Skip to main content
Log in

Adaptive vehicle posture and height synchronization control of active air suspension systems with multiple uncertainties

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

Abstract

This paper addresses the tasks of height and posture motion control for an electronically controlled active air suspension (AAS) system. A mathematical model of a vehicle body with AAS system is established to describe the dynamic characteristics and then formulated into a multi-input multi-output nonlinear system by considering parametric uncertainties and unmodelled dynamics. Based on this mathematical model, a synchronization control strategy is proposed to adjust the heights of adjacent AASs simultaneously, driving the pitch and roll angles closely to an arbitrarily neighborhood of zero, achieving global uniform ultimate boundedness. The proposed controller is robust to parametric uncertainties and external disturbances. A projection operator is utilized to limit the estimated parameters to their corresponding prescribed bounds in finite time. A co-simulation is conducted by combining a virtual vehicle plant with ASS system in AMEsim with the proposed synchronization controller in MATLAB/Simulink. Simulation results demonstrate that the proposed synchronization controller is effective and robust.

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

Access this article

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

Instant access to the full article PDF.

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. Aly, A.A., Salem, F.A.: Vehicle suspension systems control: a review. Int. J. Control Autom. Syst. 2(2), 46–54 (2013)

    Google Scholar 

  2. Zhao, J., Wong, P.K., Ma, X.B., Xie, Z.C.: Chassis integrated control for active suspension, active front steering and direct yaw moment systems using hierarchical strategy. Veh. Syst. Dyn. 55(1), 72–103 (2017)

    Google Scholar 

  3. Zhao, J., Wong, P.K., Xie, Z.C., Wei, C.Y., He, F.: Integrated variable speed-fuzzy PWM control for ride height adjustment of active air suspension systems. In: Proceedings of the American Control Conference, pp. 1–3, Chicago, America (2015)

  4. Zhao, J., Wong, P.K., Xie, Z.C., Ma, X.B., Hua, X.: Design and control of an automotive variable hydraulic damper using cuckoo search optimized PID method. Int. J. Autom. Technol. 20(1), 51–63 (2019)

    Google Scholar 

  5. Ma, X.B., Wong, P.K., Zhao, J., Xie, Z.C.: Cornering stability control for vehicles with active front steering system using TS fuzzy based sliding mode control strategy. Mech. Syst. Signal Process. 125, 347–364 (2019)

    Google Scholar 

  6. Braun, J.: Race Track Development of a Hydraulic Ride Height Control System. SAE Technical Paper (1996)

  7. Kim, H., Lee, H., Kim, H.: Asynchronous and synchronous load levelling compensation algorithm in air spring suspension. In: Proceedings of the International Conference Control, Automatic Systems, Seoul, South Korea (2007)

  8. Kim, H., Lee, H.: Height and levelling control of automotive air suspension system using sliding mode approach. IEEE Trans. Veh. Technol. 60(5), 2027–2041 (2011)

    Google Scholar 

  9. Sun, X.Q., Cai, Y.F., Chen, L., Liu, Y.L., Wang, S.H.: Vehicle height and posture control of the electronic air suspension system using the hybrid system approach. Veh. Syst. Dyn. 54(3), 328–352 (2016)

    Google Scholar 

  10. Zhao, J., Wong, P.K., Xie, Z.C., Wei, C.Y., Zhao, R.C.: Design and evaluation of a rode comfort of based suspension system using an optimal stiffness-determination method. Trans. Can. Soc. Mech. Eng. 40(5), 773–785 (2016)

    Google Scholar 

  11. Sun, X.Q., Cai, Y.F., Wang, S.H., Liu, Y.L., Chen, L.: Design of a hybrid model predictive controller for the vehicle height adjustment system of an electronic air suspension. Proc. IMechE. D J. Automob. Eng. 230(11), 1504–1520 (2016)

    Google Scholar 

  12. Ma, X.B., Wong, P.K., Zhao, J., Zhong, J.H., Huang, Y., Xu, X.: Design and testing of a nonlinear model predictive controller for ride height control of automotive semi-active air suspension systems. IEEE Access 6, 63777–63793 (2018)

    Google Scholar 

  13. Chang, F., Lu, Z.H.: Dynamic model of an air spring and integration into a vehicle dynamics model. Proc. IMechE. D J. Automob. Eng. 222(10), 1813–1825 (2008)

    Google Scholar 

  14. Lee, S.J.: Development and analysis of an air spring model. Int. J. Automot. Technol. 11(4), 471–479 (2010)

    Google Scholar 

  15. Löcken, F., Welsch, M.: The dynamic characteristic and hysteresis effect of an air spring. Int. J. Appl. Mech. Eng. 20(1), 127–145 (2015)

    Google Scholar 

  16. Qin, Y.C., Wang, Z.F., Xiang, C.L., Hashemi, E., Khajepour, A., Huang, Y.J.: Speed independent road classification strategy based on vehicle response: theory and experimental validation. Mech. Syst. Sig. Process. 117, 653–666 (2019)

    Google Scholar 

  17. Qin, Y.C., Wang, Z.F., Xiang, C.L., Dong, M.M., Hu, C., Wang, R.R.: A novel global sensitivity analysis on the observation accuracy of the coupled vehicle model. Veh. Syst. Dyn. 57(10), 1445–1466 (2019)

    Google Scholar 

  18. Nieto, A.J., Morales, A.L., Gonzalez, A., Chicharro, J.M., Pintado, P.: An analytical model of pneumatic suspensions based on an experimental characterization. J. Sound Vib. 313(1), 290–307 (2008)

    Google Scholar 

  19. Carneiro, J.F., de Almeida, F.G.: Reduced-order thermodynamic models for servo-pneumatic actuator chambers. Proc. IMechE. I J. Syst. Control Eng. 220(4), 301–314 (2006)

  20. Wong, P.K., Xie, Z.C., Zhao, J., Xu, T., He, F.: Analysis of automotive rolling lobe air spring under alternative factors with finite element model. J. Mech. Sci. Technol. 28(12), 5069–5081 (2014)

    Google Scholar 

  21. Zhao, R.C., Xie, W., Wong, P.K., Cabecinhas, D., Silvestre, C.: Robust ride height control for active air suspension systems with multiple unmodeled dynamics and parametric uncertainties. IEEE Access 7, 59185–59199 (2019)

    Google Scholar 

  22. Lee, H.K., Choi, G.S., Choi, G.H.: A study on tracking position control of pneumatic actuators. Mechatronics 12(64), 813–831 (2002)

    Google Scholar 

  23. Taghizadeh, M., Najafi, F., Ghaffari, A.: Multimodel PD-control of a pneumatic actuator under variable loads. Int. J. Adv. Manuf. Technol. 48(5–8), 655–662 (2010)

    Google Scholar 

  24. Boubakir, A., Plestan, F., Labiod, S., Boudjema, F.: Design and experimentation of an observer-based linear adaptive control applied to an electropneumatic actuator. IET Control Theory Appl. 10(11), 1288–1298 (2016)

    Google Scholar 

  25. Boubakir, A., Plestan, F., Labiod, S., Boudjema, F.: Design and experimental study of a dynamical adaptive backstepping-sliding mode control scheme for position tracking and regulating of a low-cost pneumatic cylinder. Int. J. Robust Nonlinear Control 26(4), 853–875 (2016)

    Google Scholar 

  26. Zhao, F., Ge, S.S., Tu, F.W., Qin, Y.C., Dong, M.M.: Adaptive neural network control for active suspension system with actuator saturation. IET Control Theory Appl. 10(14), 1696–1705 (2016)

    Google Scholar 

  27. Tsai, Y.C., Huang, A.C.: Multiple-surface sliding controller design for pneumatic servo systems. Mechatronics 18(9), 506–512 (2008)

    Google Scholar 

  28. Girin, A., Plestan, F., Brun, X., Glumineau, A.: High-order sliding-mode controllers of an electropneumatic actuator: application to an aeronautic benchmark. IEEE Trans. Control Syst. Technol. 17(3), 633–645 (2009)

    Google Scholar 

  29. Sun, X.Q., Cai, Y.F., Yuan, C.C., Wang, S.H., Chen, L.: Fuzzy sliding mode control for the vehicle height and levelling adjustment system of an electronic air suspension. Chin. J. Mech. Eng. 31(25), UNSP25 (2018)

  30. Smaoui, M., Brun, X., Thomasset, D.: A study on tracking position control of an electropneumatic system using backstepping design. Control Eng. Pract. 14(8), 923–933 (2006)

    Google Scholar 

  31. Rao, Z., Bone, G.M.: Nonlinear modeling and control of servo pneumatic actuators. IEEE Trans. Control Syst. Technol. 16(3), 562–569 (2008)

    Google Scholar 

  32. Taheri, B., Case, D., Richer, E.: Force and stiffness backstepping-sliding mode controller for pneumatic cylinders. IEEE/ASME Trans. Mechatron. 19(6), 1799–1809 (2014)

    Google Scholar 

  33. Meng, D.Y., Tao, G.L., Li, A.M., Li, W.: Precision synchronization motion trajectory tracking control of multiple pneumatic cylinders. Asian J. Control 18(5), 1749–1764 (2016)

    Google Scholar 

  34. Koren, Y.: Cross-coupled biaxial computer control for manufacturing systems. J. Dyn. Syst. Meas. Contr. 102(4), 265–272 (1980)

    Google Scholar 

  35. Sun, D.: Position synchronization of multiple motion axes with adaptive coupling control. Automatica 39(6), 997–1005 (2003)

    Google Scholar 

  36. Pan, H.H., Sun, W.C., Gao, H.J., Jing, X.J.: Disturbance observer-based adaptive tracking control with actuator saturation and its application. IEEE Trans. Autom. Sci. Eng. 13(2), 868–875 (2016)

    Google Scholar 

  37. Sun, W.C., Liu, Y.B., Gao, H.J.: Constrained sampled-data arc for a class of cascaded nonlinear systems with applications to motor-servo systems. IEEE Trans. Ind. Appl. 15(2), 766–775 (2019)

    Google Scholar 

  38. Yao, B., Tomizuka, M.: Adaptive robust control of MIMO nonlinear systems in semi-strict feedback forms. Automatica 38(9), 1305–1321 (2001)

    Google Scholar 

  39. Cai, Z., de Queiroz, M.S., Dawson, D.M.: A sufficiently smooth projection operator. IEEE Trans. Autom. Control 51(1), 135–139 (2006)

    Google Scholar 

  40. Polycarpou, M.M.: Stable adaptive neural control scheme for nonlinear systems. IEEE Trans. Autom. Control 41(3), 447–451 (1996)

    Google Scholar 

Download references

Acknowledgements

This study was funded by the University of Macau Research Grant (Grant Numbers MYRG-2016-00212-FST, MYRG-2017-00135-FST and MYRG-2018-00198-FST), and by the Portuguese Fundação para a Ciência e a Tecnologia (FCT) through ISR (Grant Number LARSyS UID/EEA/50009/2019).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pak Kin Wong.

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

Zhao, R., Xie, W., Wong, P.K. et al. Adaptive vehicle posture and height synchronization control of active air suspension systems with multiple uncertainties. Nonlinear Dyn 99, 2109–2127 (2020). https://doi.org/10.1007/s11071-019-05412-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05412-9

Keywords

Navigation