Extracting second-order structures from single-input state-space models: Application to model order reduction

Jérôme Guillet; Benjamin Mourllion; Abderazik Birouche; Michel Basset

doi:10.2478/v10006-011-0039-5

.blurhash-client-img { display: none !important; }

Extracting second-order structures from single-input state-space models: Application to model order reduction

International Journal of Applied Mathematics and Computer Science

Volume 21 (2011): Issue 3 (September 2011)

By: Jérôme Guillet, Benjamin Mourllion, Abderazik Birouche and Michel Basset

Open Access

|Sep 2011

Abstract

This paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations with real matrices and has been applied to reduce a single-input second-order form model by balanced truncation and modal truncation.

References

Antoulas, A.C. (2005)., Advances in Design and Control, SIAM, Philadelphia, PA.
Open DOI Search in Google Scholar
Bai, Z., Li, R.-C. and Su, Y. (2008). A unified Krylov projection framework for structure-preserving model reduction,W.H. Schilders, H.A. van der Vorst and J. Rommres (Eds.), Springer, Berlin/Heidelberg, pp. 75-94.
Open DOI Search in Google Scholar
Chahlaoui, Y., Lemonnier, D., Meerbergen, K., Vandendorpe, A. and Dooren, P.V. (2002). Model reduction of second order systems,
Search in Google Scholar
Chahlaoui, Y., Lemonnier, D., Vandendorpe, A. and Dooren, P. V. (2006). Second-order balanced truncation,415(2-3): 373-384.
Open DOI Search in Google Scholar
Dorf, R.C. and Bishop, R.H. (2008)., 11th Edn., Prentice Hall, Upper Saddle River, NJ.
Search in Google Scholar
Ersal, T., Fathy, T.H., Louca, L., Rideout, D. and Stein, J. (2007). A review of proper modeling techniques,
Open DOI Search in Google Scholar
Fortuna, L., Nunnari, G. and Gallo, A. (1992)., Springer-Verlag, Berlin/Heidelberg.
Open DOI Search in Google Scholar
Freund, R.W. (2005). PadéeA-type model reduction of second-order and higher-order linear dynamical systems,V.M. P. Benner and D. Sorensen (Eds.),, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Berlin/Heidelberg, pp. 191-223.
Search in Google Scholar
Friswell, M.I. (1999). Extracting second-order system from state-space representations,37(1): 132-135.
Open DOI Search in Google Scholar
Friswell, M.I., Garvey, S.D. and Penny, J.E.T. (1995). Model reduction using dynamic and iterated IRS techniques,186(2): 311-323.
Open DOI Search in Google Scholar
Glover, K. (1984). All optimal Hankel-norm approximation of linear multivariable systems and their∞-error bounds,39(6): 1115-1193.
Open DOI Search in Google Scholar
Gohberg, I., Lancaster, P. and Rodman, L. (1982)., Academic Press, New York, NY.
Search in Google Scholar
Gugercin, S. (2004). A survey off-road model reduction by balanced truncation and some new results,77(8): 748-766.
Open DOI Search in Google Scholar
Guyan, R. (1964). Reduction of stiffness and mass matrices,3(2): 380.
Open DOI Search in Google Scholar
Houlston, P.R. (2006). Extracting second order system matrices from state space system,220(8): 1147-1149.
Open DOI Search in Google Scholar
Hughes, P. and Skelton, R. (1980). Controllability and observability of linear matrix-second-order systems,47(2): 415-420.
Open DOI Search in Google Scholar
Koutsovasilis, P. and Beitelschmidt, M. (2008). Comparison of model reduction techniques for large mechanical systems,20(2): 111-128.
Open DOI Search in Google Scholar
Li, J.-R. and White, J. (2001). Reduction of large circuit models via low rank approximate gramians,11(5): 1151-1171.
Search in Google Scholar
Li, R.-C. and Bai, Z. (2006). Structure-preserving model reduction,J. Dongarra, K. Madsen and J. WaésAniewski (Eds.), Lecture Notes in Computer Science, Vol. 3732, Springer-Verlag, Berlin/Heidelberg, pp. 323-332.
Open DOI Search in Google Scholar
Meyer, D.G. and Sirnivasan, S. (1996). Balancing and model reduction for second-order form linear systems,41(11): 1632-644.
Open DOI Search in Google Scholar
Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction,ac-26(1): 17-32.
Open DOI Search in Google Scholar
Prells, U. and Lancaster, P. (2005). Isospectral vibrating systems. Part 2: Structure preserving transformation,163: 275-298.
Search in Google Scholar
Reis, T. and Stykel, T. (2007). Balanced truncation model reduction of second-order systems,, DFG Research Center Matheon, Berlin.
Search in Google Scholar
Salimbahrami, S.B. (2005)., Ph.D. thesis, Technical University of Munchen, Munchen.
Search in Google Scholar
Schilders, W.H.A. (2008). Introduction to model order reduction,W.H. Schilders, H.A. van der Vorst and J. Ronnres (Eds.), Springer, Berlin/Heidelberg, pp. 3-32.
Open DOI Search in Google Scholar
Sorensen, D. and Antoulas, A. (2004). Gramians of structured systems and an error bound for structure-preserving model reduction,V.M.P. Benner and D. Sorensen (Eds.),, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Heidelberg/Berlin, pp. 117-130.
Search in Google Scholar
Stykel, T. (2006). Balanced truncation model reduction of second-order systems,
Search in Google Scholar
Tisseur, F. and Meerbergen, K. (2001). The quadratic eigenvalue problem,43(2): 235-286.
Open DOI Search in Google Scholar
Yan, B., Tan, S.-D. and Gaughy, B.M. (2008). Second-order balanced truncation for passive order reduction of RLCK circuits,55(9): 942-946.
Open DOI Search in Google Scholar

Articles in this issue

DOI: https://doi.org/10.2478/v10006-011-0039-5 | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X

Journal RSS Feed

Language: English

Page range: 509 - 519

Published on: Sep 22, 2011

Published by: University of Zielona Góra

In partnership with: Paradigm Publishing Services

Publication frequency: 4 issues per year

Keywords:

second-order form model,

preservation of the structural conditions,

Related subjects:

© 2011 Jérôme Guillet, Benjamin Mourllion, Abderazik Birouche, Michel Basset, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 21 (2011): Issue 3 (September 2011)