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Authors
Valerie Pommier Budinger; Julien Richelot; Joel Bordeneuve-Guibe

Digital Object Identifier (DOI)
10.3182/20060912-3-DE-2911.00112

Page Numbers:
644-649

Index Terms
active control,damping,predictive control,piezoelectric actuators,finite element analysis

Abstract
In this article, a Generalized Predictive Control (GPC) is used to perform the active damping of a structure with sloshing phenomena. The studied flexible structure has been designed to have the same dynamic behavior than an aircraft wing (the first bending mode has a frequency of 1.59 Hz). It is composed by a free-clamped beam and a tank and is equipped with piezoelectric actuators. The purposes here are on the one hand to perform the damping of the structure i.e. to perform as efficiently as possible the vibratory disturbances rejection and on the other hand to evaluate the performances of the GPC control law, in the domain of flexible structures. The first part of the article deals with the sizing and the modeling of the active structure using the Lagrangian approach and a FEM software. The second part concerns the control law. The used control law - i.e. GPC - has been chosen because of its good control performances, its compactness and its robustness in front of model mismatches. These advantages are particularly interesting in this study, because the control must be performed for several levels of filling of the tank, in a MIMO, multimodes context. Experiments have been performed (for the control of the first bending mode and the control of the first bending and twisting modes). In each case, GPC is efficient. Moreover, the use of GPC leads to a unique global behavior for the controlled structure, whatever the tank's filling configuration may be.

References

[1] Ikeda T. (1993), Fundamentals of Piezoelectricity, Oxford Science
    Publications. W.-K. Chen, Linear Networks and Systems
    (Book style). Belmont, CA: Wadsworth, pp. 123-135.
[2] B. Nogarede (2003), "Moteurs Piézoélectriques", Techniques de
    l'Ingénieur.
[3] W. Haas, K. Schlacher, R. Gahleitner (2000), Modelling of
    Electromechanical Systems, Johannes Kepler University
    Linz.
[4] Gerardin G., Rixen D. (1997), Mechanical vibrations: theory and
    applications to structural dynamics, John Wiley & sons.
[5] V. Pommier, M. Budinger, P. Lever, J. Richelot, J. Bordeneuve-Guibé
     (2004), "FEM design of a piezoelectric active control
    structure. Application to an aircraft wing model",
    International Conference on Noise and Vibration
    Engineering ISMA04, Leuven, 20-22 Septembre, Belgique.
[6] J. Richalet, A. Rault, J. L. Testud, J. Papon (1978), "Model
    predictive heuristic control: applications to industrial
    processes", Automatica, vol. 14, no. 6, pp. 413-428.
[7] D. W. Clarke, C. Mohtadi, P. S. Tuffs (1987), "Generalized
    predictive control: Part 1, the basic algorithm, and Part 2,
    extensions and interpretations", Automatica, vol. 23, no. 2,
    pp. 137-160.
[8] D. W. Clarke, C. Mohtadi (1989), "Properties of generalized
    predictive control", Automatica, vol. 25, no. 6, pp. 859-875.
[9] C. Goh, T. K. Caughey (1985), "On the Stability Problem Caused
    by Finite Actuator Dynamics in the Control of Large Space
    Structure", Int. J. of Control, vol. 41, pp. 787-802.