Modeling and Dynamic Analysis of an Electrical Helmholtz Resonator for Active Control of Resonant Noise

Abstract

This paper describes a theoretical and experimental investigation into an electrical Helmholtz resonator (EHR): that is, an active noise control (ANC) loudspeaker used in conjunction with a microphone and a feedback controller for suppressing resonant noise in an acoustic cavity. The microphone is collocated with the loudspeaker and a band pass filter of second-order is used as the control filter inside the controller. The EHR is configured as such in order to suppress an acoustic mode that is within the volume velocity drive frequency range of the loudspeaker used. The concepts of impedance and passivity are used to develop the mathematical model as well as to study its dynamics. From these, it is theoretically shown that the EHR for single-mode suppression is an extremely low-impedance acoustic damping device that electrically realizes the pressure neutralization mechanism of a conventional Helmholtz resonator (HR). Experimental work is also presented, in which an EHR is constructed to suppress the Helmholtz mode of an acoustic cavity at about 40 Hz by more than 40 dB, to justify the mathematical model and also to verify the dynamic control mechanism.