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Diagnosis of nonlinear systems using the concept of differential transcendence degree

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

Abstract

In this chapter we tackle the diagnosis problem in nonlinear systems by using the concept of differential transcendence degree of a differential field extension, as well as, we consider the algebraic observability concept of the variable which models the failure presence for the solvability of the diagnosis problem. The construction of a reduced order uncertainty observer to estimate the fault variable is the main ingredient in our approach. Finally, three examples are presented in order to apply the proposed methodology. Numerical simulations of these examples are presented to illustrate the effectiveness of the suggested approach.

Keywords

Nonlinear System Fault Detection Fault Diagnosis Diagnosis Problem Diagnosability Condition 
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.

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References

  1. 1.
    E. Alcorta-Garcia, P.M. Frank (1997) Deterministic nonlinear observer-based approaches to fault diagnosis:a survey. Control Eng. Practice, 5, 663–670.CrossRefGoogle Scholar
  2. 2.
    J. Chen, R.J. Patton (1998) Robust model-based fault diagnosis for dynamic systems. Kluwer Academic, Boston.Google Scholar
  3. 3.
    J. Chen, R.J. Patton, H.Y. Zhang (1996) Design of unknown input observers and robust fault detection filters. International Journal of Control, 63, 85–105.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    C. De Persis, A. Isidori (2001) A geometric approach to nonlinear fault detection and isolation. IEEE Transactions on Automatic Control, 46(6), 853–865.CrossRefzbMATHGoogle Scholar
  5. 5.
    S. Diop, M. Fliess (1991) Nonlinear, observability, identifiability and persistent trajectories. In IEEE Conference on Decision and Control, Brighton, England, 714–719.Google Scholar
  6. 6.
    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
  7. 7.
    S. Diop, R. Martínez-Guerra (2001) On an algebraic and differential approach of nonlinear system diagnosis. In IEEE Conference on Decision and Control, Orlando, FL, USA, 585–589.Google Scholar
  8. 8.
    M. Fliess (1986) A note on the invertibility of nonlinear input-output differential systems. Systems & Control Letters, 8, 147–151.MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    P.M. Frank (1990) Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: a survey. Automatica, 26, 459–474.CrossRefzbMATHGoogle Scholar
  10. 10.
    P.M. Frank (1994) Enhancement of robustness in observer-based fault detection, International Journal of Control, 59, 955–981.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    P.M. Frank, X. Ding (1994) Frequency domain approach to optimally robust residual generation and evaluation for model based fault diagnosis. Automatica, 30(5), 789–804.CrossRefzbMATHGoogle Scholar
  12. 12.
    P.M. Frank, X. Ding (1997) Survey of robust residual generation and evaluation methods in observer-based fault detection systems, Journal of Process Control, 7, 403–424.CrossRefGoogle Scholar
  13. 13.
    H. Hammouri, M. Kinnaert, E.H. El Yaagoubi (1999) Observer based approach to fault detection and isolation for nonlinear systems. IEEE Transactions on Automatic Control, 44(10).Google Scholar
  14. 14.
    R. Iserman (1984) Process fault detection based on modeling and estimation methods: a survey. Automatica, 20(4), 387–404.CrossRefGoogle Scholar
  15. 15.
    R. Iserman, P. Balle (1997) Trends in the application of model-based fault detection and diagnosis of technical process. Control Eng. Practice, 5, 709–719.CrossRefGoogle Scholar
  16. 16.
    P. Kudva, N. Viswanadham, A. Ramakrishna (1980) Observers for linear systems with unknown inputs. IEEE Transactions on Automatic Control, 25, 113–115.MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    R. Martínez-Guerra, R. Garrido, A. Osorio-Mirón (2002) High-gain nonlinear observers for the fault detection problem: application to a bioreactor. In IFAC Publications, Editorial Elsevier Sc. Ltd, Nonlinear Control Systems, Edits: Kurzhanski/Fradkov, Vol.3, ISBN 0-08- 043560-2, 1567–1572.Google Scholar
  18. 18.
    R. Martínez-Guerra, R. Garrido, A. Osorio-Mirón (2001) Parametric and state estimation by means of high-gain nonlinear observers: application to a bioreactor. In American Control Conference, Arlington, Virginia, Washington, D.C., USA, 4603–4604.Google Scholar
  19. 19.
    M.A. Massoumnia (1986) A geometric approach to the synthesis of failure detection filters. IEEE Transactions on Automatic Control, 31(3), 389–396.MathSciNetGoogle Scholar
  20. 20.
    M.A. Massoumnia, G.C. Verghese, A.S. Willsky (1989) Failure detection and identification, IEEE Transactions on Automatic Control, 34, 316–321.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    R.J. Patton, P.M. Frank, R.N. Clark (1989) Fault diagnosis in dynamical systems, theory and application, Prentice Hall.Google Scholar
  22. 22.
    M. Perrier, J. Feyo de Azevedo, E.C. Ferreira, D. Dochain (2000) Tuning of observer-based estimators: Theory and application to the on-line estimation of kinetic parameters. Control Eng. Practice, 8, 377–388.CrossRefGoogle Scholar
  23. 23.
    R. Seliger, P.M. Frank (2000) Robust observer-based fault diagnosis in nonlinear uncertain systems. In Issues of fault diagnosis for dynamic systems, Eds. Patton, Frank, Clark, Springer, 145–187.Google Scholar
  24. 24.
    M. Staroswiecki, G. Comtet-Varga (1999) Fault detectability and isolability in algebraic dynamic systems, In Proc. of European Control Conference (ECC99), Karlsruhe, Germany.Google Scholar
  25. 25.
    F. Szigeti, C.E. Vera, J. Bokor, A. Edelmayer (2001) Inversion based fault detection and isolation. In IEEE Conference on Decision and Control, Orlando, FL, USA, 1005–1010.Google Scholar
  26. 26.
    A. Tornambe (1989) Use of asymptotic observers having high-gain in the state and parameter estimation. In IEEE Conference on Decision and Control, Tampa, FL, USA, 1791–1794.Google Scholar
  27. 27.
    N. Viswanadham, R. Srichander (1987) Fault detection using unknown-input observers. Control Theory and Advanced Technology, 3, 91–101.MathSciNetGoogle Scholar
  28. 28.
    A.S. Willsky (1976) A survey of design methods for failure detection in dynamic systems, Automatica, 12, 601–611.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    W‥unnenberg (1990) Observer-based fault detection in dynamic system. VDI-Fortschrittsber., VDI-Verlag, Reihe 8, Nr. 222, D‥usseldorf, Germany.Google Scholar
  30. 30.
    F. Szigeti, C.E. Vera, J. Bokor (2001) Inversion based fault detection and isolation. In IEEE Conference of Decision and Control, Orlando, FL, USA, 1005–1010.Google Scholar
  31. 31.
    J.C. Cruz-Victoria, R. Martínez-Guerra, J.J. Rincón-Pasaye (2008) On nonlinear systems diagnosis using differential and algebraic methods. Journal of the Franklin Institute, 345, 102–118.CrossRefzbMATHGoogle Scholar
  32. 32.
    R. Martínez-Guerra, J.L. Mata-Machuca, J.J. Rincón-Pasaye (2013) Fault diagnosis viewed as a left invertibility problem. ISA Transactions, 52, 652–661.CrossRefGoogle Scholar
  33. 33.
    R. Martínez-Guerra, J. de León-Morales (1997) On nonlinear observers. In Proc. Conference on Control Applications (CCA), Hartford, Connecticut, USA, 324–328.Google Scholar
  34. 34.
    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

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

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