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On the frequency scaling in continuous-time modeling (2005)
| Venue: | TABLE I ESTIMATED RESONANCE FREQUENCIES AND DAMPING RATIOS OF THE VILLA PASO BRIDGE. (Hz) (%) 1.5761 ± 0.0014 0.67 ± 0.09 2.6650 ± 0.0023 0.95 ± 0.09 3.5098 ± 0.0026 0.74 ± 0.07 3.7775 ± 0.0033 1.03 ± 0.08 f0ζ f0 std f0( )± ζ std ζ |
| Citations: | 10 - 2 self |
BibTeX
@INPROCEEDINGS{Pintelon05onthe,
author = {R. Pintelon and I. Kollár},
title = {On the frequency scaling in continuous-time modeling},
booktitle = {TABLE I ESTIMATED RESONANCE FREQUENCIES AND DAMPING RATIOS OF THE VILLA PASO BRIDGE. (Hz) (%) 1.5761 ± 0.0014 0.67 ± 0.09 2.6650 ± 0.0023 0.95 ± 0.09 3.5098 ± 0.0026 0.74 ± 0.07 3.7775 ± 0.0033 1.03 ± 0.08 f0ζ f0 std f0( )± ζ std ζ},
year = {2005},
pages = {318321}
}
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Abstract
Abstract- When identifying continuous-time systems in the Laplace domain, it is indispensable to scale the frequency axis to guarantee the numerical stability of the normal equations. Without scaling, identification in the Laplace domain is often impossible even for modest model orders of the transfer function. Although the optimal scaling depends on the system, the model, and the excitation signal, the arithmetic mean of the maximum and minimum angular frequencies in the frequency band of interest is commonly used as a good compromise [1-3]. In this paper we show (i) that the optimal frequency scaling also strongly depends on the estimation algorithm, and (ii) that the median of the angular frequencies is a better compromise for improving the numerical stability than the arithmetic mean. I. PROBLEM STATEMENT Consider the identification of rational transfer function models in the Laplace variable with (1) starting from measured input/output spectra, or frequency response functions,. The goal is to estimate the numerator and denominator coefficients for a given value of the order of the numerator and denominator polynomials. Since parametrization (1) is not identifiable ( for any non-zero real number), the parameter vector should be constrained, for example, or. From a numerical point of view it is often better to use the full s G s θ, ( ) B s θ, () A s θ, () bns
Keyphrases
continuous-time modeling laplace domain arithmetic mean numerical stability frequency band normal equation continuous-time system optimal scaling estimation algorithm angular frequency input output spectrum excitation signal numerical point denominator coefficient optimal frequency good compromise 1-3 transfer function modest model order frequency axis denominator polynomial rational transfer function model minimum angular frequency parameter vector statement consider non-zero real number frequency response function
