Frequency Response Function Measurements of Multivariable Systems via Local Rational Modeling

The frequency response function (FRF) is a fundamental property of a linear time-invariant system that describes the system's frequency-dependent behavior. Accurately measuring the FRF of multivariable lightly damped systems in a time-efficient manner is difficult due to spectral leakage and long-lasting transient phenomena. In the past, local rational modeling techniques have been introduced that mitigate these difficulties. This article presents an overview of the existing techniques for multivariable systems and proposes a new local rational modeling technique that is both consistent and stochastically efficient in measuring the nonparametric FRF. The proposed technique is successfully validated on simulation examples of a generic multivariable lightly damped system. Its practical applicability is illustrated by characterizing the FRF of an aluminum plate.