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Passive Parametric Macromodeling by Using Sylvester State-Space Realizations

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Informatics in Control, Automation and Robotics

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 325))

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Abstract

A judicious choice of the state-space realization is required in order to account for the assumed smoothness of the state-space matrices with respect to the design parameters. The direct parameterization of poles and residues may be not appropriate, due to their possible non-smooth behavior with respect to design parameters. This is avoided in the proposed technique, by converting the pole-residue description to a Sylvester description which is computed for each root macromodel. This technique is used in combination with suitable parameterizing schemes for interpolating a set of state-space matrices, and hence the poles and residues indirectly, in order to build accurate parametric macromodels. The key features of the present approach are first the choice of a proper pivot matrix and second, finding a well-conditioned solution of a Sylvester equation. Stability and passivity are guaranteed by construction over the design space of interest. Pertinent numerical examples validate the proposed Sylvester technique for parametric macromodeling.

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Notes

  1. 1.

    The exact generic realization \({\mathcal {S}} ({\mathbf {g}}) \) is analytically unknown in the sense that for each new value of \({\mathbf {g}}\) an oracle (or black-box function) has to be consulted.

  2. 2.

    Note that multilinear interpolation satisfies both positivity and partition of unity.

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Acknowledgments

This research has been funded by the Research Foundation Flanders (FWO) and the Interuniversity Attraction Poles Programme BESTCOM initiated by the Belgian Science Policy Office.

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Authors and Affiliations

  1. Ghent University—IMinds, Gaston Crommenlaan 8 Bus 201, B9050, Gent, Belgium

    Elizabeth Rita Samuel, Luc Knockaert & Tom Dhaene

Authors
  1. Elizabeth Rita Samuel
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  2. Luc Knockaert
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  3. Tom Dhaene
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Corresponding author

Correspondence to Elizabeth Rita Samuel .

Editor information

Editors and Affiliations

  1. Institute of Science and Technology, University of Angers, Angers, France

    Jean-Louis Ferrier

  2. Ford Research and Advanced Engineering, Dearborn, Michigan, USA

    Oleg Gusikhin

  3. University Paris-Est Créteil (UPEC), Créteil, France

    Kurosh Madani

  4. Mechanical and Aerospace Engineering 3135 Mackenzie, 1125 Colonel By Drive, Carleton University, Ottawa, Ontario, Canada

    Jurek Sasiadek

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Samuel, E.R., Knockaert, L., Dhaene, T. (2015). Passive Parametric Macromodeling by Using Sylvester State-Space Realizations. In: Ferrier, JL., Gusikhin, O., Madani, K., Sasiadek, J. (eds) Informatics in Control, Automation and Robotics. Lecture Notes in Electrical Engineering, vol 325. Springer, Cham. https://doi.org/10.1007/978-3-319-10891-9_18

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  • DOI: https://doi.org/10.1007/978-3-319-10891-9_18

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10890-2

  • Online ISBN: 978-3-319-10891-9

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