Optimal virtual mechanical impedances for the vibroacoustic active control of a thin plate

In order to reduce the acoustic power radiated by a flexible panel, dual colocated actuator / sensor pairs are used to modify its vibration. The control strategy implemented for harmonic disturbances leads to locally impose a virtual mechanical impedance to the structure, using the linear relation between the actuator input and the control output of each pair. This virtual mechanical impedance is computed in order to minimize the radiated acoustic power. The proposed approach consists in two steps: (1) the matrix of optimal virtual mechanical impedance is calculated by measuring the primary disturbance and the transfer functions between actuators and structural/acoustic sensors and (2) the virtual mechanical impedance objective is achieved using a real-time integral controller. It is shown that such an optimal control approach leads to better sound power reduction than a classical active damping strategy where the virtual mechanical impedance is defined as real positive. Theoretical and experimental results are compared, also showing that the method proposed here is robust regarding variations of the primary disturbance.