  Absorbing airborne noise at frequencies below 300 Hz is a particularly vexing
problem due to the absence of natural sound absorbing materials at these
frequencies. The prevailing solution for low-frequency sound absorption is the
use of passive narrow-band resonators, whose absorption level and bandwidth can
be further enhanced using nonlinear effects. However, these effects are
typically triggered at high intensity levels, without much control over the
form of the nonlinear absorption mechanism. In this study, we propose,
implement, and experimentally demonstrate a nonlinear active control framework
on an electroacoustic resonator prototype, allowing for unprecedented control
over the form of non-linearity, and arbitrarily low sound intensity thresholds.
More specifically, the proposed architecture combines a linear feedforward
control on the front pressure through a first microphone located at the front
face of the loudspeaker, and a nonlinear feedback on the membrane displacement
estimated through the measurement of the pressure inside the back cavity with a
second microphone located in the enclosure. It is experimentally shown that
even at a weak excitation level, it is possible to observe and control the
nonlinear behaviour of the system. Taking the cubic nonlinearity as an example,
we demonstrate numerically and experimentally that in the low frequency range
([50 Hz, 500 Hz]), the nonlinear control law allows improving the sound
absorption performance, i.e. enlarging the bandwidth of optimal sound
absorption while increasing the maximal absorption coefficient value, and
producing only a negligible amount of nonlinear distortion. The reported
experimental methodology can be extended to implement various types of hybrid
linear and/or nonlinear controls, thus opening new avenues for managing wave
nonlinearity and achieving non-trivial wave phenomena.
