An H∞/MinMax periodic control in a two-dimensional structural acoustic model with piezoceramic actuators

A feedback control computational methodology for reducing acoustic sound pressure levels in a two-dimensional cavity with a flexible boundary (a beam) is investigated. The control is implemented in this model through voltages to piezoceramic patches on the beam which are excited in a manner (out-of-phase) so as to produce pure bending moments. The incorporation of the output feedback control in this system leads to a problem with unbounded input and output terms. By writing the resulting system as an abstract Cauchy equation, the problem of reducing interior pressure levels can be posed in the context of an H_∞ /MinMax time-domain state-space formulation. A summary of extensive computational efforts comparing output feedback to full state feedback and investigating the effect of the number and location of sensors on performance of the control is presented