Skip to main content

The fault detection problem in nonlinear systems using residual generators

  • Chapter
  • First Online:
Book cover Fault Detection and Diagnosis in Nonlinear Systems

Part of the book series: Understanding Complex Systems ((UCS))

  • 1644 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Bellman (1953) Stability of Differential Equations. New York, McGraw-Hill.

    MATH  Google Scholar 

  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.

    Article  MathSciNet  Google Scholar 

  3. S. Diop, M. Fliess (1991) On nonlinear observability. In Proc. 1st European Control Conference, Paris, Hermes, 152-157.

    Google Scholar 

  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.

    Article  Google Scholar 

  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. 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. 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.

    MathSciNet  Google Scholar 

  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.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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.

    Article  MathSciNet  MATH  Google Scholar 

  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. 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.

    Article  MATH  Google Scholar 

  13. R. Martínez-Guerra, J. de León-Morales (1996) Nonlinear estimators: a differential algebraic approach. Appl. Math. Lett., 9, 21-25.

    Article  MATH  Google Scholar 

  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. 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. 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. 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. 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. 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.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Martinez-Guerra, R., Mata-Machuca, J.L. (2014). The fault detection problem in nonlinear systems using residual generators. In: Fault Detection and Diagnosis in Nonlinear Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-03047-0_1

Download citation

Publish with us

Policies and ethics