Backstepping boundary control for noise reduction in finite ducts

In this paper, we develop a boundary controller to actively cancel acoustic disturbances in an enclosed duct of finite length using a loudspeaker. Given a distributed parameter acoustic model and the actuator electrical dynamics at the boundary, Lyapunov-type arguments are used to design a model-based backstepping boundary control law that asymptotically regulates the noise within the duct. Dynamic simulation results demonstrate the improved performance achieved by the proposed active noise cancellation algorithm.