Passivity Preserving Multipoint Model Order Reduction using Reflective Exploration

Elizabeth Rita Samuel, Luc Knockaert, Tom Dhaene

2014

Abstract

Reduced state-space models obtained by model order reduction methods must be accurate over the whole frequency range of interest and must also preserve passivity. In this paper, we propose multipoint reduction technique using reflective exploration for adaptively choosing the expansion points. The projection matrices obtained from the expansion points are merged to form the overall projection matrix. In order to obtain a more compact model the projection matrix is truncated based on its singular values. Finally, the reduced order model is obtained, while ensuring that the passivity of the reduced system is preserved during the reduction process.

References

  1. Anderson, B. and Vongpanitlerd, S. (1973). Network Analysis and Synthesis. Prentice-Hall, Englewood Cliffs, NJ.
  2. Balas, G., Chiang, R., Packard, A., and Safonov, M. (2005). Robust Control Toolbox User's Guide. The MathWorks, Inc., Version 3.
  3. Beyer, U. and Smieja, F. (1996). Data exploration with reflective adaptive models. Computational Statistics & Data Analysis, 22(2):193 - 211.
  4. Boyd, S., El Ghaoui, L., Feron, E., and Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory.
  5. Feldmann, P. and R. Freund, W. (1995). Efficient linear circuit analysis by Padè approximation via the Lanczos process. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14(5):639-649.
  6. Ferranti, F., Nakhla, M., Antonini, G., Dhaene, T., Knockaert, L., and Ruehli, A. (2011). Multipoint full-wave model order reduction for delayed peec models with large delays. IEEE Transactions on Electromagnetic Compatibility, 53(4):959-967.
  7. Freund, R. W. (2000). Krylov-subspace methods for reduced-order modeling in circuit simulation. J. Comput. Appl. Math., 123:395-421.
  8. Gahinet, P. and Apkarian, P. (1993). An LMI-based parametrization of all H8 controllers with applications. Proceedings of the 32nd Conference on Decision and Control, pages 656-661.
  9. Gahinet, P., Nemirovski, A., Laub, A., and Chilali, M. (1995). LMI Control Toolbox User's Guide. The MathWorks, Inc., Version 1.
  10. Gallivan, K., Grimme, G., and Dooren, P. (1996). A rational Lanczos algorithm for model reduction. Numerical Algorithms, 12(1):33-63.
  11. Geest, J. D., Dhaene, T., Fach, N., and Zutter, D. D. (1999). Adaptive CAD-model building algorithm for general planar microwave structures. IEEE Transactions on Microwave Theory and Techniques, 47(9):1801-1809.
  12. Khalaj-Amirhosseini, M. (2006). Progress in electromagnetics research. 60:107-117.
  13. Knockaert, L. and De Zutter, D. (2000). Laguerre-SVD reduced-order modeling. IEEE Transactions on Microwave Theory and Techniques, 48(9):1469-1475.
  14. Knockaert, L., Dhaene, T., Ferranti, F., and Zutter, D. D. (2011). Model order reduction with preservation of passivity, non-expansivity and Markov moments. Systems & Control Letters, 60(1):53-61.
  15. Odabasioglu, A., Celik, M., and Pileggi, L. (1998). PRIMA: passive reduced-order interconnect macromodeling algorithm. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 17(8):645-654.
  16. Phillips, J. (2004). Variational interconnect analysis via PMTBR. pages 872 - 879.
  17. Phillips, J., Daniel, L., and Silveira, L. (2003). Guaranteed passive balancing transformations for model order reduction. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 22(8):1027 - 1041.
  18. Silveira, L. and Phillips, J. (2006). Resampling plans for sample point selection in multipoint model-order reduction. Computer-Aided Design of Integrated Circuits and Systems, IEEE Transactions on, 25(12):2775-2783.
  19. Wang, H., Tan, S. X.-D., and Rakib, R. (2012). Compact modeling of interconnect circuits over wide frequency band by adaptive complex-valued sampling method. ACM Trans. Des. Autom. Electron. Syst., 17(1):5:1-5:22.
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Paper Citation


in Harvard Style

Rita Samuel E., Knockaert L. and Dhaene T. (2014). Passivity Preserving Multipoint Model Order Reduction using Reflective Exploration . In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-758-039-0, pages 483-491. DOI: 10.5220/0005018804830491


in Bibtex Style

@conference{icinco14,
author={Elizabeth Rita Samuel and Luc Knockaert and Tom Dhaene},
title={Passivity Preserving Multipoint Model Order Reduction using Reflective Exploration},
booktitle={Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2014},
pages={483-491},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005018804830491},
isbn={978-989-758-039-0},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Passivity Preserving Multipoint Model Order Reduction using Reflective Exploration
SN - 978-989-758-039-0
AU - Rita Samuel E.
AU - Knockaert L.
AU - Dhaene T.
PY - 2014
SP - 483
EP - 491
DO - 10.5220/0005018804830491