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

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Języki publikacji
EN
Abstrakty
EN
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.
Rocznik
Strony
509--519
Opis fizyczny
Bibliogr. 29 poz., tab., wykr.
Twórcy
autor
autor
autor
autor
  • Laboratory of Modelling, Intelligence, Processes and Systems, University of Haute-Alsace, ENSISA, 12 rue des freres Lumiere, 68093 Mulhouse Cedex, France, jerome.guillet@uha.fr
Bibliografia
  • [1] Antoulas, A. C. (2005). Approximation of Large-Scale Dynamical Systems, Advances in Design and Control, SIAM, Philadelphia, PA.
  • [2] Bai, Z., Li, R.-C. and Su, Y. (2008). A unified Krylov projection framework for structure-preserving model reduction, in W. H. Schilders, H.A. van der Vorst and J. Rommres (Eds.) Model Order Reduction: Theory, Research Aspects and Applications, Springer, Berlin/Heidelberg, pp. 75-94.
  • [3] Chahlaoui, Y., Lemonnier, D., Meerbergen, K., Vandendorpe, A. and Dooren, P. V. (2002). Model reduction of second order systems, Proceedings of the 15th International Symposium on Mathematical Theory of Networks and Systems of Notre Dame, South Bend, IN, USA.
  • [4] Chahlaoui, Y., Lemonnier, D., Vandendorpe, A. and Dooren, P. V. (2006). Second-order balanced truncation, Linear Algebra and Its Applications 415(2-3): 373-384.
  • [5] Dorf, R. C. and Bishop, R. H. (2008). Modern Control Systems, 11th Edn., Prentice Hall, Upper Saddle River, NJ.
  • [6] Ersal, T., Fathy, T. H., Louca, L., Rideout, D. and Stein, J. (2007). A review of proper modeling techniques, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Seattle, WA, USA.
  • [7] Fortuna, L., Nunnari, G. and Gallo, A. (1992). Model Order Reduction Techniques with Applications in Electrical Engineering, Springer-Verlag, Berlin/Heidelberg.
  • [8] Freund, R. W. (2005). Padé-type model reduction of secondorder and higher-order linear dynamical systems, in V.M. P. Benner and D. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Berlin/Heidelberg, pp. 191-223.
  • [9] Friswell, M. I. (1999). Extracting second-order system from state-space representations, American Institute of Aeronautics and Astronautics Journal 37(1): 132-135.
  • [10] Friswell, M. I., Garvey, S. D. and Penny, J. E. T. (1995). Model reduction using dynamic and iterated IRS techniques, Journal of Sound and Vibration 186(2): 311-323.
  • [11] Glover, K. (1984). All optimal Hankel-norm approximation of linear multivariable systems and their L infinity-error bounds, International Journal of Control 39(6): 1115-1193.
  • [12] Gohberg, I., Lancaster, P. and Rodman, L. (1982). Matrix Polynomials, Academic Press, New York, NY.
  • [13] Gugercin, S. (2004). A survey off-road model reduction by balanced truncation and some new results, International Journal of Control 77(8): 748-766.
  • [14] Guyan, R. (1964). Reduction of stiffness and mass matrices, American Institute of Aeronautics and Astronautics Journal 3(2): 380.
  • [15] Houlston, P. R. (2006). Extracting second order system matrices from state space system, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 220(8): 1147-1149.
  • [16] Hughes, P. and Skelton, R. (1980). Controllability and observability of linear matrix-second-order systems, Journal of Applied Mechanics 47(2): 415-420.
  • [17] Koutsovasilis, P. and Beitelschmidt, M. (2008). Comparison of model reduction techniques for large mechanical systems, Multibody System Dynamics 20(2): 111-128.
  • [18] Li, J.-R. and White, J. (2001). Reduction of large circuit models via low rank approximate gramians, International Journal of Applied Mathematics and Computer Science 11(5): 1151-1171.
  • [19] Li, R.-C. and Bai, Z. (2006). Structure-preserving model reduction, in J. Dongarra, K. Madsen and J. Waśniewski (Eds.) PARA 2004, Lecture Notes in Computer Science, Vol. 3732, Springer-Verlag, Berlin/Heidelberg, pp. 323-332.
  • [20] Meyer, D.G . and Sirnivasan, S. (1996). Balancing and model reduction for second-order form linear systems, IEEE Transactions on Automatic Control 41(11): 1632-644.
  • [21] Moore, B. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction, IEEE Transactions on Automatic Control ac-26(1): 17-32.
  • [22] Prells, U. and Lancaster, P. (2005). Isospectral vibrating systems. Part 2: Structure preserving transformation, Operator Theory 163: 275-298.
  • [23] Reis, T. and Stykel, T. (2007). Balanced truncation model reduction of second-order systems, Technical report, DFG Research Center Matheon, Berlin.
  • [24] Salimbahrami, S. B. (2005). Structure Preserving Order Reduction of Large Scale Second Order Models, Ph.D. thesis, Technical University of Munchen, Munchen.
  • [25] Schilders, W. H. A. (2008). Introduction to model order reduction, in W. H. Schilders, H. A. van der Vorst and J. Ronnres (Eds.) Model Order Reduction: Theory, Research Aspects and Applications, Springer, Berlin/Heidelberg, pp. 3-32.
  • [26] Sorensen, D. and Antoulas, A. (2004). Gramians of structured systems and an error bound for structure-preserving model reduction, in V. M. P. Benner and D. Sorensen (Eds.), Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, Vol. 45, Springer-Verlag, Heidelberg/Berlin, pp. 117-130.
  • [27] Stykel, T. (2006). Balanced truncation model reduction of second-order systems, Proceedings of 5th MATHMOD, Vienna, Austria.
  • [28] Tisseur, F. and Meerbergen, K. (2001). The quadratic eigenvalue problem, Society for Industrial and Applied Mathematics Review 43(2): 235-286.
  • [29] Yan, B., Tan, S.-D. and Gaughy, B. M. (2008). Second-order balanced truncation for passive order reduction of RLCK circuits, IEEE Transactions on Circuits and Systems II 55(9): 942-946.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPZ1-0073-0023
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