Skip to main content
SpringerLink
Log in

Robust dynamic output feedback second-order sliding mode controller for uncertain systems

  • Regular Paper
  • Control Theory
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm to stabilize a linear MIMO uncertain system having relative degree two. Introducing a suitable dynamic compensator into the sliding variable, the additional degree of freedom can be used to robustly guarantee the closed-loop system stability once the system is in the sliding mode. A modified asymptotically stable second-order sliding mode control is analyzed and the proposed controller can obtain the real second-order sliding mode. Finally, the feasibility of the proposed method is illustrated by a numerical example.

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

References

  1. S. H. Zak and S. Hui, “Output feedback variable structure controllers and state estimators for uncertain/nonlinear dynamic systems,” IEE Proc. D, Control Theory and Applications, vol. 140, no. 1, pp. 41–49, 1993.

    Article  Google Scholar 

  2. S. V. Yallapragada, B. S. Heck, and J. D. Finney, “Reaching condition for variable structure control with output feedback,” Journal of Guidance, Control and Dynamics, vol. 19, no. 4, pp. 848–853, 1996.

    Article  MATH  Google Scholar 

  3. C. M. Kwan, “On variable structure output feedback Controller,” IEEE Trans. Automatic Control, vol. 41, no. 11, pp. 1691–1693, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  4. C. Edwards and S. K. Spurgeon, Sliding Mode Control Theory and Application, Taylor & Francis, London, 1998.

    Google Scholar 

  5. M. C. Pai, “Observer-based adaptive sliding mode control for robust tracking and model following,” International Journal of Control, Automation, and Systems, vol. 11, no. 2, pp. 225–232, 2013.

    Article  Google Scholar 

  6. Q. Khan, A. I. Bhatti, S. Iqbal, and M. Iqbal, “Dynamic integral sliding mode for MIMO uncertain nonlinear systems,” International Journal of Control, Automation, and Systems, vol. 9, no. 1, pp. 151–160, 2011.

    Article  Google Scholar 

  7. H. C. Ting, J. L. Chang, and Y. P. Chen, “Applying output feedback integral sliding mode controller to uncertain time-delay systems with mismatched disturbances,” International Journal of Control, Automation, and Systems, vol. 9, no. 6, pp.1056–1066, 2011.

    Article  Google Scholar 

  8. A. Levant, “Sliding order and sliding accuracy in the sliding mode control,” International Journal of Control, vol. 58, no. 6, pp. 1247–1263, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  9. A. Levant, “High-order sliding mode, differentiation and output-feedback control,” International Journal of Control, vol. 76, no. 9–10, pp. 924–941, 2003.

    Article  MathSciNet  MATH  Google Scholar 

  10. Z. Song and H. Li, “Second-order sliding mode control with backstepping for aeroelastic systems based on finite-time technique,” International Journal of Control, Automation, and Systems, vol. 11, no. 2, pp. 416–421, 2013.

    Article  Google Scholar 

  11. G. Bartolini, A. Ferrara, and E. Usai, “Chattering avoidance by second-order sliding mode control,” IEEE Trans. on Automatic Control, vol. 43, no. 2, pp. 241–246, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  12. A. Levant, “Robust exact differentiation via sliding mode technique,” Automatica, vol. 34, no. 3, pp. 379–384, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  13. J. Davila, L. Fridman, and A. Levant, “Secondorder sliding-mode observer for mechanical systems,” IEEE Trans. on Automatic Control, vol. 50, no. 11, pp. 1785–1789, 2005.

    Article  MathSciNet  Google Scholar 

  14. J. X. Xu, F. Zheng, and T. H. Lee, “On sampled data variable structure control systems,” Variable Structure Systems, Sliding Mode and Nonlinear Control, K. D. Young and U. Ozguner, Eds, vol. 247, pp.69–92, Spring-Verlag, London, 1999.

    Article  MathSciNet  Google Scholar 

  15. L. W. Chang, “A MIMO sliding control with a first-order plus integral sliding condition,” Automatica, vol. 27, no. 5, pp. 853–858, 1991.

    Article  MathSciNet  Google Scholar 

  16. J. M. Schumacher, “Almost stability subspaces and high gain feedback,” IEEE Trans. on Automatic Control, vol. 29, no. 7, pp. 620–628, 1984.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. Gadewadikar, F. L. Lewis, L. Xie, V. Kucera, and M. Abu-Khalaf, “Parameterization stabilizing H ∞ static state-feedback gains: application to output-feedback design,” Automatica, vol. 43, no. 9, pp. 1597–1604, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  18. V. Syrmos, C. Abdallah, P. Dorato, and K. Grigoriadis, “Static output feedback — a survey,” Automatica, vol. 33, no. 2, pp. 125–137, 1997.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Oriental Institute of Technology, Banchiao, New Taipei City, 220, Taiwan

    Jeang-Lin Chang

Authors
  1. Jeang-Lin Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jeang-Lin Chang.

Additional information

Recommended by Editor Yoshito Ohta.

Jeang-Lin Chang received his B.S. and M.S. degrees in Control Engineering, his Ph.D. degree in Electrical and Control Engineering from National Chiao Tung University, Taiwan, R.O.C., in 1992, 1994, and 1999, respectively. He was with the Mechanical Research Laboratory, Industrial Technology Research Institute, Taiwan, during 1997–1999. In 1999, he joined the Department of Electrical Engineering, Oriental Institute of Technology, as an Assistant Professor. He is currently a Professor and a Dean of Research and Development. His research interests include sliding mode control, motion control, and signal processing.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chang, JL. Robust dynamic output feedback second-order sliding mode controller for uncertain systems. Int. J. Control Autom. Syst. 11, 878–884 (2013). https://doi.org/10.1007/s12555-012-0070-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-012-0070-9

Keywords

Search

Navigation