Some implications of causality in the active control of sound
Active noise control is evaluated for a variety of primary source waveforms in a one-dimensional free field, and white noise primary sources in a one-dimensional enclosure with varying end conditions. A study is made of the consequences of changes in cost function. Frequency and time domain methods of defining optimum causal controllers are reviewed, and the ability of an adaptive controller to approximate the optimum is evaluated. Time and frequency domain models of sound fields are compared, and good agreement shown, for both one-dimensional (duct) and three-dimensional (room) enclosed sound fields. The performance of finite causal secondary source controllers in reverberant rooms is observed for varying microphone locations and wall reflection coefficients. Multi-sensor, single-secondary active control systems for three-dimensional reverberant enclosures are briefly studied, for secondary sources near to and remote from the primary source. Constraints of causality, finite length, and calculation delay are imposed, with consequent effects on controller configuration and resulting sound field with primary and secondary sources in operation. Comparison is made between the sound field due to the primary source alone, the sound field due to primary and optimal secondary source, and the sound field due to primary and realizable secondary source.