Noise from auxiliary subsystems, amplified by their own control system, can couple to the output signal of gravitational wave detectors, limiting the maximum attainable sensitivity. Subtraction filters can be used to mitigate this coupling of noise by adding a secondary disturbance path with the purpose of canceling the noise in the output of the detector. The aim of this paper is to develop a systematic approach for the design and online adaptive estimation of subtraction filters. The proposed method adaptively updates the subtraction filter without the need for external perturbations to the system, providing a robust approach towards handling the time-varying couplings in the system as well as reducing the need for detector downtime. The method is validated on a representative simulation of the Advanced Virgo+ gravitational wave detector, illustrating that the method is capable of suppressing the coupling of noise from an auxiliary subsystem while the coupling varies over time.

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.

Some of the feedback loops in the Advanced Virgo+ Gravitational Wave detector exhibit strong coupling and this coupling also varies over time. This paper presents a method to decouple the loops using a decoupling matrix, removing restrictions on the attainable performance of the feedback loops. The presented method performs batch-wise identification of the coupling matrix using only a single sinusoid per loop as perturbation by exploiting the specific structure of the plant to interpolate between frequency bins. The presented method is implemented on AdV+ and is shown to lead to significant decoupling of the loops and to keep the interaction terms low over time.

Dynamic error budgets are an essential tool in identifying opportunities for improvements in a control system for Gravitational Wave detectors, but their potential is often not fully utilized in the control design. This paper presents a model and dynamic error budget for a challenging nested control system in the Advanced Virgo detector in combination with a systematic control design framework for one of the controllers. This framework fully utilizes the dynamic error budget by using H₂ synthesis to allow for fast iterations in the control design when dealing with conflicting control objectives. Simulations together with experimental results on Advanced Virgo illustrate the effectiveness of the presented framework.

Gravitational Wave detectors require feedback control to control the length between the sensitive components of the detector. The degrees of freedom in the control system are inherently coupled and the level of interaction furthermore varies over time. A systematic control design approach for the feedback controllers is presented which provides a guide on how to cope with the varying levels of interaction. A new controller for one of the loops has been designed and experimental results measured on the Gravitational Wave detector Advanced Virgo show a significant reduction in the root mean square error of the loop with the new controller.