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Research Papers

Energy Extraction-Based Robust Linear Quadratic Gaussian Control of Acoustic-Structure Interaction in Three-Dimensional Enclosure

[+] Author and Article Information
F. Liu

Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: liu.feng@cummins.com

B. Fang

Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: bfang@hit.edu.cn

A. G. Kelkar

Professor
Department of Mechanical Engineering,
Iowa State University,
Ames, IA 50011
e-mail: akelkar@iastate.edu

1Present address: former Graduate Student, currently employed as a research scientist for Cummins Inc.

2Present address: former Visiting Scholar, currently with Harbin Institute of Technology, Nan Gang District, Harbin, China, 150001.

3Corresponding author.

Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received August 5, 2003; final manuscript received March 3, 2014; published online May 5, 2014. Assoc. Editor: John A. Main.

J. Vib. Acoust 136(4), 041008 (May 05, 2014) (8 pages) Paper No: VIB-03-1054; doi: 10.1115/1.4027206 History: Received August 05, 2003; Revised March 03, 2014

This paper presents an linear quadratic Gaussian (LQG)-based robust control strategy for active noise reduction in a 3D enclosure wherein acoustic-structure interaction dynamics is present. The acoustic disturbance is created by the piezo-actuated vibrating boundary surface of the enclosure. The control signal is generated by the speaker which is noncollocated with the sensing microphone mounted inside the enclosure. The dynamic model of the system is obtained using frequency-domain system identification techniques. The state weighting matrix in the LQG cost function is determined analytically in the closed-form which allows the control designer to directly penalize the total acoustic energy of the system. The robustness of the controller is also ensured to guarantee the closed-loop stability against the unmodeled dynamics and parametric uncertainties. Simulation and experiment results are given which demonstrate the effectiveness of the proposed control methodology.

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References

Nelson, P. A., and Elliott, S. J., 1992, Active Control of Sound, Academic Press, London.
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Banks, H. T., Silcox, R. J., and Smith, R. C., 1992, “The Modeling and Control of Acoustic/Structure Interaction Problems Via Piezoceramic Actuators: 2D Numerical Examples,” ICASE, NASA Langley Research Center, Hampton, VA, NASA Report No. 92–17.
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Fang, B., Kelkar, A. G., and Joshi, S. M., 2002, “Modelling and Control of Acoustic-Structure Interaction in 3D Enclosure,” 41st IEEE Conference on Decision and Control, Las Vegas, NV, December 10-13, pp. 873–878. [CrossRef]
Liu, F., 2002, “Active Feedback Control of Acoustic Noise in 3D Enclosures,” M.S. thesis, Iowa State University, Ames, IA.
Fahy, F., 1987, Sound and Structural Vibration, Academic Press, London.
Juang, J.-N., 1994, Applied System Identification, Prentice-Hall Inc, Hoboken, NJ.
Koopmann, G. H., and Fahnline, J. B., 1997, Designing Quiet Structure—A Sound Power Minimization Approach, Academic Press, London.
Skogestad, S., and Postlethwaite, I., 2005, Multivariable Feedback Control Analysis and Design, 2nd ed., John Wiley, New York.

Figures

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Fig. 1

3D acoustic enclosure setup in laboratory

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Fig. 2

Comparison of the identified and measured FRF's

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Fig. 6

Experimental open- and closed-loop frequency response

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Fig. 9

Standard from of additive uncertainty

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Fig. 10

N-Δ configuration

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Fig. 3

An LQG optimal control system

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Fig. 4

Simulated open- and closed-loop frequency response

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Fig. 5

Experimental setup

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Fig. 7

Time response for multitone (225 Hz, 265 Hz, and 290 Hz) disturbance

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Fig. 8

Additive uncertainty of the plant

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Fig. 11

||NYdWd|| ∞ versus frequency

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