Advertisement

The fault detection problem in nonlinear systems using residual generators

  • Rafael Martinez-Guerra
  • Juan Luis Mata-Machuca
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

In this chapter we study the fault detection problem using residual generators based upon high gain nonlinear observers in a differential algebraic framework. We analyze the stability of the residual generator when a fault occurs. We also consider two faults types: constant and time-varying faults. It is shown that under some mild conditions over the aforementioned faults the residual is different from zero.

Keywords

Nonlinear System Fault Detection Nonlinear Observer Fault Case Residual Generator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    R. Bellman (1953) Stability of Differential Equations. New York, McGraw-Hill.zbMATHGoogle Scholar
  2. 2.
    M.J. Corless, G. Leitmann (1981) Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems. IEEE Transactions on Automatic Control, 64, 1139-1144.MathSciNetCrossRefGoogle Scholar
  3. 3.
    S. Diop, M. Fliess (1991) On nonlinear observability. In Proc. 1st European Control Conference, Paris, Hermes, 152-157.Google Scholar
  4. 4.
    R. Martínez-Guerra, S. Diop (2004) Diagnosis of nonlinear systems: an algebraic and differential approach. IEE Proceedings – Control Theory and Applications, 151, 130–135.CrossRefGoogle Scholar
  5. 5.
    S. Diop, R. Martínez–Guerra (2001) An algebraic and data derivative information approach to nonlinear system diagnosis. In European Control Conference, Porto, Portugal, 2334-2339.Google Scholar
  6. 6.
    S. Diop, R. Martínez–Guerra (2001b) On an algebraic and differential approach of nonlinear system diagnosis. In Proc. IEEE Conference on Decision and Control, Orlando, FL, USA, 585-589.Google Scholar
  7. 7.
    M. Fliess. (1989) Generalisation non lineaire de la forme canonique de commande et linearisation par bouclage. C. R. Acad. Sci. Paris, I-308, 3777-3779.MathSciNetGoogle Scholar
  8. 8.
    J.P. Gauthier, H. Hammouri, S. Othman (1992) A simple observer for nonlinear systems: applications to bioreactors. IEEE Transactions on Automatic Control, 37, 875-880.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    H. Hammouri, M. Kinnaert, E.H. El Yaagoubi (1999) Application of nonlinear observer to fault detection and isolation. New Directions in Nonlinear Observers Design, Lecture Notes in Control and Information Sciences, Vol. 244. (H. Nijmeijer and T. I. Fossen, eds). Berlin, Springer, 423-443.Google Scholar
  10. 10.
    P. Kaboré, S. Othman, T. F. McKenna, H. Hammouri (2000) Observer-based fault diagnosis for a class of non-linear systems: application to a free radical copolymerization reaction. International Journal of Control, 73, 787-803.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    R. Martínez-Guerra (1993) Estimation of the states of a class of bilinear systems: a differential algebraic approach. In Proc. Conference on Decision and Control, Texas, USA, 735-736.Google Scholar
  12. 12.
    R. Martínez-Guerra, J. de León-Morales (1994) Observers for a multi-input multi-output bilinear systems class: a differential algebraic approach. J. Math. Comput. Modell., 20, 125- 132.CrossRefzbMATHGoogle Scholar
  13. 13.
    R. Martínez-Guerra, J. de León-Morales (1996) Nonlinear estimators: a differential algebraic approach. Appl. Math. Lett., 9, 21-25.CrossRefzbMATHGoogle Scholar
  14. 14.
    R. Martínez-Guerra, R. Garrido, A. Osorio-Mirón (2000) A comparative study of linear and nonlinear observers applied to a CSTR. In 4th. Int. Symp. of the School of Chem. Eng., IPN, Mexico, DF, 259-270.Google Scholar
  15. 15.
    R. Martínez-Guerra, R. Garrido, A. Osorio-Mirón (2000) Fault detection in CSTR using nonlinear observers. In IASTED Int. Conf. on Intelligence Systems and Control (ISC 2000), Honolulu, HI, 262-267.Google Scholar
  16. 16.
    R. Martínez-Guerra, S. Diop, R. Garrido, A. Osorio-Mirón (2001) Diagnosis of nonlinear systems using a reduced order fault observer: application to a bioreactor. Journees Franco- Mexicaines d’Automatique Appliquee, September 12-14, IRCCyN, Nantes, France.Google Scholar
  17. 17.
    R. Martínez-Guerra, R. Garrido, A. Osorio-Mirón (2001) High-gain nonlinear observer for the fault detection problem: application to a bioreactor. In 5th IFAC Symposium Nonlinear Control Systems, St Petersburg, Russia, 426-431.Google Scholar
  18. 18.
    R. Martínez-Guerra, R. Garrido, A. Osorio-Mirón (2001) On nonlinear system diagnosis via high-gain observers: a case study. In IEEE Proc. Conference on Control Applications, Mexico, DF, 726-731.Google Scholar
  19. 19.
    R. Martínez-Guerra, R. Suárez, J. de León-Morales (2001) Asymptotic output tracking of a class of nonlinear systems by means of an observer. Int. J. Robust Nonlinear Control, 11, 373-391.CrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Rafael Martinez-Guerra
    • 1
  • Juan Luis Mata-Machuca
    • 2
  1. 1.Departamento de Control AutomaticoCINVESTAV-IPNMexico, D.F.Mexico
  2. 2.Unidad Profesional Interdisciplinaria en Ingenieria y Tecnologias AvanzadasInstituto Politecnico Nacional Academia de MecatronicaMexico, D.F.Mexico

Personalised recommendations