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TECHNICAL PAPERS

An Improved Acoustic Model for Active Noise Control in a Duct

[+] Author and Article Information
Benjamin J. Zimmer

Meikle Automation, Kitchener, Ontario, Canada

Stanley P. Lipshitz, Kirsten A. Morris

Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada

John Vanderkooy

Department of Physics, University of Waterloo, Waterloo, Ontario, Canada

Edmund E. Obasi

RDWI Ltd., Calgary, Alberta, Canada

J. Dyn. Sys., Meas., Control 125(3), 382-395 (Sep 18, 2003) (14 pages) doi:10.1115/1.1592192 History: Received September 07, 2001; Revised March 29, 2003; Online September 18, 2003
Copyright © 2003 by ASME
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References

Elliot,  S. J., and Nelson,  P. A., 1993, “Active noise control,” IEEE Signal Process. Mag., 10, pp. 12–35.
Seto, W. W. 1972, Theory and Problems of Acoustics, McGraw-Hill, Inc., New York.
Hong,  J., Akers,  J. C., Venugopal,  R., Lee,  M.-N., Sparks,  A. G., Washabaugh,  P. D., and Bernstein,  D. S., 1996, “Modeling, identification, and feed-back control of noise in an acoustic duct,” IEEE Trans. Control Syst. Technol., 4, pp. 283–291.
Hull,  A. J., Radcliffe,  C. J., and Southward,  S. C., 1993, “Global active noise control of a one-dimensional acoustic duct using a feedback controller,” ASME J. Dyn. Syst., Meas., Control, 115, pp. 488–494.
Hull,  A. J., and Radcliffe,  C. J., 1991, “An eigenvalue based acoustic impedance measurement technique,” ASME J. Vibr. Acoust., 113, pp. 250–254.
Hull,  A. J., Radcliffe,  C. J., and MacCluer,  C. R., 1991, “State estimation of the nonself-adjoint acoustic duct system,” ASME J. Dyn. Syst., Meas., Control, 113, pp. 122–126.
Morris,  K. A., 1998, “Noise reduction in ducts achievable by point control,” ASME J. Dyn. Syst., Meas., Control, 120, pp. 216–223.
Spiekermann,  C. E., and Radcliffe,  C. J., 1988, “Decomposing one-dimensional acoustic pressure response into propagating and standing waves,” J. Acoust. Soc. Am., 84(4), pp. 1536–1541.
Levine,  H., and Schwinger,  J., 1948, “On the radiation of sound from an unflanged circular pipe,” Phys. Rev., 73, pp. 383–406.
Hu,  J. S., 1995, “Active sound attenuation in finite-length ducts using close-form transfer function models,” ASME J. Dyn. Syst., Meas., Control, 117, pp. 143–154.
Birdsong,  C., and Radcliffe,  C. R., 1999, “A compensated acoustic actuator for systems with strong dynamic pressure coupling,” ASME J. Vibr. Acoust., 121, pp. 89–94.
Lane,  S. A., and Clark,  R. L., 1998, “Improving loudspeaker performance for active noise control applications,” J. Audio Eng. Soc., 46, pp. 508–518.
Morse, P. M., and Feshbach, H. 1953, Methods of Theoretical Physics, McGraw-Hill, Inc., New York.
Beranek, L. L., 1986, Acoustics, American Institute of Physics, Inc., New York.
Pierce, A. D. 1981, Acoustics: An Introduction to Its Physical Principles and Applications, McGraw-Hill, New York.
Morse, P. M., and Ingard, K. N., 1986, Theoretical Acoustics, Princeton University Press.
Pazy, A. 1983, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York.
Obasi, E. E., 2002, An Improved One-Dimensional Duct Model and RobustHController Design for Active Noise Control, M. Math. Thesis, University of Waterloo.
Zimmer, B. 1999, An Improved One-Dimensional Model for Active Noise Control, M. Math. Thesis, University of Waterloo.

Figures

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Acoustical duct system.
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Normalized impedance ZL0c (Solid) and the rational approximation to ZL0c(dashed). (For our duct, normalized frequency is f/537.)
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Measured (dashed) and calculated (solid) input voltage to loudspeaker cone acceleration frequency responses.
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Measured (dashed) and calculated (solid) canceller speaker to mid microphone frequency responses, with rigid plug at x=0.
Grahic Jump Location
Measured (dashed) canceller speaker to mid microphone frequency response, with loudspeaker at x=0. Calculation is with rigid.
Grahic Jump Location
Measured (dashed) and calculated (solid) disturbance speaker to end microphone frequency responses.
Grahic Jump Location
Measured (dashed) and calculated (solid) disturbance speaker to mid microphone frequency responses.
Grahic Jump Location
Measured (dashed) and calculated (solid) canceller speaker to end microphone frequency responses.
Grahic Jump Location
Measured (dashed) and calculated (solid) canceller speaker to mid microphone frequency responses.

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