Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2017 | Vol. 11, nr 1 | 3--12
Tytuł artykułu

Frequency-weighted model order reduction combined with the model decomposition

Wybrane pełne teksty z tego czasopisma
Warianty tytułu
Języki publikacji
Physical objects, in practice, are frequently represented by the LTI (Linear Time Invariant) models consisting of linear differential equations with constant coefficients. The LTI models of complex objects often have a large size. Designing a control system or performing a realtime object simulation on large-scale models may not be possible. Model Order Reduction (MOR) is an operation performed to reduce the size of a model with retaining its most important features. In the case where the reduced model has to approximate the frequency characteristics of the original model within the given range of adequacy, the Frequency-Weighted (FW) method should be used. The FW method requires to select the appropriate parameters of the input and / or output filters in order to obtain the best results. This selection is not an unique operation - which means that it is advisable to use an evolutionary algorithm that performs multiple reduction operations to match the relevant parameters. It is possible to reduce the computational complexity of the FW reduction process by decomposing the model into parts. The purpose of the paper is to compare the Frequency-Weighted order reduction combined with a various model decompositions based on the Schur complement, Schur and the Schur-Sylvester methods. The research is conducted on linearized models of the one-phase zone of the evaporator of the once-through steam BP-1150 boiler. The stability and accuracy of the reduced models are analyzed.

Opis fizyczny
Bibliogr. 23 poz., fig.
  • [1] Antoulas A.: Approximation of Large-Scale Systems, SIAM, Philadelphia (2005).
  • [2] Glover K.: All optimal Hankel-norm approximations of linear multivariable systems and their L∞ - error bounds, Int. J. Control, vol. 39, pp. 1115–1193, (1984).
  • [3] Varga A., Anderson B.: Accuracy enhancing methods for the frequency-weighted balancing related model reduction, Proc. of CDC'2001, pp. 3659-3664, Orlando, Florida (2001).
  • [4] Laub A., Heath M., Paige C., Ward R.: Computation of System Balancing Transformations and Other Applications of Simultaneous Diagonalization Algorithms, IEEE Trans. on Automatic Control, vol. AC-32, no. 2, (1987).
  • [5] Varga A.: Numerical methods and software tools for model reduction, Proc. of 1st MATHMOD Conference, vol. 2, pp. 226-230, Wien (1994).
  • [6] Varga A.: Balancing-free square-root algorithm for computing singular perturbation approximations, Proc. of 30th IEEE CDC, Brighton, UK (1991).
  • [7] Safonov M., Chiang R.: A Schur Method for Balanced-Truncation Model Reduction, IEEE Trans. Automat. Contr., vol. 34, no. 7, pp. 729-733, (1989).
  • [8] Obinata G., Anderson B.: Model Reduction for Control System Design, Springer-Verlag, London (2001).
  • [9] Enns D.: Model reduction with balanced realizations: An error bound and a frequency weighted generalization, Proc. 23-th IEEE Conf. Dec. Control, pp. 127-132, Las Vegas (1984).
  • [10] Tsubakino D., Fujimoto K.: Weighted balanced realization and model reduction for nonlinear systems, Transactions of the Society of Instrument and Control Engineers, Vol. 44, No. 1, pp. 44-51, (2008).
  • [11] Sreeram V., Ghafoor A.: Frequency Weighted Model Reduction Technique with Error Bounds, IEEE American Control Conference, June 8-10, pp. 2584-2589, Portland, USA (2005).
  • [12] Li L., Paganini F.: Structured frequency weighted model reduction, Decision and Control. Proceedings. 42nd IEEE Conference on, Volume: 3, pp. 2841-2846, (2003).
  • [13] Wang G., Sreeram V., Liu W.: A New Frequency-Weighted Balanced Truncation Method and an Error Bound, IEEE Transactions on Automatic Control, VOL. 44, NO. 9, pp. 1734-1737, (1999).
  • [14] Beghi A., Portone A.: Model reduction by sub-structuring, proceedings of the 10th Mediterranean Conference on Control and Automation – MED2002, July 9-12, Lisbon, Portugal (2002).
  • [15] Vandendorpe A., Dooren P.: Model Reduction of Interconnected Systems, volume 13 of Mathematics in Industry, Model Order Reduction: Theory, Research Aspects and Applications, Springer Berlin Heidelberg, pp. 305-321, (2008).
  • [16] Reis T., Stykel T.: A survey on model reduction of coupled systems, volume 13 of Mathematics in Industry, Model Order Reduction: Theory, Research Aspects and Applications, Springer Berlin Heidelberg, pp. 133-155, (2008).
  • [17] Lutowska A.: Model Order Reduction for Coupled Systems using Low-rank Approximations, Technische Universiteit Eindhoven, phd. thesis, (2012).
  • [18] Zhang F.: The Schur complement and its applications, Springer-Verlang, New York (2005).
  • [19] Blömeling F.: Multi-level substructuring combined with model order reduction methods, Linear Algebra and its Applications 436, pp. 3864-3882, (2012).
  • [20] Stewart G.: Matrix Algorithms. Volume II: Eigensystems, SIAM, Philadelphia (2001).
  • [21] Safonov M., Jonckheere E., Verma M., Limebeer D.: Synthesis of Positive Real Multivariable Feedback Systems, Int. J. Control, vol. 45, no. 3, pp. 817-842, (1987).
  • [22] Rydel M.: Zredukowane hierarchiczne modele złożonych obiektów sterowania na przykładzie kotła energetycznego, [Hierarchical reduced models of complex control objects on the example of the power boiler], PhD thesis, Faculty of Electrical Engineering, Automatic Control and Informatics, Opole University of Technology, Opole (2008).
  • [23] Stanisławski W., Rydel M.: Hierarchical mathematical models of complex plants on the basis of power boiler example, Archives of Control Sciences, vol. 20, no. 4, pp. 381-416, (2010).
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Identyfikator YADDA
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.