Journal of Vibration Engineering & Technologies

, Volume 6, Issue 6, pp 441–451 | Cite as

Constrained Active Suspension Control with Parameter Uncertainty for Non-stationary Running Based on LMI Optimization

  • Li-Xin GuoEmail author
  • Li-Ping Zhang
Original Paper



The research on a constrained robust H control of half-car active suspension-based linear matrix inequality (LMI) optimization method was carried out for non-stationary vehicle running conditions in this study.


The H state feedback controller of active vehicle suspension system was proposed which contains the time-domain hard constraints and differential equation model of the half-car control system with parameter uncertainty for non-stationary running was established.


The results of vehicle dynamics analysis indicate that the dynamic performance of this half-car active suspension controlled by the proposed control strategy is obviously superior to the performances of passive suspensions.


The proposed control strategy shows good stability, even though vehicles are in non-stationary running and the actual system parameters (including unsprung mass, suspension rigidity, and tire rigidity) are uncertain. Moreover, besides improving the vehicle ride comfort, the proposed control method can also ameliorate the dynamic flexibility of vehicle suspension system, static-dynamic load ratio response characteristic of vehicle tyres, and requirement of constrained control forces.


Active suspension \(H_{\infty }\) control LMI optimization Parameter uncertainty Half-car model Vehicle ride comfort Parameter perturbation 



The study was financially supported by National Natural Science Foundation of China (51875096, 51275082).


  1. 1.
    Chantranuwathana S, Peng H (2004) Adaptive robust force control for vehicle active suspensions. Int J Adapt Control Signal Process 18:83–102CrossRefGoogle Scholar
  2. 2.
    Chen PC, Huang AC (2006) Adaptive sliding control of active suspension systems with uncertain hydraulic actuator dynamics. Veh Syst Dyn 44:357–368CrossRefGoogle Scholar
  3. 3.
    Sankaranarayanan V, Emekli ME, Guvenc BA et al (2008) Semiactive suspension control of a light commercial vehicle. IEEE/ASME Trans Mechatron 13:598–604CrossRefGoogle Scholar
  4. 4.
    Ma MM, Chen H (2011) Disturbance attenuation control of active suspension with non-linear actuator dynamics. IET Control Theory Appl 5:112–122MathSciNetCrossRefGoogle Scholar
  5. 5.
    Chen H, Guo K-H (2005) Constrained H (infinity) control of active suspensions, an LMI approach. IEEE Trans Control Syst Technol 13:412–421CrossRefGoogle Scholar
  6. 6.
    Hrovat D (1993) Applications of optimal control to advanced automotive suspension design. ASME J Dyn Syst Meas Control 115:328–342CrossRefGoogle Scholar
  7. 7.
    Ulsoy A, Hrovat D, Tseng T (1994) Stability robustness of LQ and LQG active suspensions. ASME J Dyn Syst Meas Control 116:123–131CrossRefGoogle Scholar
  8. 8.
    Huang J, Chen HY (2006) Adaptive sliding controller with self-tuning fuzzy compensation for vehicle suspension control. Mechatronics 16:607–622CrossRefGoogle Scholar
  9. 9.
    Yahaya MS, Johari HS (2004) A class of proportional-integral sliding mode control with application to active suspension system. Syst Control Lett 51:217–223MathSciNetCrossRefGoogle Scholar
  10. 10.
    Yoshimura T, Konishi H (2007) Active suspension design of a one-wheel car model using adaptive sliding mode control. Int J Veh Syst Model Test 2:193–207Google Scholar
  11. 11.
    Guida D, Pappalardo CM (2015) Control design of an active suspension system for a quarter-car model with hysteresis. J Vib Eng Technol 3(3):277–299Google Scholar
  12. 12.
    Kalaivani R, Lakshmi P, Rajeswari K (2015) An improved type-2 fuzzy logic approach based sliding mode controller for vehicle active suspension system. J Vib Eng Technol 3(4):431–446Google Scholar
  13. 13.
    Liu ZY, Wagner J (2002) Nonlinear model reduction for dynamic and automotive system descriptions. ASME J Dyn Syst Meas Control 124:637–647CrossRefGoogle Scholar
  14. 14.
    Metered H, Bonello P, Oyadiji SO (2010) An investigation into the use of neural networks for the semi-active control of a magnetorheologically damped vehicle suspension. Proc Inst Mech Eng Part D J Autom Eng 224(D7):829–848CrossRefGoogle Scholar
  15. 15.
    Lin J, Lian RJ (2011) Intelligent control of active suspension systems. IEEE Trans Ind Electron 58(2):618–628MathSciNetCrossRefGoogle Scholar
  16. 16.
    Jin Y, Yu D, Song X (2007) An integrated-error-based adaptive neuron control and its application to vehicle suspension systems. In: Proc. IEEE Int. Conf. Contr. Automat, pp 564-569, 2007Google Scholar
  17. 17.
    Alleyne A, Hedrick J (1995) Nonlinear adaptive control of active suspension. IEEE Trans Control Syst Technol 3:91–101CrossRefGoogle Scholar
  18. 18.
    Lin J-S, Kannellakopoulos I (1997) Nonlinear design of active suspensions. IEEE Control Syst Mag 17:45–49CrossRefGoogle Scholar
  19. 19.
    Fialho I, Balas GJ (2002) Road adaptive active suspension design using linear parameter-varying gain-scheduling. IEEE Trans Control Syst Technol 10:43–54CrossRefGoogle Scholar
  20. 20.
    Du HP, Zhang N (2007) H∞ control of active vehicle suspensions with actuator time delay. J Sound Vib 301:236–252MathSciNetCrossRefGoogle Scholar
  21. 21.
    Lu Z, Wang H, Yao HL, Liu J, Hu Z (2015) A quasi-static method for predicting vehicle-road coupling vibration generated by pavement unevenness. J Vib Eng Technol 3(2):223–236Google Scholar
  22. 22.
    Li H, Gao H, Liu H (2011) Robust quantised control for active suspension systems. IET Control Theory Appl 5(17):1955–1969MathSciNetCrossRefGoogle Scholar
  23. 23.
    Smith M, Wang F-C (2002) Controller parameterization for disturbance response decoupling, application to vehicle active suspension control. IEEE Trans Control Syst Technol 10:393–407CrossRefGoogle Scholar
  24. 24.
    Akçay H, Türkay S (2009) Influence of tire damping on mixed H2/H∞ synthesis of half-car active suspensions. J Sound Vib 322:15–28CrossRefGoogle Scholar
  25. 25.
    Sun WC, Gao HJ, Kaynak O (2011) Finite frequency H∞ control for vehicle active suspension systems. IEEE Trans Control Syst Technol 19:416–422CrossRefGoogle Scholar
  26. 26.
    Moradi M, Fekih A (2015) A stability guaranteed robust fault tolerant control design for vehicle suspension systems subject to actuator faults and disturbances. IEEE Trans Control Syst Technol 23(3):1164–1171CrossRefGoogle Scholar
  27. 27.
    Wang RR, Jing H, Karimi HR, Chen N (2015) Robust fault-tolerant H-infinity control of active suspension systems with finite-frequency constraint. Mech Syst Signal Process 62–63(10):341–355CrossRefGoogle Scholar
  28. 28.
    Boyd S, Ghaoui LE, Feron E, Balakishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, PhiladelphiaCrossRefGoogle Scholar
  29. 29.
    Scherer C, Gahinet P, Chilali M (1997) Multi-objective output-feedback control via LMI optimization. IEEE Trans Autom Control 42:896–911CrossRefGoogle Scholar
  30. 30.
    Gobbi M, Levi F, Mastinu G (2006) Multi-objective stochastic optimization of the suspension system of road vehicles. J Sound Vib 298:1055–1072CrossRefGoogle Scholar
  31. 31.
    Savaresi S, Silani E, Bittanti S (2005) Acceleration-driven-damper (ADD): an optimal control algorithm for comfort-oriented semi-active suspensions. J Dyn Syst Meas Control 127:218–229CrossRefGoogle Scholar

Copyright information

© Krishtel eMaging Solutions Private Limited 2018

Authors and Affiliations

  1. 1.School of Mechanical Engineering and AutomationNortheastern UniversityShenyangChina
  2. 2.School of Automobile and Traffic EngineeringLiaoning University of TechnologyJinzhouChina

Personalised recommendations