Output Feedback Sliding Mode Control of Uncertain Systems in the Presence of State Delay with Applications

  • X. Han
  • E. Fridman
  • S. K. Spurgeon
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 412)

Abstract

This chapter considers the development of sliding mode control strategies for linear, time delay systems with bounded disturbances that are not necessarily matched. The emphasis is on the development of frameworks that are constructive and applicable to real problems. For many systems it may not be practical to measure all the system states and therefore a static output feedback sliding mode control design paradigm is considered. The novel feature of the method is that Linear Matrix Inequalities (LMIs) are derived to compute solutions to both the existence problem and the finite time reachability problem that minimize the ultimate bound of the reduced-order sliding mode dynamics in the presence of time varying delay and unmatched disturbances. The methodology is therefore constructive and provides guarantees on the level of closed-loop performance that will be achieved by uncertain systems which experience delay. An uncertain model with both matched and unmatched disturbances from the literature provides a tutorial example of the proposed method. A case study involving the practical application of the design methodology in the area of liquid monopropellant rocket motor control is also presented.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Benton, R.E., Smith, D.A.: A static-output feedback design procedure for robust emergency lateral control of a highway vehicle. IEEE Trans. Automatic Control Syst. Technol. 13, 618–623 (2005)CrossRefGoogle Scholar
  2. 2.
    Brockman, M.L., Corless, M.: Quadratic boundedness of nominally linear systems. Int. J. Control 71, 1105–1117 (1998)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Cao, Y.Y., Lam, J., Sun, Y.X.: Static output feedback stabilization: An ILMI approach. Automatica 34, 1641–1645 (1998)MATHCrossRefGoogle Scholar
  4. 4.
    Choi, H.H.: Variable structure output feedback control for a class of uncertain dynamic systems. Automatica 38, 335–341 (2002)MATHCrossRefGoogle Scholar
  5. 5.
    Crusius, C.A.R., Trofino, A.: Sufficient LMI conditions for output feedback control problems. IEEE Trans. Automatic Control 44, 1053–1057 (1999)MathSciNetMATHCrossRefGoogle Scholar
  6. 6.
    Edwards, C.: A practical method for the design of sliding mode controllers using linear matrix inequalities. Automatica 40, 1761–1769 (2004)MATHCrossRefGoogle Scholar
  7. 7.
    Edwards, C., Akoachere, A., Spurgeon, S.K.: Sliding mode output feedback controller design using linear matrix inequalities. IEEE Trans. Automatic Control 46, 115–119 (2001)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Edwards, C., Spurgeon, S.K.: Sliding mode stabilization of uncertain systems using only output information. Int. J. Control 62, 1129–1144 (1995)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    El-Khazali, R., Decarlo, R.A.: Output feedback variable sturcture controllers. IEEE Trans. Automatic Control 31, 805–816 (1995)MathSciNetMATHGoogle Scholar
  10. 10.
    Fernando, C., Fridman, L.: Analysis and Design of Integral Sliding Manifolds for Systems With Unmatched Perturbations. IEEE Trans. Automatic Control 51, 853–858 (2006)CrossRefGoogle Scholar
  11. 11.
    Fridman, E.: New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems. Systems Control Letters 42, 233–240 (2001)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Fridman, E., Dambrine, M.: Control under Quantization, Saturation and Delay: A LMI approach. Automatica 10, 2258–2264 (2009)CrossRefGoogle Scholar
  13. 13.
    Fridman, E., Dambrine, M., Yeganefar, N.: On matrix inequalities approach to input to state stability. Automatica 44, 2364–2369 (2008)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Gouaisbaut, F., Dambrine, M., Richard, J.P.: Robust control of delay systems: a sliding mode control design via LMI. Systems and Control Letters 46, 219–230 (2002)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Han, X., Fridman, E., Spurgeon, S.K., Edwards, C.: On the design of sliding mode static output feedback controllers for systems with state delay. IEEE Trans. Industrial Electronics 56, 3656–3664 (2009)CrossRefGoogle Scholar
  16. 16.
    He, Y., Wang, Q.G., Lin, C., Wu, M.: Delay range dependent stability for systems with time-varying delay. Automatica 43, 371–376 (2007)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Huang, D., Nguang, S.K.: Robust H  ∞  static output feedback control of fuzzy systems: An ILMI approach. IEEE Trans. Syst. 36, 216–222 (2006)Google Scholar
  18. 18.
    Jafarov, E.M.: Robust sliding mode controller design techniques for stabilisation of multivariable time-delay systems with parameter perturbations and external disturbances. International Journal of Systems Science 36, 433–444 (2005)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Li, X., DeCarlo, R.A.: Robust sliding mode control of uncertain time delay systems. Int. J. Control 76, 1296–1305 (2003)MathSciNetMATHCrossRefGoogle Scholar
  20. 20.
    Shaked, U.: An LPD approach to robust H 2 and H  ∞  static output feedback design. IEEE Trans. Automatic Control 48, 866–872 (2003)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Seuret, A., Edwards, C., Spurgeon, S., Fridman, E.: Static output feedback sliding mode control design via an artificial stabilizing delay. IEEE Trans. Automatic Control 54, 256–265 (2009)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, New York (1992)MATHGoogle Scholar
  23. 23.
    Xiang, J., Wei, W., Su, H.: An ILMI approach to robust static output feedback sliding mode control. Int. J. Control 79, 1930–1935 (2006)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Xie, L., Fridman, E., Shaked, U.: Robust H  ∞  control of distributed delay systems with application to combustion control. IEEE Trans. Automatic Conrol 46, 1930–1935 (2001)MathSciNetMATHCrossRefGoogle Scholar
  25. 25.
    Zak, S.H., Hui, S.: On variable structure output feedback controllers for uncertain dynamic systems. IEEE Trans. Automatic Control 38, 1509–1512 (1993)MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Zheng, F., Cheng, M., Gao, W.: Variable Structure Control of Time-delay Systems with a Simulation Study on Stabilizing Combustion in Liquid Propellant Rocket Motors. Automatica 31, 1031–1037 (1995)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • X. Han
    • 1
  • E. Fridman
    • 2
  • S. K. Spurgeon
    • 1
  1. 1.Instrumentation, Control and Embedded Systems Research Group, School of Engineering and Digital ArtsKent UniversityKentUK
  2. 2.School of Electrical EngineeringTel Aviv UniversityTel AvivIsrael

Personalised recommendations