Active noise control of sound wave in a one-dimensional duct

This paper describes a feedback controller for reducing traveling waves in a one-dimensional duct with air flow. The one end of the relevant duct is open to the air, and a fan is installed at the other end. In order to control and reduce the noisy sound radiating from the open end of the duct, the amplitude of the traveling waves propagating to the open end from the fan should be minimized, because the power of sound radiation from the open end depends on the amplitude of the traveling waves. Based on the mathematical model derived earlier by the authors (1997) on the sound pressure in the duct, a finite-dimensional controller is designed for the electric speaker equipped near the open-end of the duct to reduce the noise from flowing outside. Simulation studies provide some numerical results