851–2866, 2018.

    Article  Google Scholar 

  2. G. Wang, “ESO-based terminal sliding mode control for uncertain full-car active suspension systems,” International Journal of Automotive Technology, vol. 21, no. 3, pp. 691–702, 2020.

    Article  Google Scholar 

  3. N. G. Yavar and M. A. Seyyed, “Chaotic dynamics of the vertical model in vehicles and chaos control of active suspension system via the fuzzy fast terminal sliding mode control,” Journal of Mechanical Science and Technology, vol. 35, no. 1, pp. 31–43, 2021.

    Article  Google Scholar 

  4. B. Sofiane, C. Mohammed, L. Zhang, and T. Yang, “Constrained model predictive control for time-varying delay systems: Application to an active car suspension,” International Journal of Control, Automation, and Systems, vol. 14, no. 1, pp. 51–58, 2016.

    Article  Google Scholar 

  5. D. C. Hyun, J. L. Chang, and T. L. Myo, “Fuzzy preview control for half-vehicle electro-hydraulic suspension system,” International Journal of Control, Automation, and Systems, vol. 16, no. 5, pp. 2489–2500, 2018.

    Article  Google Scholar 

  6. J. O. Pedro, S. Nhlapo, and L. J. Mpanza, “Model predictive control of half-car active suspension systems using particle swarm optimization,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 14438–14443, 2020.

    Article  Google Scholar 

  7. R. Hao, H. Wang, S. Liu, M. Yang, and Z. Tian, “Multi-objective command filtered adaptive control for nonlinear hydraulic active suspension systems,” Nonlinear Dynamics, no. 105, pp. 1559–1579, 2021.

  8. Y. Q. Han, W. J. He, N. Li, and S. L. Zhu, “Adaptive tracking control of a class of nonlinear systems with input delay and dynamic uncertainties using multi-dimensional Taylor network,” International Journal of Control, Automation, and Systems, vol. 19, no. 12, pp. 4078–4089, 2021.

    Article  Google Scholar 

  9. Y. J. Liu, Q. Zeng, S. Tong, C. Chen, and L. Liu, “Actuator failure compensation-based adaptive control of active suspension systems with prescribed performance,” IEEE Transactions on Industrial Electronics, vol. 67, no. 8, pp. 7044–7053, 2020.

    Article  Google Scholar 

  10. Y. J. Liang, N. Li, D. X. Gao, and Z. S. Wang, “Optimal vibration control for nonlinear systems of tracked vehicle half-car suspensions,” International Journal of Control, Automation, and Systems, vol. 15, no. 4, pp. 1675–1683, 2017.

    Article  Google Scholar 

  11. X. F. Zhong, S. Y. Han, J. Zhou, and Y. H. Chen, “Design of optimal disturbance attenuation controller for networked T∞S fuzzy vehicle active suspension with control delay,” International Journal of Fuzzy Systems, vol. 21, no. 2, pp. 676–684, 2019.

    Article  MathSciNet  Google Scholar 

  12. Y. J. Liang, Y. J. Lu, D. X. Gao, and Z. S. Wang, “Applications of approximate optimal control to nonlinear systems of tracked vehicle suspensions,” International Journal of Computational Intelligence Systems, vol. 14, no. 174, pp. 1–9, 2021.

    Google Scholar 

  13. Q. Meng, C. Qian, Z. Y. Sun, and C. C. Chen, “A homogeneous domination output feedback control method for active suspension of intelligent electric vehicle,” Nonlinear Dynamics, no. 103, pp. 1627–1644, 2021.

  14. J. Zhao, X. Wang, P. K. Wong, Z. Xie, J. Jia, and W. Li, “Multi-objective frequency domain-constrained static output feedback control for delayed active suspension systems with wheelbase preview information,” Nonlinear Dynamics, no. 103, pp. 1757–1774, 2021.

  15. A. M. S. Hisham, E. M. Khaled, and S. Mostafa, “Invariant sets in saturated and robust vehicle suspension control,” Arabian Journal for Science and Engineering, no. 45, pp. 7055–7064, 2020.

  16. Y. Yin, B. Luo, H. Ren, Q. Fang, and C. Zhang, “Robust control design for active suspension system with uncertain dynamics and actuator time delay,” Journal of Mechanical Science and Technology, vol. 36, no. 12, pp. 6319–6327, 2022.

    Article  Google Scholar 

  17. A. H. Samba, T. A. Yeremou, N. L. Nneme, and J. H. S. Idellette, “Improved networked iterative learning fault-tolerant control algorithm for systems with time-delays, random packet losses, limited communication and actuator failure,” International Journal of Control, Automation, and Systems, vol. 20, no. X, pp. 1–9, 2022.

    Google Scholar 

  18. A. Lin and X. Su, “Fault-tolerant controller design for active suspension system with proportional differential sliding mode observer,” International Journal of Control, Automation, and Systems, vol. 17, no. 7, pp. 1751–1761, 2019.

    Article  Google Scholar 

  19. S. D. Nguyen and V. Q. Nguyen, “SD-TCSs control deriving from fractional-order sliding mode and fuzzy-compensator,” International Journal of Control, Automation, and Systems, vol. 20, no. 5, pp. 1745–1755, 2022.

    Article  Google Scholar 

  20. T. Yuvapriya, P. Lakshmi, and S. Rajendiran, “Vibration suppression in full car active suspension system using fractional order sliding mode controller,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 40, no. 217, pp. 1–11, 2018.

    Google Scholar 

  21. X. Dong, D. Zhao, B. Yang, and C. Han, “Fractional-order control of active suspension actuator based on parallel adaptive clonal selection algorithm,” Journal of Mechanical Science and Technology, vol. 30, no. 6, pp. 2769–2781, 2016.

    Article  Google Scholar 

  22. M. Gong and X. Yan, “Robust control strategy of heavy vehicle active suspension based on road level estimation,” International Journal of Automotive Technology, vol. 22, no. 1, pp. 141–153, 2021.

    Article  Google Scholar 

  23. C. Ozbek, O. C. Ozguney, R. Burkan, and N. Yagiz, “Design of a fuzzy robust-adaptive control law for active suspension systems,” Sådhanå, vol. 45, no. 194, pp. 1–16, 2020.

    MathSciNet  Google Scholar 

  24. W. Qin, P. Ge, F. Liu, and S. Long, “Adaptive robust control for active suspension systems: targeting nonholonomic reference trajectory and large mismatched uncertainty,” Nonlinear Dynamics, no. 104, pp. 3861–3880, 2021.

  25. S. Farzad and S. Mokhtar, “Optimal sliding mode control design for constrained uncertain nonlinear systems using T−S fuzzy approach,” Iranian Journal of Science and Technology, Transactions of Electrical Engineering, no. 46, pp. 549–563, 2022.

  26. A. S. Mahdi, “Suppression of chaotic vibrations in suspension system of vehicle dynamics using chattering-free optimal sliding mode control,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 41, no. 210, pp. 1–10, 2019.

    ADS  Google Scholar 

  27. Y. M. Ghazally, H. Wang, and Y. Tian, “Optimized fast terminal sliding mode control for a half-car active suspension systems,” International Journal of Automotive Technology, vol. 21, no. 4, pp. 805–812, 2020.

    Article  Google Scholar 

  28. W. Li, Z. Xie, P. K. Wong, X. Ma, Y. Cao, and J. Zhao, “Nonfragile H∞ control of delayed active suspension systems in finite frequency under nonstationary running,” Journal of Dynamic Systems, Measurement, and Control, vol. 141, no. 061001, pp. 1–16, 2019.

    Google Scholar 

  29. Y. Guan, Q. L. Han, H. Yao, and X. Ge, “Robust event-triggered H∞ controller design for vehicle active suspension systems,” Nonlinear Dynamics, no. 94, pp. 627–638, 2018.

  30. M. J. Hu, J. H. Park, and J. Cheng, “Robust fuzzy delayed sampled-data control for nonlinear active suspension systems with varying vehicle load and frequency-domain constraint,” Nonlinear Dynamics, no. 105, pp. 2265–2281, 2021.

  31. C. Wei, K. Zhang, Y. Cai, Z. Wang, and W. Yu, “A new method of static output-feedback H∞ controller design for 5 DOF vehicle active suspension system,” Journal of the Brazilian Society of Mechanical Sciences and Engineering, vol. 40, no. 132, pp. 1–12, 2018.

    CAS  Google Scholar 

  32. H. D. Choi, C. K. Ahn, M. T. Lim, and M. K. Song, “Dynamic output-feedback H∞ control for active half-vehicle suspension systems with time-varying input delay,” International Journal of Control, Automation, and Systems, vol. 14, no. 1, pp. 59–68, 2016.

    Article  Google Scholar 

  33. C. Wei, Y. Cai, K. Zhang, Z. Wang, and W. Yu, “Novel optimal design approach for output-feedback H∞ control of vehicle active seat-suspension system,” Asian Journal of Control, vol. 21, no. 6, pp. 1–12, 2018.

    Google Scholar 

  34. B. W. Dhammartna, G. A. Vinayak, and M. P. Balasaheb, “Extended disturbance observer based robust sliding mode control for active suspension system,” International Journal of Dynamics and Control, no. 9, pp. 1681–1694, 2021.

  35. T. Hamid, “Reduced vibration of off-road vehicle nonlinear suspension system using an adaptive integral sliding mode neural network controller,” International Journal of Dynamics and Control, no. 8, pp. 291–301, 2020.

  36. F. Cao, H. Sun, Y. Li, and S. Tong, “Fuzzy adaptive fault-tolerant control for a class of active suspension systems with time delay,” International Journal of Fuzzy Systems, vol. 21, no. 7, pp. 2054–2065, 2019.

    Article  MathSciNet  Google Scholar 

  37. G. Lee, M. Hyun, D. Kang, and S. Heo, “High-efficiency active suspension based on continuous damping control,” International Journal of Automotive Technology, no. 23, pp. 31–40, 2022.

  38. S. R. Gampa, S. K. Mangipudi, K. Jasthi, B. B. Mahesh, P. Goli, D. Das, and V. E. Balas, “Pareto optimality based PID controller design for vehicle active suspension system using grasshopper optimization algorithm,” Journal of Electrical Systems and Information Technology, no. 9, num. 24, 2022.

  39. C. Y. Hsiao and Y. H. Wang, “Evaluation of ride comfort for active suspension system based on self-tuning fuzzy sliding mode control,” International Journal of Control, Automation, and Systems, vol. 20, no. 4, pp. 1131–1141, 2022.

    Article  Google Scholar 

  40. M. Dehghan, M. M. Fateh, and M. Ghalehnoie, “A fuzzy-supervised impedance control for an active suspension system,” Journal of Vibration Engineering and Technologies, 2022.

  41. G. Barbaraci and G. V. Mariotti, “Influence on the dynamic behavior of full car equipped by magnetorheological damper via switch on/off and h∞ controller,” Proc. of International Automotive Conference with Exhibition, pp. 1–16, 2011.

  42. F. Viadero-Monasterio, B. L. Boada, M. J. L. Boada, and V. Diaz, “H∞ dynamic output feedback control for a networked control active suspension system under actuator faults,” Mechanical Systems and Signal Processing, vol. 162, no. 1, 108050, 2022.

    Article  Google Scholar 

  43. T. Liu, X. Wang, J. Zhao, P. K. Wong, and Y. Wang, “Robust H-infinity fuzzy output feedback control for path following of FWID-EVs with actuator saturation,” International Journal of Fuzzy Systems, vol. 25, pp. 1674–1688, 2023.

    Article  Google Scholar 

  44. M. Tica, G. Dobre, G. Barbaraci, and G. V. Mariotti, “Optimal damping constant of the quarter car shock absorber,” Proc. of the 4th International Conference on Power Transmissions, pp. 1–14, 2012.

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Shenyang Jianzhu University, No. 25, Hunnan East Road, Hunnan District, Shenyang, China

    Chunyu Wei

Authors
  1. Chunyu Wei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chunyu Wei.

Ethics declarations

The author declares that there is no competing financial interest or personal relationship that could have appeared to influence the work reported in this paper.

Additional information

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

Chunyu Wei received his Ph.D. degree in mechanical engineering from Zhejiang University in 2013. His research interests include modeling and simulation of mechanical dynamics, vehicle dynamics, vibration control, and intelligent manufacturing.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wei, C. Modeling and Simulation of Active Half-vehicle Suspension Based on a New Output-feedback H∞ Controller. Int. J. Control Autom. Syst. 22, 775–784 (2024). https://doi.org/10.1007/s12555-022-0829-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-022-0829-6

Keywords

Search

Navigation