Development of a frequency-domain filtered-x intensity ANC algorithm

A theoretical model for plane wave active intensity control in a finite duct is developed and validated experimentally using a frequency domain adaptive filtered-x control algorithm with a cross-spectrum active intensity error measurement. A square duct terminated by a primary acoustic source at one end and open termination to radiate into a free space at the other end is used for plane wave propagation intensity studies. A secondary active control source is positioned nearly midway between the primary source and open termination. Results from the model and experiment show that for optimal sound cancellation out the open duct end, one has zero intensity everywhere in the duct. However, also predicted by the model and confirmed experimentally, is that moving the error intensity sensor to a position between the primary and secondary source leads to zero intensity between the sources, but also radiation out the open end for frequencies where the intensity sensor position is not a half-wavelength multiple distance from the secondary source. The duct intensity model and experimental results confirm that for optimal active noise cancellation both sources convert no mechanical energy to acoustical power. Intensity analysis of active noise cancellation systems also provides a basis for secondary source efficiency optimization through proper source positioning in the duct.