Time-domain analysis and synthesis of active noise control systems in ducts

Abstract

This paper presents time-domain analysis and synthesis of active low-frequency noise control systems in rigid-walled ducts. In contrast to frequency-domain analysis, time-domain modeling provides a direct physical insight of the noise cancellation mechanism, where noise signals are assumed to be arbitrary real functions of time instead of harmonics. The time-domain analysis is based on a state-space model which is derived from the governing wave equation using combined numerical (finite difference) and analytical techniques. Optimal feedback control laws are synthesized for a variety of active noise control systems with different sensor and source arrangements. The responses of closed-loop systems are simulated, and the results are compatible with those of transfer function synthesis. In addition, the active control systems so designed have the potential of providing global, broadband, and optimal noise reductions without running into the annoying feedback problems in most feedforward control systems.