Advertisement

On nonlinear system diagnosis via high-gain observers: a case study

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

Abstract

In this chapter we study the diagnosis problem for a bioreactor process. The solvability of the problem is translated in terms of the observability of the variable which models the failure presence.We obtain an algebraic relation that depends on input, output (u and y respectively) and their time derivatives, which is satisfied by the given fault component. The main ingredient is the construction of a high-gain nonlinear observer which is based upon the multi-output generalized observability canonical form to estimate the fault.

Keywords

Fault Detection Nonlinear Observer State Estimation Problem Fault Component Fault Estimator 
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.
    G. Bastin, D. Dochain (1990) On-line Estimation and Adaptive Control of Bioreactors. Amsterdam, Elsevier.Google Scholar
  2. 2.
    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
  3. 3.
    M. Farza, K. Busawon, H. Hammouri (1998) Simple Nonlinear Observers for On-line Estimation of Kinetic Rates in Bioreactors. Automatica, 34(3), 301–318.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    J. P. Gauthier, H. Hammouri, S. Othman (1992) A simple Observer for Nonlinear System: Application to Bioreactors. IEEE Transactions on Automatic Control, 37, 875–880.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    P. Kaboré, S. Othman, T. F. McKena, H. Hammouri (2000) Observer-Based Fault Diagnosis for a Class of Non-Linear systems: Application to a Free Radical Copolimerization Reaction. International Journal of Control, 73(9), 787–803.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    R. Martínez-Guerra, J. de León-Morales (1996) Nonlinear Estimators: A Differential Algebraic Approach. Appl. Math. Lett., 9(4), 21–25.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    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, Honolulu, Hawaii, USA, 262–267.Google Scholar
  8. 8.
    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
  9. 9.
    R. Martínez-Guerra, J. de León-Morales (1994) Observers for a Multi-input Multi-output Bilinear Systems Class: A Differential Algebraic Approach. J. of Math. and Computer Modelling, 20, 125–132.CrossRefzbMATHGoogle Scholar
  10. 10.
    R. Martínez-Guerra, I. R. Ramírez-Palacios, E. Alvarado-Trejo (1998) On Parametric and State Estimation: Application to a Simple Academic Example. In IEEE Conference on Decision and Control, 764–765.Google Scholar
  11. 11.
    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
  12. 12.
    G. Stephanopoulos, K.Y. San (1984) Studies on On-line Bioreactor Identification. Biotechnology and Bioengineering, 26, 1176–1188.CrossRefGoogle Scholar
  13. 13.
    A. Tornambe (1989) Use of Asymptotic Observers Having High-Gain in the State and Parameter Estimation. IEEE Conference on Decision and Control, Tampa, FL, USA, 1791–1794.Google Scholar
  14. 14.
    K. Watanabe, D. M. Himmelblau (1983) Fault Diagnosis in Nonlinear Chemical Process. Part1, Theory. Part II, Application to a chemical Reactor. AIChE Journal, 29(2), 243–261.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

Personalised recommendations