Skip to main content
SpringerLink
Log in

Control of active suspension system considering nonlinear actuator dynamics

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

Abstract

Application of the state-dependent Riccati equation and approximating sequence of Riccati equation techniques for the control of active suspension system considering nonlinear actuator dynamics will be investigated. First, equation of motion of the vehicle model is written in terms of the nonlinear state equations. Then, a performance index is formed for the minimization of the acceleration of the sprung mass, suspension deflection, velocity of the sprung mass, tire deflection, velocity of the unsprung mass, pressure decrease through the piston, and rate of pressure decrease through the piston. A sinusoidal bump and road roughness are considered as the road disturbances. After that, control input is expressed in terms of the Riccati differential equation variables and the state variables. Finally, quarter vehicle suspension system model of a Ford Fiesta Mk2 is taken into consideration in numerical simulations to test the performances of the both techniques. The results are compared to those of equivalent passive suspension system.

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

Similar content being viewed by others

References

  1. Rajamani, R., Hedrick, J.K.: Adaptive observers for active automotive suspensions: theory and experiment. IEEE Trans. Control Syst. Technol. 3(1), 86–93 (1995)

    Article  Google Scholar 

  2. Dangor, M., Dahunsi, O.A., Pedro, J.O., Ali, M.M.: Evolutionary algorithm-based PID controller tuning for nonlinear quarter-vehicle electrohydraulic vehicle suspensions. Nonlinear Dyn. 78, 2795–2810 (2014)

    Article  Google Scholar 

  3. Renn, J.-C., Wu, T.-H.: Modeling and control of a new 1/4T servo-hydraulic vehicle active suspension system. J. Mar. Sci. Technol. 15(3), 265–272 (2007)

    Google Scholar 

  4. Alleyne, A., Liu, R.: A simplified approach to force control for electro-hydraulic systems. Control Eng. Pract. 8, 1347–1356 (2000)

    Article  Google Scholar 

  5. Alleyne, A., Hedrick, J.K.: Nonlinear adaptive control of active suspensions. IEEE Trans. Control Syst. Technol. 3(1), 94–101 (1995)

    Article  Google Scholar 

  6. Chen, P.-C., Huang, A.-C.: Adaptive sliding control of active suspension systems with uncertain hydraulic actuator dynamics. Veh. Syst. Dyn. 44(5), 357–368 (2006)

    Article  Google Scholar 

  7. Lin, J., Lian, R.-J., Huang, C.-N., Sie, W.-T.: Enhanced fuzzy sliding mode controller for active suspension systems. Mechatronics 19, 1178–1190 (2009)

    Article  Google Scholar 

  8. Lin, J.-S., Kanellakopoulos, I.: Nonlinear design of active suspensions. IEEE Control Syst. Mag. 17, 45–49 (1997)

    Article  Google Scholar 

  9. Fialho, I., Balas, G.J.: Road adaptive active suspension design using linear parameter-varying gain-scheduling. IEEE Trans. Control Syst. Technol. 10(1), 43–54 (2002)

    Article  Google Scholar 

  10. Gaspar, P., Szabo, Z., Szederkenyi, G., Bokor, J.: Design of a two-level controller for an active suspension system. Asian J. Control 14(3), 664–678 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  11. Bui, T.H., Suh, J.H., Kim, S.B., Nguyen, T.T.: Hybrid control of an active suspension system with full-vehicle model using H\(\infty \), and nonlinear adaptive control methods. KSME Int. J. 16(12), 1613–1626 (2002)

    Article  Google Scholar 

  12. Fateh, M.M., Zirkohi, M.M.: Adaptive impedance control of a hydraulic suspension system using particle swarm optimisation. Veh. Syst. Dyn. 49(12), 1951–1965 (2011)

    Article  Google Scholar 

  13. Chantranuwathana, S., Peng, H.: Adaptive robust force control for vehicle active suspensions. Int. J. Adapt. Control Signal Process. 18, 83–102 (2004)

    Article  Google Scholar 

  14. Sun, W., Gao, H., Yao, B.: Adaptive robust vibration control of full-vehicle active suspensions with electrohydraulic actuators. IEEE Trans. Control Syst. Technol. 21(6), 2417–2422 (2013)

    Article  Google Scholar 

  15. Du, H., Zhang, N.: Fuzzy control for nonlinear uncertain electrohydraulic active suspensions with input constraint. IEEE Trans. Fuzzy Syst. 17(2), 343–356 (2009)

    Article  Google Scholar 

  16. Lin, J., Lian, R.-J.: Intelligent control of active suspension systems. IEEE Trans. Ind. Electr. 58(2), 618–628 (2011)

    Article  MathSciNet  Google Scholar 

  17. Cloutier, J.R., D’Souza, C.N., Mracek C.P.: Nonlinear regulation and nonlinear H\(\infty \) control via the state-dependent Riccati equation technique: part 1, theory; part 2, examples. In: First International Conference on Nonlinear Problems in Aviation and Aerospace, Daytona Beach, FL, USA, pp. 117–141 (1996)

  18. Mracek, C.P., Cloutier, J.R.: Control designs for the nonlinear benchmark problem via the state-dependent Riccati equation method. Int. J. Robust Nonlinear Control 8, 401–433 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  19. Cloutier, J.R., Stansbery, D.T.: The capabilities and art of state-dependent Riccati equation-based design. In: American Control Conference, Anchorage, AK, USA, pp. 86–91 (2002)

  20. Shamma, J.S., Cloutier, J.R.: Existence of SDRE stabilizing feedback. IEEE Trans. Autom. Control 48, 513–517 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  21. Cimen, T.: Systematic and effective design of nonlinear feedback controllers via the state-dependent Riccati equation (SDRE) method. Ann. Rev. Control 34, 32–51 (2010)

    Article  Google Scholar 

  22. Cimen, T.: Survey of state-dependent Riccati equation in nonlinear optimal feedback control synthesis. J. Guid. Control Dyn. 35(4), 1025–1047 (2012)

    Article  Google Scholar 

  23. Banks, S.P., Dinesh, K.: Approximate optimal control and stability of nonlinear finite and infinite-dimensional systems. Ann. Oper. Res. 98, 19–44 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  24. Tomas-Rodriguez, M., Banks, S.P.: Linear approximations to nonlinear dynamical systems with applications to stability and spectral theory. IMA J. Math. Control Inf. 20, 89–103 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  25. Cimen, T., Banks, S.P.: Global optimal feedback control for general nonlinear systems with nonquadratic performance criteria. Syst. Control Lett. 53(5), 327–346 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  26. Cimen, T., Banks, S.P.: Nonlinear optimal tracking control with application to super-tankers for autopilot design. Automatica 40(11), 1845–1863 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  27. Kilicaslan, S., Banks, S.P.: A separation theorem for nonlinear systems. Automatica 45(4), 928–935 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  28. Kilicaslan, S., Banks, S.P.: Existence of solutions of Riccati differential equations. J. Dyn. Syst. Meas. Control Trans. ASME 134, 031001 (2012)

    Article  Google Scholar 

  29. Banks, H.T., Lewis, B.M., Tran, H.T.: Nonlinear feedback controllers and compensators: a state-dependent Riccati equation approach. Comput. Optim. Appl. 37, 177–218 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Merritt, H.E.: Hydraulic Control Systems. Wiley, New York (1967)

    Google Scholar 

  31. Giua, A., Melas, M., Seatzu, C., Usai, G.: Design of a predictive semiactive suspension system. Veh. Syst. Dyn. 41(4), 277–300 (2004)

    Article  Google Scholar 

  32. Pedro, J., Ekoru, J.: NARMA-L2 control of a nonlinear half-car servo-hydraulic vehicle suspension system. Acta Polytech. Hung. J. Appl. Sci. 10(4), 5–26 (2013)

    Google Scholar 

  33. Pedro, J.O., Dangor, M., Dahunsi, O.A., Ali, M.: Differential evolution-based PID control of nonlinear full-car electrohydraulic suspensions. Math. Probl. Eng. 2013, 1–13, Article ID 261582

  34. Pedro, J.O., Dahunsi, O.A.: Neural network-based feedback linearization control of a servo-hydraulic vehicle suspension system. Int. J. Appl. Math. Comput. Sci. 21(1), 137–147 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  35. Du, H., Zhang, N.: Static output feedback control for electrohydraulic active suspensions via T-S fuzzy model approach. J. Dyn. Syst. Meas. Control Trans. ASME 131(5), 051004 (2009)

    Article  Google Scholar 

  36. Gysen, B.L.J., Paulides, J.J.H., Janssen, J.L.G., Lomonova, E.A.: Active electromagnetic suspension system for improved vehicle dynamics. IEEE Trans. Veh. Technol. 59(3), 1156–1163 (2010)

    Article  Google Scholar 

  37. Griffin, M.J.: Discomfort from feeling vehicle vibration. Veh. Syst. Dyn. 45(7–8), 679–698 (2007)

    Article  Google Scholar 

  38. European Commission: Directive 2002/44/EC of the European Parliament and the Council of 25 June 2002 on the minimum health and safety requirements regarding the exposure of workers to the risk arising from physical agents (vibration). Official Journal of the European Communities, Luxembourg (2002)

  39. ISO 2631: Mechanical Vibration and Shock-Evaluation of Human Exposure to Whole-Body Vibration-Part 1: General Requirements. International Organization for Standardization, Geneva, Switzerland (2003)

  40. Beltran-Carbajal, F., Chavez-Conde, E., Favela-Contreras, A., Chavez-Bracamontes, R.: Active nonlinear vehicle suspension based on real time estimation of perturbation signals. In: Proceedings of the 2011 IEEE International Conference on Industrial Technology (ICIT), Auburn, AL, USA, vol. s, pp. 437–442, Mart 14–16 (2011)

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Faculty of Engineering, Gazi University, Ankara, Turkey

    Sinan Kilicaslan

Authors
  1. Sinan Kilicaslan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sinan Kilicaslan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kilicaslan, S. Control of active suspension system considering nonlinear actuator dynamics. Nonlinear Dyn 91, 1383–1394 (2018). https://doi.org/10.1007/s11071-017-3951-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-017-3951-x

Keywords

Search

Navigation