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Simultaneous H∞ vibration control of fluid/plate system via reduced-order controller

The problem of active reduction of the structural vibrations induced by the sloshing of large masses of fuel inside partly full tank is considered. The proposed study focuses on an experimental device mimicking an aircraft wing made 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. First, a representative finite dimensional model of the complete system containing the first 5 structural modes of the plate and the first 2 liquid sloshing modes is derived via a model matching procedure. A simultaneous H∞ 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 H∞ controller is computed with HIFOO 2.0 and is compared with individual designs for different filling levels. Experimental results are finally provided illustrating the relevance of the chosen strategy.