LMI-based Design of Reduced Order Output Feedback Sliding Mode Controllers

저차 출력 궤환 슬라이딩 모드 제어기의 LMI 기반 설계법

  • Published : 2009.08.01

Abstract

This paper presents an LMI-based method to design a reduced order output feedback sliding mode controller for a class of uncertain systems. Using LMIs we derive an existence condition of a reduced order sliding mode control law. And we give explicit formulas of the gain matrices. Finally, we give a numerical design example, together with a design algorithm.

Keywords

Sliding surface;Variable structure control;Matching condition;LMI;Uncertainty

References

  1. H.B. Choi, 'Frequency domain interpretations of the invariance condition of the sliding mode control theory', IET Proc.-Control Theory and Appl., vol. 1, pp. 869-874, 2007 https://doi.org/10.1049/iet-cta:20060142
  2. P. Gahinet, A Nemirovski and A.J. Laub, LMI Control Toolbox User's Guide, Natic, MA:The Math Works Inc., 1995
  3. 최한호, '출력 궤환 슬라이딩 모드 제어기 설계를 위한 선형행렬부등식 접근법', 대한전기학회 논문지, 56권 7호, pp.1298-1301, 2007
  4. A.R. Galimidi, and B.R. Barmish, 'The constrained Lyapunov problem and its application to robust output feedback stabilization,' IEEE Trans. Automat Contr., vol. 31, pp. 410-419, 1986 https://doi.org/10.1109/TAC.1986.1104288
  5. 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
  6. S.K. Bag, S.K. Spurgeon, and C. Edwards, 'Output feedback sliding mode design for linear uncertain systems,' IEE Proc.-Control Theory Appl., vol. 144 pp. 209-216, 1997 https://doi.org/10.1049/ip-cta:19971122
  7. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in system and Control Theory, Philadelphia, SIAM, 1994
  8. H.H. Choi, 'Variable structure output feedback control design for a class of uncertain sysnamic systems,' Automatica, vol. 38, pp. 385-341, 2002
  9. S.H. Zak and S. Hui 'On variable structure output feedback controllers for uncertain dynamic systems' IEEE Trans. Automat. Contr., vol. 38, no. 10, pp. 1509-1512, 1993 https://doi.org/10.1109/9.241564
  10. T. Iwasaki and RE. Skelton, 'All controllers for the general $H_{\infty}$ control problem: LMI existnce condition and state space formulas,' Automatiea, vol. 30, pp. 1307-1317, 1994 https://doi.org/10.1016/0005-1098(94)90110-4
  11. 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
  12. P. Park, D.J. choi, and S,G. Kong, 'Output feedback variable structure control for linear systems with uncertainties and disturbances,' Automatica, vol. 43, pp. 72-79, 2007 https://doi.org/10.1016/j.automatica.2006.07.015
  13. 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
  14. C. Edwards, and S.K. Spurgeon, 'Linear matrix inequality methods for designing sliding mode output feedback controllers,' IEE Proc.-Control Theory Appl.., vol. 150 pp, 539-545, 2003 https://doi.org/10.1049/ip-cta:20030707