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Research Papers

Active Noise Control in a Duct With Flow

[+] Author and Article Information
Osman Yuksel

Graduate Research Assistant
Department of Mechanical Engineering,
Bogazici University,
Istanbul 34342, Turkey
e-mail: osman.yuksel@boun.edu.tr

Cetin Yilmaz

Assistant Professor
Department of Mechanical Engineering,
Bogazici University,
Istanbul 34342, Turkey
e-mail: cetin.yilmaz@boun.edu.tr

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received August 16, 2012; final manuscript received December 23, 2013; published online February 24, 2014. Assoc. Editor: Eugenio Schuster.

J. Dyn. Sys., Meas., Control 136(3), 031014 (Feb 24, 2014) (7 pages) Paper No: DS-12-1266; doi: 10.1115/1.4026410 History: Received August 16, 2012; Revised December 23, 2013

Active noise control in a one dimensional acoustic duct, in which fluid medium inside the duct has a mean flow velocity, is studied. The acoustic duct model with general boundary conditions is solved in Laplace domain and infinite dimensional system transfer functions are obtained. For controller designs, appropriate microphone, and noise canceling source locations are determined. Low order finite dimensional transfer function approximations of actual system transfer functions are obtained. It is found that, in a selected frequency range, approximations represent actual system in a satisfactory way. By using approximated system transfer functions, finite dimensional, low order, optimal H2 and H controllers are synthesized via linear matrix inequalities method. Closed loop frequency response and time domain simulations show that the controllers successfully suppress unwanted sound, which propagates along the duct.

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Figures

Grahic Jump Location
Fig. 1

Feedback design for ANC in duct

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Fig. 3

(a) Bode magnitude plot and (b) Bode phase plot for d(s) to P(x, s) transfer function at the duct end x = 3.4 m. (c) Bode magnitude plot and (d) Bode phase plot for q(s) to P(x, s) transfer function at the duct end x = 3.4 m (dotted line—exact system transfer function, solid line—approximated transfer function). Here, Ma = 0.1.

Grahic Jump Location
Fig. 4

(a) Bode magnitude plot and (b) Bode phase plot for d(s) to P(xm, s) transfer function at xm = 2.8 m. (c) Bode magnitude plot and (d) Bode phase plot for q(s) to P(xm, s) transfer function at xm = 2.8 m (dotted line—exact system transfer function, solid line—approximated transfer function). Here, Ma = 0.1.

Grahic Jump Location
Fig. 5

(a) Frequency response of uncontrolled and controlled systems at x = 2.8 m. (b) Frequency response of uncontrolled and controlled systems at the duct end at x = 3.4 m (dotted line—uncontrolled, dashed line—H2 controlled, solid line—H controlled). Here, Ma = 0.1.

Grahic Jump Location
Fig. 7

(a) Time domain uncontrolled and controlled system responses for white noise at x = 2.8 m. (b) Time domain uncontrolled and controlled system responses for white noise at the duct end x = 3.4 m (dotted line—uncontrolled, dashed line—H2 controlled, solid line—H controlled). Here, Ma = 0.1.

Grahic Jump Location
Fig. 6

(a) Time domain uncontrolled and controlled system responses at x = 2.8 m. (b) Time domain uncontrolled and controlled system responses at the duct end x = 3.4 m (dotted line—uncontrolled, dashed line—H2 controlled, solid line—H controlled). Here, Ma = 0.1.

Grahic Jump Location
Fig. 2

Frequency response of d(s) to P(x, s) transfer function at x = 2.8 m for three different Mach numbers: (a) for open BC, (b) for frequency dependent impedance BC (dotted line—Ma = 0, dashed line—Ma = 0.1, solid line—Ma = 0.3)

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