Decentralized harmonic control of sound radiation and transmission by a plate using a virtual impedance approach
Transmission Loss Setup with smart panel having eight collocated PZT/PVDF units.
Impedance control: electrical equivalent circuit for the unit.
Zones of stability of the decentralized controller using algorithm 3 as a function of loop-gain and rotation angle [defined in Eq. (26)] for a given frequency and a given virtual impedance.
Block diagram of the experimental setup.
Left: Diagonal terms of the experimental transfer matrix between dual variables . The delays due to the low-pass anti-aliasing filters and the acquisition system have been compensated. Right: Passivity test (1 if passive, 0 otherwise) of the system measured (black) and estimated (gray).
Photography of the experimental TL setup viewed from the hemi-anechoic room. The plate (1) with eight surface-mounted piezoelectric patches (black squares), the PVDF sensor electronics (2), the PZT actuator electronics (3), and the dSpace acquisition board (4).
TL with (gray) and without control (black). The mass law is indicated by a dotted line and plate modes are identified using the convention according to Eq. (3).
Comparison of the measured (gray) and predicted (black) attenuation of TL after virtual impedance control.
Measured reductions (in dB) of the SPR by the plate at 430 Hz in the case of acoustic diffuse field excitation as a function of the variables and defined in Eq. (23).
Real part of the sound intensity around the resonance of the (3,1) mode at 430 Hz without (left) and with optimal control (right) in the case of acoustic diffuse field excitation. The plate location is indicated by a rectangle. For this frequency, a 18 dB reduction in sound power in closed loop is obtained.
SPR by the plate before (black) and after control (gray). Plate modes are identified using the convention according to Eq. (3).
Comparison of the measured (gray) and predicted (black) attenuation of radiated acoustic power.
Optimal virtual added impedance matrix . The impedance defined in dual variables has a positive real part for added damping and a negative imaginary part for added stiffness.
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