An analysis of control using the weighted sum of spatial gradients in active structural acoustic control for flat panels

Active structural acoustic control uses a control metric that when minimized reduces the radiated sound. Previous research has identified the weighted sum of spatial gradients (WSSG) control metric and has shown that it is effective in attenuating the radiated sound power from a plate. The WSSG control metric is computed using weighted measurements of the structural response from four closely spaced accelerometers. In this work, it is shown that the weights used to compute WSSG directly impact the control performance and further understanding into choosing appropriate weights is presented. Weights optimized for single frequencies are investigated and shown to achieve nearly the same performance as minimizing sound power. A set of parameter-based weights for broadband frequency control is also proposed and analyzed. These parameter-based weights are inversely proportional to the square of the flexural wavenumber and can be computed using the ratio of the flexural rigidity to the mass per unit area. Both numerical and experimental results are presented using parameter-based weights for simply supported and clamped plates. The results show that the WSSG control using parameter-based weights is easy to implement and works more effectively than previous methods.