PID-like active impedance control for electroacoustic resonators to design tunable single-degree-of-freedom sound absorbers

Sound absorption at low frequencies still remains a challenge in both scientific research and engineering practice. Natural porous materials are ineffective in this frequency range, as well as acoustic resonators which present too narrow bandwidth of absorption, thus requiring alternative solutions based on active absorption techniques. In the present work, we propose an active control framework applied on a closed-box loudspeaker to enable the adjustment of the acoustic impedance at the loudspeaker diaphragm. More specifically, based on the proportionality between the pressure inside the enclosure and the axial displacement of the loudspeaker diaphragm at low frequencies, we demonstrate both analytically and experimentally that a PID-like feedback control approach allows tuning independently the compliance, the resistance and the moving mass of the closed-box loudspeaker to implement a prescribed impedance of a single-degree-of-freedom resonator. By considering different control combinations to tailor the resonator characteristics, a perfect absorption (with absorption coefficient equal to 1) is achievable at the target resonance frequency, while enlarging the effective absorption bandwidth. Moreover, the proposed feedback control strategy shows an excellent control accuracy, especially compared to the feedforward-based control formerly reported in the literature. The mismatches between the performance of experimental prototype and the model, likely to result from the control time delay and the inaccuracy in estimating the loudspeaker parameters, can be compensated directly by tuning the control parameters in the control platform. The active resonators implemented through the reported control scheme can be used to build more complex acoustic devices/structures to enable high-efficiency broadband sound absorption or other types of acoustic phenomena such as wavefront shaping.