An Observer for Nonlinear Systems Using Approximate Observer Form

근사 관측기 형태를 이용한 비선형 시스템의 관측기

  • Lee, Sungryul (Dept.of Electric Electronics Engineering, Yonsei University) ;
  • Sin, Hyeon-Seok (Dept.of Electric Electronics Engineering, Yonsei University) ;
  • Park, Mignon (Dept.of Electric Electronics Engineering, Yonsei University)
  • 이성렬 (연세대학교 전기전자공학과) ;
  • 신현석 (연세대학교 전기전자공학과) ;
  • 박민용 (연세대학교 전기전자공학과)
  • Published : 2001.06.01

Abstract

This paper presents a state observer for nonlinear systems using approximate observer from. It is shown that if a nonlinear system is approximately error linearizable, then there exists a local nonlinear observer whose estimation error converges exponentially to zero. Since the proposed method relaxes strong geometric conditions of previous works, it improves the existing results for nonlinear observer design. Finally, some example is given to show the effectiveness of this scheme.

Keywords

References

  1. A. Isidori, Nonlinear Control Systems, 2nd ed. Berlin : Springer-Verlag, 1989
  2. R. Marino, 'Adaptive observers for single output nonlinear systems,' IEEE Trans. Automat. Contr., vol. 35, pp. 1054-1058, 1990 https://doi.org/10.1109/9.58536
  3. H. Keller, 'Nonlinear observer design by transformation into a generalized observer canonical form,' Int. J. Contr., vol. 46, pp. 1915-1930, 1987 https://doi.org/10.1080/00207178708934024
  4. J. Gauthier, H. Hammouri, and S. Othman, 'A simple observer for nonlinear systems applications to bioreactors,' IEEE Trans. Automat. Contr., vol. 37, no. 6, PP. 875-880, 1992 https://doi.org/10.1109/9.256352
  5. G. Ciccarella, M. Dallamora, and A. Germani, 'A luenberger-like observer for nonlinear systems,' Int. J. Contr., vol. 57, no. 3, pp. 537-556, 1993 https://doi.org/10.1080/00207179308934406
  6. Nam H. Jo and Jin H. Seo, 'A state observer for nonlinear systems and its application to ball and beam system,' IEEE, Trans. Automat. Contr. vol. 45, no. 5, pp, 968-973, 2000 https://doi.org/10.1109/9.855562
  7. K. Nam, 'An approximate nonlinear observer with polynomial coordinate transformation maps,' IEEE Trans. Automat. Contr., vol. 42, no. 4, pp. 522-527, 1997 https://doi.org/10.1109/9.566662
  8. F. Esfandiari and H. K. Khalil, 'Output feedback stabilization of fully linearizable systems,' Int. J. Contr., vol. 56, no. 5, pp, 1007-1037, 1992 https://doi.org/10.1080/00207179208934355
  9. H. K. Khalil and F. Esfandiari, 'Serniglobal stabilization of a class of nonlinear systems using output feedback,' IEEE Trans. Automat. Conir, vol. 38, no. 9, pp. 1412-1415, 1993 https://doi.org/10.1109/9.237658
  10. H. Khalil, Nonlinear Systems, 2nd ed., Prentice Hall, 1996
  11. J. Hauser, 'Nonlinear control via approximate input-output linearization: The ball and beam example,' IEEE Trans. Automat. Conir., vol. 37, pp. 392-398, 1992 https://doi.org/10.1109/9.119645