Uppsala universitet

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


Abstract:
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.

Related publications:
Licentiate thesis by Annea Barkefors, May 2014

Paper at IEEE ICASSP 2012 illustrating the enlargement of the zone of silence with MIMO control.

Paper at IEEE ACC 2012 with results from a car compartment..

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.

Source:
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