Online decoupling of the time-varying longitudinal feedback loops for improved performance in Advanced Virgo Plus

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.