Journal of the Korean Institute of Illuminating and Electrical Installation Engineers (조명전기설비학회논문지)

The Korean Institute of IIIuminating and Electrical Installation Engineers (한국조명전기설비학회)
권호 표지
DOI QR코드

DOI QR Code

LMI-based Design of Integral Sliding Mode Controllers for Polytopic Models

폴리토픽 모델을 갖는 시스템을 위한 적분 슬라이딩 모드 제어기의 LMI 기반 설계

  • Received : 2010.03.25
  • Accepted : 2010.06.18
  • Published : 2010.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

This paper presents an LMI-based method to design an integral sliding mode controller for an uncertain system with a polytopic model. The uncertain system under consideration may have mismatched parameter uncertainties in the state matrix as well as in the input matrix. Using LMIs we derive an existence condition of a sliding surface. And we give a switching feedback control law.

Keywords

References

  1. R.A. DeCarlo, S.H. Zak, and G.P. Mathews, Variable structure control of nonlinear multivariable systems: A tutorial, IEEE Proceedings, vol. 76, pp. 212-232, 1988. https://doi.org/10.1109/5.4400
  2. V.I. Utkin, Variable structure systems with sliding modes, IEEE Trans. Automat. Contr., vol. 22, pp. 212-222, 1977. https://doi.org/10.1109/TAC.1977.1101446
  3. C. Edwards, A practical method for the design of sliding mode controllers using linear matrix inequalites, Automatica., vol. 40, pp. 1761-1769, 2004. https://doi.org/10.1016/j.automatica.2004.05.004
  4. C. Edwards, A. Akoachere, and S. K. Spurgeon, Sliding mode output feedback controller design using linear matrix inequalities, IEEE Trans. Automat. Contr., vol. 46, pp. 115-119, 2001. https://doi.org/10.1109/9.898702
  5. J. Ackermann and V.I. Utkin, Sliding mode control design based on Ackermann's formula, IEEE Trans. Automat. Contr., vol. 43, no. 2, pp. 234-237, 1998. https://doi.org/10.1109/9.661072
  6. H.H. Choi, LMI-based sliding surface design for integral sliding mode control of mismatched uncertain systems, IEEE Trans. Automat. Contr., vol. 52. no. 4, pp. 736-742, 2007. https://doi.org/10.1109/TAC.2007.894543
  7. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in system and Control Theory, Philadelphia, SIAM, 1994.
  8. M.C.M. Teixeira, and S.H. Zak, Stabilizing controller design for uncertain nonlinear systems using fuzzy models, IEEE Trans. Fuzzy Syst., vol. 7, pp. 133-142, 1999. https://doi.org/10.1109/91.755395
  9. K.-C. Jeong, D.-H. Lee, and H.-Y. Lee, A study on simulator for designing controllers of anti-swing in overhead crane, Journal of KIIEE, vol. 10, no.2 , pp. 78-86, 1996.
  10. S.-W. Bae, C.-K. Rho, Y.-H. Bae, and D.-K. Lee, Anti-swing control algorithm for the automation of overhead crane, Journal of KIIEE, vol. 17, no. 2, pp. 49-57, 2003. https://doi.org/10.5207/JIEIE.2003.17.2.049
  11. V.Y. Glizer, L.M. Fridman, and V. Turetsky, Cheap suboptimal control of an integral sliding mode for uncertain systems with delays, IEEE Trans. Automat. Contr., vol. 52, no. 10, pp. 1892-1898, 2007. https://doi.org/10.1109/TAC.2007.906201
  12. W.-J. Cao and J.-X. Xu, Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems, IEEE Trans. Automat. Contr., vol. 49, pp. 1355-1360, 2004. https://doi.org/10.1109/TAC.2004.832658
  13. H.H. Choi, Adaptive controller design for uncertain fuzzy systems using variable structure control approach, Automatica, vol. 45, no.11, pp. 2646-2650, 2009. https://doi.org/10.1016/j.automatica.2009.07.016