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We consider the problem of active reduction of vibrations in a fluid-flexible structure system. In the aerospace domain, we are actually interested in the system that couples the deflection of a plane wing and the sloshing of the fuel inside the wing's tank. The control is performed using piezoelectric patches and the main difficulty comes from the complex coupling between the flexible modes of the wing and the sloshing modes of the fuel. We establish an infinite-dimensional model for the global system and then a finite-dimensional approximation calculated using the first modes and validated on the experimental setup. A feedback controller is used to show the effectiveness of the closed loop in attenuating vibrations.