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. ... Read more

This paper presents a framework for the derivation of a noise budget and the subsequent utilization in the optimization of the control design, using the laser frequency stabilization loop in the Virgo interferometer, which is a complex nested feedback system, as an experimental case study. First, the system dynamics and noise sources are modeled and experimentally verified to produce the noise budget, after which an optimization problem using the H2 norm is formulated and tailored to the specific design requirements for the detector. The structure of the synthesized controller is then used to produce an improved control design. Experimental verification of the developed controller on the Virgo interferometer shows roughly a factor 3 reduction in root-mean-square error, illustrating the effectiveness of the presented method. ... Read more

Gravitational Wave detectors require low-noise sensors combined with high-performance feedback loops to maximize the detector sensitivity in the low-frequency detection range. Some feedback loops in the detector are strongly coupled and their coupling varies over time, which is inherent to the optical configuration and the optical readout scheme used to obtain error signals for the feedback loops. This paper presents a control-based approach to deal with the time-varying interaction among three of the longitudinal degrees of freedom in the Advanced Virgo Plus detector, using the pre-existing infrastructure of the detector. An intuitive Multiple-Input Multiple-Output stability criterion is presented that illustrates how the time-varying coupling affects the stability of the feedback loops, as well as a method that identifies the coupling online and updates a decoupling matrix accordingly. Experiment results of the proposed method on the Advanced Virgo Plus detector illustrate continuous minimization of the coupling over time. Using the derived stability criterion, it is furthermore shown that the coupling is sufficiently minimized such that the interaction terms can be neglected in the control design, resulting in an improved controller performance. ... Read more