Energetic analysis of an actively controlled one-dimensional acoustic waveguide

Abstract

The aim of this work is to show the energetic behavior when an active noise controller is applied in a one-dimensional waveguide, namely an ideal duct under the first critical frequency. In order to model the duct, a spectral element method, which is shown to be more practical for analyzing pipe networks than other commonly used analytical models, was used. The model used here consists of a duct with two sources, the primary source at one end of the duct, and the secondary source at the middle section. The error sensor was placed downstream from secondary source, and the other end of the duct was open with no flange. Three optimal control methods were applied: minimization of the potential energy density, minimization of the active intensity, and minimization of the total acoustic power radiated by the sources. It was observed that the three control methods achieved the same final result, and when the volume velocity of the secondary source was driven to the optimal volume velocity, neither the primary source nor the secondary source radiated any acoustic power. Furthermore, the controlled duct was equivalent to a duct opened-ended at the secondary source position with radiation impedance equal to zero.