H2H2 and H∞H∞ feedforward and feedback compensators for acoustic isolation

This paper investigates through numerical simulations the limits of performance for a class of feedforward and feedback compensators used for structural acoustic isolation, where the emphasis is on controlling the structural vibration that is responsible for the sound radiation. The proposed designs aim to attenuate the sound pressure transmitted through a double panel system filled with absorption material. The controller must reduce the noise radiated through the back panel when the front panel is excited by an external force that causes structural vibration. A point moment simulating a piezoelectric patch attached to the back panel is the actuator. In the feedforward setting, the pre-filter assumes full information of the exogenous disturbance. On the other hand, the feedback designs assume full information of the state. The H2H2 and H∞H∞ norms are the optimality criteria used for both the filter design and the control design. All four designs are cast in the linear matrix inequality framework and incorporate parametric uncertainties described by a bounded convex polyhedral domain. It is shown that the performance of the feedforward and the feedback compensators are equivalent when model uncertainties are not taken into account. Otherwise, considering uncertainties, the feedback compensators have a more robust behavior.