Approximation of a damped Euler-Bernoulli beam model in the Loewner framework

TL;DR

This paper applies the Loewner framework to approximate a damped Euler-Bernoulli beam model, an infinite-dimensional system with an irrational transfer function, using input-output data for efficient model reduction.

Contribution

It extends the Loewner framework to infinite-dimensional systems and demonstrates improved approximation results when applied directly to the original transfer function.

Findings

Better approximation results with direct application to the original transfer function

Effective model order reduction using only input-output measurements

Applicable to PDE-based systems like the Euler-Bernoulli beam

Abstract

The Loewner framework for model order reduction is applied to the class of infinite-dimension systems. The transfer function of such systems is irrational (as opposed to linear systems, whose transfer function is rational) and can be expressed as an infinite series of rational functions. The main advantage of the method is the fact that reduced orders models are constructed using only input-output measurements. The procedure can be directly applied to the original transfer function or to the one obtained from the finite element discretization of the PDE. Significantly better results are obtained when using it directly, as it is presented in the experiments section.