Simultaneous $H_\infty$ Vibration Control of Fluid/Plate System via Reduced-Order Controller

We consider the problem of the active reduction of structural vibrations of a plane wing induced by the sloshing of large masses of fuel inside partly full tank. This study focuses on an experimental device composed of an aluminum rectangular plate equipped with piezoelectric patches at the clamped end and with a cylindrical tip-tank, more or less filled with liquid at the opposite free end. The control is performed through piezoelectric actuators and the main difficulty comes from the complex coupling between the flexible modes of the wing and the sloshing modes of the fuel. First, a partial derivative equation model and then a finite-dimensional approximation, calculated using the first five structural modes of the plate and the first two liquid sloshing modes, is established. Second, after a model matching procedure, a simultaneous control problem associated to the vibration attenuation problem for two different fillings of the tank is stated. Due to the large scale of the synthesis model and to the simultaneous performance requirements, a reduced-order controller is computed with HIFOO 2.0 package and is compared with individual designs for different filling levels. Experimental results are finally provided illustrating the relevance of the chosen strategy.