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.@en

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.@en

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.

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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.

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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.

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