Active Sound Attenuation in Finite-Length Ducts Using Close-Form Transfer Function Models

[+] Author and Article Information
Jwu-Sheng Hu

Department of Mechanical Engineering, Wayne State University, Detroit, MI 48202

J. Dyn. Sys., Meas., Control 117(2), 143-154 (Jun 01, 1995) (12 pages) doi:10.1115/1.2835174 History: Received August 01, 1992; Online January 22, 2008


In this paper, the problem of active sound cancellation in finite-length ducts is investigated. The closed-form solution of a one-dimensional wave equation is obtained as the plant model. The controllability, observability, and transmission zeros are discussed based on the transfer function model. For ducts with totally reflective boundaries, stabilization can be achieved by using a speaker (actuator) and a microphone (sensor). Cases of collocated and noncollocated sensors and actuators are presented. A repetitive control algorithm was developed to drive the actuator so that harmonic noises in a duct are attenuated. For a duct with partially reflective boundaries, the application of repetitive control prevents sound from leaking out of the duct at a chosen end. A simulation study demonstrating the effects of this feedback control scheme is also presented.

Copyright © 1995 by The American Society of Mechanical Engineers
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