Advertisement

Diagnosis for a class of non-differentially flat and Liouvillian systems

  • 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 for non-differentially flat and Liouvillian 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, we present a simulation example dealing with a ship in smooth landing to illustrate the effectiveness of the suggested approach.

Keywords

Suggested Approach Differential Algebraic Equation Algebraic Polynomial IEEE Proceeding Diagnosis Problem 
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.
    S. Diop, M. Fliess (1991) Nonlinear, observability, identifiability and persistent trajectories. IEEE Proceedings 30th Conference on Decision and Control, CDC91, Brighton, England, 714-719.Google Scholar
  2. 2.
    S. Diop, R. Martínez-Guerra (2001) An algebraic and data derivative information approach to nonlinear system diagnosis. Proceedings European Control Conference (ECC01), Porto, Portugal, 2334-2339.Google Scholar
  3. 3.
    S. Diop, R. Martínez-Guerra (2001) On an algebraic and differential approach of nonlinear system diagnosis. IEEE Proceedings 40th Conference on Decision and Control, CDC01, Orlando, FL, 585-589.Google Scholar
  4. 4.
    M. Fliess (1986) A note on the invertibility of nonlinear input-output differential systems. Syst. Control Lett., 8, 147-151.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    M. Fliess (1991) Some remarks on gain scheduling. Proceedings European Control Conference, Grenoble, 177-181.Google Scholar
  6. 6.
    D. Gokhman (1995) Limits in differential fields of holomorphic germs. Complex Variables, 28, 27-36.MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    R. Martínez-Guerra, J. de León-Morales (1996) Nonlinear estimators: a differential algebraic approach. Appl. Math. Lett., 9, 21-25.CrossRefzbMATHGoogle 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. Proceedings American Control Conference, ACC01, Arlington, Virginia, Washington, D.C., 38073808.Google Scholar
  9. 9.
    R. Martínez-Guerra, R. Garrido, A. Osorio-Mirón (2002) High-gain nonlinear observers for the fault detection problem: application to a bioreactor. Nonlinear Control Systems (Kurshanski & Fradkov eds.), Vol. 3. IFAC Publications, Elsevier Ltd Oxford, 1567-1572.Google Scholar
  10. 10.
    R. Martínez-Guerra, J. Mendoza-Camargo (2004) Observers for a class of Liouvillian and nondifferentially flat systems. IMA J. Math. Control Inf., 21, 493-509.CrossRefzbMATHGoogle Scholar
  11. 11.
    R. Martínez-Guerra, I.R. Ramirez-Palacios, E. Alvarad-Trejo (1998) On parametric and state estimation: application to a simple academic example. IEEE Proceedings 37th Conference on Decision and Control, CDC98, Tampa, FL, pp. 764765.Google Scholar
  12. 12.
    H. Sira-Ramirez, R. Castro-Linares, E. Liceaga-Castro (2000) A Liouvillian approach for the trajectory planning-based control of helicopter models. Int. J. Robust Nonlinear Control (Special Issue on the control of underactuated nonlinear systems), 10, 301-320.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    J.C. Victoria, R. Martínez-Guerra (2002) Nonlinear systems diagnosis: a differential algebraic approach. In Proc. Latinamerican Congress of Automatic Control CLCA02, Guadalajara, Jalisco, Mexico.Google Scholar
  14. 14.
    R. Martínez-Guerra, R. González-Galán, A. Luviano-Juárez, J. Cruz-Victoria (2007) Diagnosis for a class of non-differentially flat and Liovillian systems. IMA Journal of Mathematical Control and Information, 24, 177–195.MathSciNetCrossRefzbMATHGoogle 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