Reducing Second Order Systems by an integrated state space and back Conversion procedure
| Authors: | Salimbahrami Behnam, Technical University of Munich, Germany
Lohmann Boris, Technical University of Munich, Germany
Grotmaack Rike, University of Bremen, Germany
Bunse-Gerstner Angelika, University of Bremen, Germany |
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| Topic: | 1.1 Modelling, Identification & Signal Processing |
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| Session: | Model Reduction Techniques |
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| Keywords: | Model reduction, Second-order systems, Large scale systems, Markov parameters, Reduced-order models |
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Abstract
In this paper, the Arnoldi algorithm is modified to match the first Markov parameter and some of the First moments in order reduction of large scale systems while preserving the properties of the standard reduction method using Arnoldi: an upper Hessenberg matrix as a coefficient of $\mathbf{\dot{x}}_r$, identity as a coefficient of $\mathbf{x}_r$ and a multiple of the first unit vector as the input vector. These properties are then used for order reduction of large scale second order models by first reducing in state space and then converting to second order form by introducing a numerical algorithm to find the reduced second order model.
