A Parametrized Reduced Order Model of 1D Acoustic Propagation System for Robust Spatial Multi-point Active Noise Attenuation

This paper discusses active noise feedback control over a predefined frequency range for a cylindrical and closed three-dimensional cavity. An analytical 1D acoustic model is obtained by averaging the pressure on surfaces that are perpendicular to the sound propagation direction. Furthermore, a parametrized rational reduced order transfer function is proposed relying on the Cauchy method of residues. Based on this new model a Multi-objective $\mathrm{H}_{\infty}$ control, aiming to attenuate the effect of an unknown noise in one or several points, is designed. Achieved performances are discussed in light of different design configurations using either a single or several measurement points.

[1]  Clark J. Radcliffe,et al.  Experimental Verification of the Nonself-Adjoint State Space Duct Model , 1990 .

[2]  Pierre Apkarian,et al.  Mixed H2/Hinfinity Control via Nonsmooth Optimization , 2008, SIAM J. Control. Optim..

[3]  Ian R. Petersen,et al.  Experiments in feedback control of an acoustic duct , 2000, Proceedings of the 2000. IEEE International Conference on Control Applications. Conference Proceedings (Cat. No.00CH37162).

[4]  Boaz Rafaely,et al.  H2/H∞ active control of sound in a headrest: design and implementation , 1999, IEEE Trans. Control. Syst. Technol..

[5]  Philippe Chevrel,et al.  FxLMS versus H∞ Control for Broadband Acoustic Noise Attenuation in a Cavity , 2017 .

[6]  L. R. Quartararo,et al.  Noise and Vibration Control Engineering: Principles and Applications , 1992 .

[7]  Zhenyu Yang,et al.  Theoretical modeling issue in active noise control for a one-dimensional acoustic duct system , 2009, 2008 IEEE International Conference on Robotics and Biomimetics.

[8]  Loiseau Paul,et al.  Broadband Active Noise Control Design through Nonsmooth H∞ Synthesis , 2015 .

[9]  M. Bai,et al.  Plant uncertainty analysis in a duct active noise control problem by using the H ' theory , 1998 .

[10]  Pierre Apkarian,et al.  Nonsmooth H∞ synthesis , 2005, IEEE Trans. Autom. Control..

[11]  Pierre Apkarian,et al.  Mixed H2/H∞ control via nonsmooth optimization , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[12]  Sen M. Kuo,et al.  Active noise control: a tutorial review , 1999, Proc. IEEE.

[13]  Jonathan P. How,et al.  An H_∞-optimal alternative to the FxLMS algorithm , 1998 .

[14]  Hans Zwart,et al.  An Introduction to Infinite-Dimensional Linear Systems Theory , 1995, Texts in Applied Mathematics.

[15]  Pierre Apkarian,et al.  Tuning controllers against multiple design requirements , 2012, 2013 American Control Conference.

[16]  Scott C. Douglas,et al.  Active noise control for periodic disturbances , 2001, IEEE Trans. Control. Syst. Technol..

[17]  R.T. O'Brien,et al.  /spl Hscr//sub /spl infin// active noise control of fan noise in an acoustic duct , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[18]  A. Kelkar,et al.  Modeling and Control of Acoustic Ducts , 2001 .

[19]  Ruth F. Curtain,et al.  Survey paper: Transfer functions of distributed parameter systems: A tutorial , 2009 .

[20]  Larry J. Eriksson,et al.  The selection and application of an IIR adaptive filter for use in active sound attenuation , 1987, IEEE Trans. Acoust. Speech Signal Process..

[21]  Ganapati Panda,et al.  Advances in active noise control: A survey, with emphasis on recent nonlinear techniques , 2013, Signal Process..

[22]  Philippe Chevrel,et al.  H∞ multi-objective and multi-model MIMO control design for broadband noise attenuation in an enclosure , 2016, 2016 European Control Conference (ECC).

[23]  Zhenyu Yang.  Design of active noise control using feedback control techniques for an acoustic duct system , 2004, IEEE Conference on Robotics, Automation and Mechatronics, 2004..

[24]  P. Apkarian,et al.  Nonsmooth H ∞ synthesis , 2005 .