Advertisement

Adaptive Regulation—Rejection of Unknown Disturbances

  • Ioan Doré Landau
  • Rogelio Lozano
  • Mohammed M’Saad
  • Alireza Karimi
Part of the Communications and Control Engineering book series (CCE)

Abstract

This chapter addresses the problem of attenuation (rejection) of unknown disturbances without measuring them by using a feedback approach. In this context, the disturbance model is unknown and time varying while the model of the plant is known (obtained by system identification) and almost invariant. This requires an adaptive approach. The term “adaptive regulation” has been coined to characterize this control paradigm. Direct and indirect adaptive regulation strategies using the internal model principle and the Youla-Kucera parameterization will be presented. The evaluation of the methodology is done in real time on an active vibration control system using an inertial actuator.

Keywords

Internal Model Adaptive Regulation Unknown Disturbance Adaptation Gain Secondary Path 
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.

References

  1. Amara FB, Kabamba PT, Ulsoy AG (1999a) Adaptive sinusoidal disturbance rejection in linear discrete-time systems—Part I: Theory. J Dyn Syst Meas Control 121:648–654 CrossRefGoogle Scholar
  2. Amara FB, Kabamba PT, Ulsoy AG (1999b) Adaptive sinusoidal disturbance rejection in linear discrete-time systems—Part II: Experiments. J Dyn Syst Meas Control 121:655–659 CrossRefGoogle Scholar
  3. Anderson BDO (1998) From Youla-Kucera to identification, adaptive and nonlinear control. Automatica 34:1485–1506 MATHCrossRefGoogle Scholar
  4. Åström KJ, Wittenmark B (1995) Adaptive control, 2nd edn. Addison Wesley, Boston MATHGoogle Scholar
  5. Bengtsson G (1977) Output regulation and internal models—a frequency domain approach. Automatica 13:333–345 MATHCrossRefGoogle Scholar
  6. Bodson M (2005) Rejection of periodic disturbances of unknown and time-varying frequency. Int J Adapt Control Signal Process 19:67–88 MathSciNetMATHCrossRefGoogle Scholar
  7. Bodson M, Douglas SC (1997) Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency. Automatica 33:2213–2221 MathSciNetMATHCrossRefGoogle Scholar
  8. Constantinescu A (2001) Commande robuste et adaptative d’une suspension active. Thèse de doctorat, Institut National Polytechnique de Grenoble Google Scholar
  9. Constantinescu A, Landau ID (2003) Direct controller order reduction by identification in closed loop applied to a benchmark problem. Eur J Control 9(1) Google Scholar
  10. Ding Z (2003) Global stabilization and disturbance suppression of a class of nonlinear systems with uncertain internal model. Automatica 39:471–479 MATHCrossRefGoogle Scholar
  11. Ficocelli M, Amara FB (2009) Adaptive regulation of MIMO linear systems against unknown sinusoidal exogenous inputs. Int J Adapt Control Signal Process 23(6):581–603 MATHGoogle Scholar
  12. Francis BA, Wonham WM (1976) The internal model principle of control theory. Automatica 12:457–465 MathSciNetMATHCrossRefGoogle Scholar
  13. Gouraud T, Gugliemi M, Auger F (1997) Design of robust and frequency adaptive controllers for harmonic disturbance rejection in a single-phase power network. In: Proc of the European control conference, Bruxelles Google Scholar
  14. Hillerstrom G, Sternby J (1994) Rejection of periodic disturbances with unknown period—a frequency domain approach. In: Proc of American control conference, Baltimore, pp 1626–1631 Google Scholar
  15. Ioannou PA, Sun J (1996) Robust adaptive control. Prentice Hall, Englewood Cliffs MATHGoogle Scholar
  16. Johnson CD (1976) Theory of disturbance-accomodating controllers. In: Leondes CT (ed) Control and dynamical systems, vol 12, pp 387–489 Google Scholar
  17. Karimi A (2002) Design and optimization of restricted complexity controllers—benchmark. http://lawww.epfl.ch/page11534.html
  18. Landau ID, Zito G (2005) Digital control systems—design, identification and implementation. Springer, London Google Scholar
  19. Landau ID, M’Sirdi N, M’Saad M (1986) Techniques de modélisation récursive pour l’analyse spectrale paramétrique adaptative. Rev Trait Signal 3:183–204 Google Scholar
  20. Landau ID, Constantinescu A, Loubat P, Rey D, Franco A (2001a) A methodology for the design of feedback active vibration control systems. In: Proc European control conference 2001, Porto, Portugal Google Scholar
  21. Landau ID, Karimi A, Constantinescu A (2001b) Direct controller order reduction by identification in closed loop. Automatica 37(11):1689–1702 MathSciNetMATHCrossRefGoogle Scholar
  22. Landau ID, Constantinescu A, Rey D (2005) Adaptive narrow band disturbance rejection applied to an active suspension—an internal model principle approach. Automatica 41(4):563–574 MathSciNetMATHCrossRefGoogle Scholar
  23. Landau ID, Alma M, Martinez JJ, Buche G (2010, to appear) Adaptive suppression of multiple time varying unknown vibrations using an inertial actuator. IEEE Trans Control Syst Technol Google Scholar
  24. Landau ID, Alma M, Martinez JJ, Buche G (2011) Adaptive suppression of multiple time-varying unknown vibrations using an inertial actuator. IEEE Trans Control Syst Technol doi: 10.1109/TCST.2010.2091641 Google Scholar
  25. Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice-Hall, Englewood Cliffs Google Scholar
  26. Marino R, Santosuosso GL, Tomei P (2003) Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency. Automatica 39:1755–1761 MathSciNetMATHCrossRefGoogle Scholar
  27. S Fekri MA, Pasqual A (2006) Issues, progress and new results in robust adaptive control. Int J Adapt Control Signal Process, 519–579 Google Scholar
  28. Serrani A (2006) Rejection of harmonic disturbances at the controller input via hybrid adaptive external models. Automatica 42:1977–1985 MathSciNetMATHCrossRefGoogle Scholar
  29. Tsypkin YZ (1997) Stochastic discrete systems with internal models. J Autom Inf Sci 29(4–5):156–161 Google Scholar
  30. Valentinotti S (2001) Adaptive rejection of unstable disturbances: application to a fed-batch fermentation. Thèse de doctorat, École Polytechnique Fédérale de Lausanne Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  • Ioan Doré Landau
    • 1
  • Rogelio Lozano
    • 2
  • Mohammed M’Saad
    • 3
  • Alireza Karimi
    • 4
  1. 1.Département d’AutomatiqueGIPSA-LAB (CNRS/INPG/UJF)St. Martin d’HeresFrance
  2. 2.UMR-CNRS 6599, Centre de Recherche de Royalieu, Heuristique et Diagnostic des Systèmes ComplexesUniversité de Technologie de CompiègneCompiègneFrance
  3. 3.Centre de Recherche (ENSICAEN), Laboratoire GREYCÉcole Nationale Supérieure d’Ingénieurs de CaenCaen CedexFrance
  4. 4.Laboratoire d’AutomatiqueÉcole Polytechnique Fédérale de LausanneLaussanneSwitzerland

Personalised recommendations