Frequency Response Function (FRF) measurements are widely used in gravitational wave detectors, e.g., for the design of controllers, calibrating signals, and diagnosing problems with system dynamics. The aim of this paper is to present GraFIT: a toolbox that enables fast, inexpensive, and accurate identification of FRF measurements for gravitational wave detectors compared to the commonly used approaches, including common spectral analysis techniques. The toolbox builds upon recent developments in non-parametric system identification by utilizing a local modeling technique, which is particularly effective in reducing the impact of transient effects. It is furthermore designed to be user-friendly, handling systems of arbitrary input-output dimensions, and systems operating in a closed loop. The toolbox is validated on two experimental case studies of the Virgo detector, illustrating more than a factor 3 reduction in the estimated standard deviation using GraFIT for the same measurement times and comparable estimated standard deviations with up to ten times less data using GraFIT with respect to the commonly used spectral analysis method. As a result, GraFIT can reduce commissioning time and detector downtime due to noise injections, while also improving the overall quality of the measurements.

The increasing demands for motion control result in a situation where Linear Parameter-Varying (LPV) dynamics have to be taken into account. Inverse-model feedforward control for LPV motion systems is challenging, since the inverse of an LPV system is often dynamically dependent on the scheduling sequence. The aim of this paper is to develop an identification approach that directly identifies dynamically scheduled feedforward controllers for LPV motion systems from data. In this paper, the feedforward controller is parameterized in basis functions, similar to, e.g., mass-acceleration feedforward, and is identified by a kernel-based approach such that the parameter dependency for LPV motion systems is addressed. The resulting feedforward includes dynamic dependence and is learned accurately. The developed framework is validated on an example.