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.

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.