Finite Element and Subspace Identification Approaches to Model Development of a Smart Acoustic Box with Experimental Verification

Authors: Tamara Nestorović, Jean Lefèvre, Stefan Ringwelski, Ulrich Gabbert

Abstract:

Two approaches for model development of a smart acoustic box are suggested in this paper: the finite element (FE) approach and the subspace identification. Both approaches result in a state-space model, which can be used for obtaining the frequency responses and for the controller design. In order to validate the developed FE model and to perform the subspace identification, an experimental set-up with the acoustic box and dSPACE system was used. Experimentally obtained frequency responses show good agreement with the frequency responses obtained from the FE model and from the identified model.

Keywords: Acoustic box, experimental verification, finite element model, subspace identification.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1081029

References:

[1] J. Lefèvre, U. Gabbert, ''Finite Element Simulation of Smart Structures for Active Vibration and Acoustic Control'', PAMM Proc. Appl. Math. Mech. 3 (2003), pp. 296-297 DOI 10.1002/pamm.200310420.
[2] F. Laugwitz, J. Lefèvre, G. Schmidt, T. Nestorović , U. Gabbert, ''Experimental and numerical investigation of a smart acoustic box'', International Conference on Modal Analysis, Noise and Vibration Engineering ISMA2006 Leuven, Belgium, in CD-Proceedings of ISMA2006, editors P. Sas, M. de Munck, pp. 223-232.
[3] J. Lefèvre, U. Gabbert, ''Finite Element Modelling of Vibro-Acoustic Systems for Active Noise Reduction'', Technische Mechanik 25 (3-4), 2005, pp. 241-247.
[4] COSAR General Purpose Finite Element Package Manual 1992 FEMCOS mbH Magdeburg http://www.femcos.de
[5] P. Van Overschee, B. De Moor, Subspace Identification for Linear Systems: Theory, Implementation, Applications, Kluwer Academic Publishers, Boston 1996.
[6] M. Viberg, ''Subspace-based methods for the identification of linear time-invariant systems'', Automatica 31(12), 1995, pp. 1835-1851.
[7] T. Nestorović -Trajkov, H. Köppe, U. Gabbert, ''Active Vibration Control Using Optimal LQ Tracking System with Additional Dynamics'', International Journal of Control, vol. 78, no. 15, 15 October 2005, pp. 1182-1197.
[8] T. Nestorović , H. Köppe, U. Gabbert, ''Subspace Identification for the model based controller design of a funnel-shaped structure'', Facta Universitatis, Series Mechanics, Automatic Control and Robotics, vol. 4, no. 17, 2005, pp. 257-263.
[9] T. Nestorović -Trajkov, U. Gabbert, ''Active control of a piezoelectric funnel-shaped structure based on subspace identification'', Structural Control and Health Monitoring, vol. 13, no. 6, November/December 2006, pp. 1068-1079.
[10] T. Nestorović, Controller Design for the Vibration Suppression of Smart Structures (Ph.D. thesis), Fortschritt-Berichte VDI Reihe 8, Nr. 1071, D├╝sseldorf: VDI Verlag 2005.
[11] G. F. Franklin, J. D. Powell, M. L. Workman, Digital Control of Dynamic Systems, third edition, Addison-Wesley Longman, Inc., 1998.
[12] R. J. Vaccaro, Digital Control: A State-Space Approach, McGraw-Hill, Inc., 1995.
[13] T. Nestorović -Trajkov, U. Gabbert, ''Overall virtual design and testing of adaptive mechatronic systems'', Proceedings of the conference Mechatronische Systeme - Entwurf, Anwendungen und Perspektiven, organized in the frame of TEMPUS Project "Restrukturierung und Einf?hrung der Mechatronik an den Universit├ñten in Serbien", September 27-28, 2006, Ni┼í, Serbia (to be published).
[14] Matlab Help, Signal Processing Tooxbox, n4sid, http://www.mathworks.com/access/helpdesk/help/toolbox/ident/n4sid.html