Generalized control metric for active structural acoustic control: A novel understanding for controlling symmetric structures

Abstract

Active structural acoustic control (ASAC) is a strategy aiming at controlling the radiated sound of the structure by controlling the vibration. Generally, controlling the vibration is not the same as controlling the radiated sound. Therefore, the choice of the control metric also referred to as the cost function in ASAC is a very important research topic and has been received a lot of attentions by researchers. Previous research has identified a novel control metric named the weighted sum of spatial gradients (WSSG). An analysis has shown that WSSG is able to closely approximates the performance of using radiated sound power as the control objective by choosing the right weights. In this paper, based on previous findings, a generalized control metric of active structural acoustic control for symmetric structures is discussed and analyzed. For symmetric structures, the radiated resistance matrix is always bisymmetric. It will be shown that controlling the vibration is able to achieve the performance of directly controlling the radiated sound power provided that the secondary plant matrix is overdetermined. A uniformed control metric for active structural acoustic control of symmetric structures will be presented and analyzed.