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Design and Analysis of Linear Quadratic Gaussian
Feedforward Controllers for Active Noise Control.
Annea Barkefors
,
Mikael Sternad
, Uppsala University
and
Lars-Johan Brännmark
, Dirac Research AB
IEEE Transactions on Audio, Speech and Language Processing,
vol. 22, no. 12, December 2014, pp. 1777-1791.
DOI 10.1109/TASLP.2014.2349856.
© 2014 IEEE
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Abstract:
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A method for sound field control applied to active
noise control is presented and evaluated. The method uses
Linear quadratic Gaussian (LQG) feedforward control to find
a Minimal Mean Square Error (MMSE)-optimal linear sound
field controller under a causality constraint. It is obtained
by solving a polynomial matrix spectral factorization and a
linear (Diophantine) polynomial matrix equation.
An important
component in the design is the control signal penalty term
of the criterion. Its use and influence is here discussed and
evaluated using measured room impulse responses. The results
indicate that the use of a relatively simple, frequency-weighted
penalty on individual control signals provides most of the benefits
obtainable by the considered more advanced alternative.
We also
introduce and illustrate several tools for performance analysis.
An analytical expression for the attainable performance clearly
reveals the performance loss generated by having to use a
causal controller instead of the ideal noncausal controller. This
loss is largest at low frequencies.
Furthermore, we introduce a
measure of the reproducibility of the target noise sound field with
given control loudspeaker setups and room transfer functions. It
describes how well a controller that uses an input subspace of
dimension equal to the effective rank of the system is able to
reproduce a target sound field. This performance measure can
e.g. be used to support the selection of good combinations of
placements of control loudspeakers.
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Related publications:
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Licentiate thesis by Annea Barkefors, May 2014
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Paper at IEEE ICASSP 2012 illustrating the enlargement
of the zone of silence with MIMO control.
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Paper at IEEE ACC 2012 with results from a car compartment..
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Robust Sound Field Control for Audio Reproduction.
A polynomial approach to discrete-time acoustic
modeling and filter design.
PhD Thesis by Lars-Johan Brännmark, 2011.
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Source:
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