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Adaptive Regulation—Rejection of Unknown Disturbances

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Book cover Adaptive Control

Part of the book series: Communications and Control Engineering ((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.

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Notes

  1. 1.

    Throughout this chapter it is assumed that the order of the disturbance model is known but the parameters of the model are unknown (the order can be estimated from data if necessary).

  2. 2.

    The complex variable z −1 will be used for characterizing the system’s behavior in the frequency domain and the delay operator q −1 will be used for describing the system’s behavior in the time domain.

  3. 3.

    The “only if” does not apply if D p divides A.

  4. 4.

    Of course it is assumed that D p and B do not have common factors.

  5. 5.

    In Tsypkin (1997), such an error equation is provided and it can be used for developing a direct adaptive control scheme. This idea has been used in Valentinotti (2001), Amara et al. (1999a, 1999b), Landau et al. (2005).

  6. 6.

    The magnitude of the adaptation gain gives an indication upon the variance of the parameter estimation error—see Chap. 3.

  7. 7.

    The convergence towards zero of ε 0(t) can be proven also with the “bounded growth” lemma of Goodwin and Sin (Chap. 11, Lemma 11.1).

  8. 8.

    These experiments have been carried out by M. Alma (GIPSA-LAB).

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Authors and Affiliations

  1. Département d’Automatique, GIPSA-LAB (CNRS/INPG/UJF), PO Box 46, 38402, St. Martin d’Heres, France

    Prof. Ioan Doré Landau

  2. UMR-CNRS 6599, Centre de Recherche de Royalieu, Heuristique et Diagnostic des Systèmes Complexes, Université de Technologie de Compiègne, PO Box 20529, 60205, Compiègne, France

    Prof. Rogelio Lozano

  3. Centre de Recherche (ENSICAEN), Laboratoire GREYC, École Nationale Supérieure d’Ingénieurs de Caen, Campus Côte de Nacre, bd. Maréchal Juin 6, 14032, Caen Cedex, France

    Prof. Mohammed M’Saad

  4. Laboratoire d’Automatique, École Polytechnique Fédérale de Lausanne, 1015, Laussanne, Switzerland

    Prof. Alireza Karimi

Authors
  1. Prof. Ioan Doré Landau
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  2. Prof. Rogelio Lozano
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  3. Prof. Mohammed M’Saad
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  4. Prof. Alireza Karimi
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Corresponding author

Correspondence to Ioan Doré Landau .

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© 2011 Springer-Verlag London Limited

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Landau, I.D., Lozano, R., M’Saad, M., Karimi, A. (2011). Adaptive Regulation—Rejection of Unknown Disturbances. In: Adaptive Control. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-0-85729-664-1_14

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  • DOI: https://doi.org/10.1007/978-0-85729-664-1_14

  • Publisher Name: Springer, London

  • Print ISBN: 978-0-85729-663-4

  • Online ISBN: 978-0-85729-664-1

  • eBook Packages: EngineeringEngineering (R0)

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