Skip to main content
SpringerLink
Log in

Robust control design for active suspension system with uncertain dynamics and actuator time delay

  • Original Article
  • Published:
Journal of Mechanical Science and Technology Aims and scope Submit manuscript

Abstract

The control performance of the vehicle will degrade due to the uncertain dynamics between the mathematical nominal plant description and the actual physical system. A robust control scheme is designed for an active suspension system so as to improve the system control performance. In the design of a robust control scheme, the real parametric uncertainties, as well as the structural uncertainty and time delay of the actuator, are taken into account, which is more realistic than the traditional control methods. Robustness performance and stability of the system are investigated and discussed in the paper. The μ synthesis controller is designed and compared with the H∞ control algorithm as well as the traditional passive suspension system. The control performance is validate under two typical road excitation conditions including the random road and the speed bump road. Simulation results show the effectiveness of the proposed control schemes compared to a H∞ approach.

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

Abbreviations

f s :

Active suspension force from hydraulic actuator

s d :

Suspension deflection (m)

a b :

Vehicle body vertical acceleration (m/s2)

F U :

Upper linear fractional transformation (LFT) function

e p :

Weighted evaluation values of vehicle performance

d 1, d 2 :

Noises from measurement sensors

x b :

Sprung mass displacement (m)

x w :

Un-spring mass displacement (m)

K(s):

The feedback gain of active suspension controller

y :

Measurement state information form sensors, y = [xs − xu; ẍs]

References

  1. J.-S. Lin and K. Ioannis, Nonlinear design of active suspensions, IEEE Control System, 17 (3) (1997) 45–59.

    Article  Google Scholar 

  2. C. W. Lim, Y. J. Park and S. J. Moon, Robust saturation controller for linear time-invariant system with structured real parameter uncertainties, Journal of Sound and Vibration, 294 (1) (2006) 1–14.

    Article  MathSciNet  MATH  Google Scholar 

  3. T. Van der Sande, P. Zegelaar, I. Besselink and H. Nijmeijer, A robust control analysis for a steer-by-wire vehicle with uncertainty on the tyre forces, Vehicle System Dynamics, 54 (9) (2016) 1247–1268.

    Article  Google Scholar 

  4. J. Busch and B. Dieter, Optimisation of lateral car dynamics taking into account parameter uncertainties, Vehicle System Dynamics, 52 (2) (2014) 166–185.

    Article  Google Scholar 

  5. S.-B. Choi and S.-S. Han, H∞ control of electrorheological suspension system subjected to parameter uncertainties, Mechatronics, 13 (7) (2003) 639–657.

    Article  Google Scholar 

  6. R. Wang, J. Hui and H. R. Karimi, Robust fault-tolerant H∞ control of active suspension systems with finite-frequency constraint, Mechanical Systems and Signal Processing, 62–63 (10) (2015) 341–355.

    Article  Google Scholar 

  7. W. Sun, Y. Zhao, J. Li, L. Zhang and H. Gao, Active suspension control with frequency band constraints and actuator input delay, IEEE Transactions on Industrial Electronics, 59 (1) (2012) 530–537.

    Article  Google Scholar 

  8. H. Li, J. Yu, C. Hilton and H. Liu, Adaptive sliding-mode control for nonlinear active suspension vehicle systems using T-S fuzzy approach, IEEE Transactions on Industrial Electronics, 60 (8) (2013) 3328–3338.

    Article  Google Scholar 

  9. M. Coric, J. Deur, J. Kasac, H. E. Tseng and D. Hrovat, Optimization of active suspension control inputs for improved vehicle handling performance, Vehicle System Dynamics, International Journal of Vehicle Mechanics and Mobility, 54 (11) (2016) 1574–1600.

    Article  Google Scholar 

  10. W. Sun, H. Gao and K. Okyay, Vibration isolation for active suspensions with performance constraints and actuator saturation, IEEE Transactions on Mechatronics, 20 (2) (2015) 675–683.

    Article  Google Scholar 

  11. B. Xu and Y. Jia, Mixed H2/H∞controller design of multiple constraints vehicle active suspension system, Computer Simulation, 29 (3) (2012) 44–48.

    MathSciNet  Google Scholar 

  12. J. Guan, D. Huo and X. Ji, Sliding mode force tracking control for active hydro-pneumatic suspension, Journal of Vibroengineering, 18 (1) (2016) 458–475.

    Google Scholar 

  13. H. Ren, S. Chen, Y. Zhao, G. Liu and L. Yang, Observer-based hybrid control algorithm for semi-active suspension systems, Journal of Central South University, 23 (9) (2016) 2268–2275.

    Article  Google Scholar 

  14. Y. Hu, M. Z. Q. Chen and Z. Hou, Multiplexed model predictive control for active vehicle suspensions, International Journal of Control, 88 (2) (2015) 347–363.

    Article  MathSciNet  MATH  Google Scholar 

  15. W. Sun, Y. LI, J. Huang and N. Zhang, Efficiency improvement of vehicle active suspension based on multi-objective integrated optimization, Journal of Vibration and Control (2015) 1–16.

  16. S. Kiriczi and R. Kashani, Control of active suspension with parameter uncertainty and non-white road unevenness disturbance input, SAE Technical Paper (1990) 75–81.

  17. B. Lin, X. Su and X. Li, Fuzzy sliding mode control for active suspension system with proportional differential sliding mode observer, Asian Journal of Control, 21 (1) (2019) 264–276.

    Article  MathSciNet  MATH  Google Scholar 

  18. Y. Yang and J. M. Lee, A switching control strategy for nonlinear systems under uncertainty, 2013 13th International Conference on Control, Automation and Systems (ICCAS 2013) (2013) 976–980.

  19. G. Yin, N. Chen and P. Li, Improving handling stability performance of four-wheel steering vehicle via μ-synthesis robust control, IEEE Transactions on Vehicular Technology, 56 (5) (2007) 2432–2439.

    Article  Google Scholar 

  20. M. M. Farsangi, Y. H. Song and M. Tan, Multi-objective design of damping controllers of FACTS devices via mixed H 2/H∞ with regional pole placement, International Journal of Electrical Power and Energy Systems, 25 (5) (2003) 339–346.

    Article  Google Scholar 

  21. D.-W. Gu, P. Petko and M. M. Konstantinov, Robust Control Design with MATLAB®, Springer Science and Business Media (2005).

  22. S. Skogestad and P. Ian, Multivariable Feedback Control: Analysis and Design, New York, Wiley, 2 (2007).

    MATH  Google Scholar 

  23. P. Gaspar, I. Szaszi and J. Bokor, Robust servo control design for mechanical systems using mixed uncertainty modeling, IEEE European Control Conference (2003) 342–347.

  24. Y. J. Cha, A. K. Agrawal and S. J. Dyke, Time delay effects on large-scale MR damper based semi-active control strategies, Smart Materials and Structures, 22 (1) (2012) 1–13.

    Google Scholar 

  25. J. Taylor, Robust bode methods for feedback controller design of uncertain systems, Ph.D. Thesis, Carnegie Mellon University (2014).

  26. G. A. Ingram, M. A. Franchek, V. Balakrishnan and G. Surnilla, Robust SISO H∞ controller design for nonlinear systems, Control Engineering Practice, 13 (11) (2005) 1413–1423.

    Article  Google Scholar 

  27. Gaspar, Peter I. Szaszi and J. Bokor, Design of robust controllers for active vehicle suspension using the mixed μ synthesis, Vehicle System Dynamics, 40 (4) (2003) 193–228.

    Article  Google Scholar 

  28. K. Zhou and J. C. Doyle, Robust and Optimal Control, Prentice Hall, New Jersey (1996).

    MATH  Google Scholar 

  29. Z. C. Wu, S. Z. Chen, L. Yang and B. Zhang, Model of road roughness in time domain based on rational function, Transaction of Beijing Institute of Technology, 29 (9) (2009) 795–798.

    Google Scholar 

  30. R. Hongbin, C. Sizhong and W. Zhicheng, Model of excitation of random road profile in time domain for a vehicle with four wheels, 2011 International Conference on Mechatronic Science, Electric Engineering and Computer (MEC) (2011) 2332–2335.

Download references

Acknowledgments

This work is financially supported by the NSFC Grants 5200 2025.

Author information

Authors and Affiliations

  1. China North Vehicle Research Institute, Beijing, China

    Yunbao Yin, Qiang Fang & Chunsheng Zhang

  2. The UAV Center of the Army Aviation Academy, Beijing, China

    Bo Luo

  3. School of Mechanical Engineering, Beijing Institute of Technology, Beijing, China

    Hongbin Ren

Authors
  1. Yunbao Yin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bo Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hongbin Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Qiang Fang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chunsheng Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hongbin Ren.

Additional information

Yunbao Yin received his M.E. degree in School of Vehicle Engineering, China North Vehicle Research Institute, Beijing, China in 2008. His research interests include vehicle dynamic and control, design and test of active suspension system.

Luo Bo is currently the Deputy Director of the UAV Center of the Army Aviation Institute. He obtained a master’s degree from the Artillery Command Academy in 2009. His research interests are UAV combat application, helicopter/UAV coordination, UAV mission equipment, etc.

Hongbin Ren received Ph.D. degree in Mechanical Engineering from Beijing Institute of Technology. He studied at the University of Michigan in Dearborn, Dearborn, USA, from 2012.10 to 2014.04 as a visiting scholar. Now he is an Assistant Professor in Beijing Institute of Technology. His current research interests include vehicle dynamics, state observer theory, motion planning, optimization, and optimal control.

Qiang Fang received his M.E. degree in School of Vehicle Engineering, China North Vehicle Research Institute, Beijing, China in 2011. His research interests include vehicle dynamic and control, design and test of suspension system.

Chunsheng Zhang received her M.E. degree in School of Vehicle Engineering, China North Vehicle Research Institute, Beijing, China in 2007. Her research interests include vehicle dynamic and control, design and test of suspension system.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yin, Y., Luo, B., Ren, H. et al. Robust control design for active suspension system with uncertain dynamics and actuator time delay. J Mech Sci Technol 36, 6319–6327 (2022). https://doi.org/10.1007/s12206-022-1143-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12206-022-1143-1

Keywords

Search

Navigation