Skip to main content

Fault diagnosis viewed as a left invertibility problem

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

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

  • 1623 Accesses

Abstract

This chapter deals with the fault diagnosis problem, some new properties are found using the left invertibility condition through the concept of differential output rank. Two schemes of nonlinear observers are used to estimate the fault signals for comparison purposes, one of these is a proportional reduced order observer (see Lemma 3.1) and the other is a sliding mode observer. The methodology is tested in a real time implementation of a three-tank system.

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. E. Alcorta García, P. Frank P (1997) Deterministic nonlinear observer-based approaches to fault diagnosis: a survey. Control Eng. Pract., 5, 663–670.

    Google Scholar 

  2. P. Frank, X. Ding (1977) Survey of robust residual generation and evaluation methods in observer-based fault detection systems. Journal of Process Control, 7, 403–424.

    Article  Google Scholar 

  3. A. Willsky (1976) A survey of design methods in observer-based fault detection systems. Automatica, 1(2), 601–611.

    Article  MathSciNet  Google Scholar 

  4. Massoumnia, G. Verghese, A. Willsky (1989) Failure detection and identification. IEEE Transactions on Automatic Control, 34, 316–321.

    Article  MathSciNet  MATH  Google Scholar 

  5. J. Chen, R. Patton (1999) Robust model-based fault diagnosis for dynamic systems. Kluwer Academic Publishers.

    Google Scholar 

  6. M. Blanke, M. Kinnaert, J. Lunze, M. Staroswiecki (2003) Diagnosis and fault-tolerant control, Springer, Berlin.

    Book  MATH  Google Scholar 

  7. H. Noura, D. Theilliol, J.C. Ponsart, A. Chamseddine (2009) Fault-tolerant control systems: design and practical applications, Springer, London.

    Book  Google Scholar 

  8. C. De Persis, A. Isidori (2001) A geometric approach to nonlinear fault detection and isolation. IEEE Transactions on Automatic Control, 46(6), 853–865.

    Article  MATH  Google Scholar 

  9. C. Join, J.C. Ponsart, D. Sauter, D. Theilliol (2005) Nonlinear filter design for fault diagnosis: application to the three-tank system. IEE Proc. Control Theory Appl., 152(1), 55–64.

    Article  Google Scholar 

  10. M. Fliess, C. Join, H. Mounier (2005) An introduction to nonlinear fault diagnosis with an application to a congested internet router. Advances in Communication Control Networks, C. T. Abdallah, J. Chiasson (Eds), Lecture Notes, Conf. Inf. Sci., Springer, Berlin, 308, 327–343.

    Google Scholar 

  11. C. Join, H. Sira-Ramírez, M. Fliess (2005) Control of an uncertain three tank system via on-line parameter identification and fault detection. In Proc. of 16th Triennial World IFAC Conference (IFAC’05), Prague, Czech Republic.

    Google Scholar 

  12. M. Fliess (1988) Nonlinear Control Theory and Differential Algebra. In Modelling and Adaptive Control, Byrnes C. Kurzhanski A. (eds.). Lecture Notes in Control and Information Sciences, 105, Springer, Berlin, 134–145.

    Google Scholar 

  13. M. Fliess, C. Join, H. Sira-Ramírez (2004) Robust residual generation for nonlinear fault diagnosis: an algebraic setting with examples. International Journal of Control, 14(77).

    Google Scholar 

  14. M. Fliess, C. Join, H. Sira-Ramirez (2008) Non-linear estimation is easy, Int. J. Modelling Identification and Control, 4(1), 12–27.

    Article  Google Scholar 

  15. A.M. Nagy, B. Marx, G. Mourot, G. Schutz, J. Ragot (2009) State estimation of the three-tank system using a multiple model. In IEEE Conference on Decision and Control, Shanghai, P.R. China, 7795–7800.

    Google Scholar 

  16. Amira DTS200: Laboratory setup three tank system, Amira Gmbh, Duisburgh, Germany, 1996.

    Google Scholar 

  17. D. Theilliol, H. Noura, J.C. Ponsart (2002) Fault diagnosis and accommodation of a threetank system based on analytical redundancy. ISA Transactions, 41, 365–382.

    Article  Google Scholar 

  18. E. Kolchin (1973) Differential Algebra and Algebraic Groups. New York, Academic Press.

    MATH  Google Scholar 

  19. M. Fliess (1986) A note on invertibility of nonlinear input–output differential systems. System & Control Letters, 8, 147–151.

    Article  MathSciNet  MATH  Google Scholar 

  20. H.K. Khalil (2002) Nonlinear Systems. Prentice Hall.

    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). Fault diagnosis viewed as a left invertibility problem. In: Fault Detection and Diagnosis in Nonlinear Systems. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-03047-0_6

Download citation

Publish with us

Policies and ethics