State-Space Design and Test on a Virgo Superattenuator of a Low-Frequency Vertical Control System for the Einstein Telescope

Gravitational wave detectors are being upgraded to enhance their sensitivity, pushing the limits imposed by their infrastructure. Next-generation observatories, such as the Einstein Telescope and Cosmic Explorer, are currently under design, with the aim of achieving significant improvements in sensitivity and opening new prospects for scientific research. Achieving sensitivity down to 2–3 Hz is one of the major challenges for nextgeneration detectors. In fact, below 10 Hz, seismic noise remains a major challenge, as ground vibrations propagate to the mirrors. In Virgo, the solution developed to mitigate seismic noise led to the SuperAttenuator, a mechanical system that provides seismic isolation at frequencies above 4 Hz. However, seismic noise is amplified in the range of 0.1-3 Hz, increasing the mirror motion with respect to the ground. This work focuses on the development of a control system aimed at damping the vertical resonances of the SuperAttenuator using State-Space modeling and Full- State Feedback techniques. A mechanical model of the SuperAttenuator has been developed and validated using experimental data acquired from the Virgo detector. A Full-State Feedback controller has been designed, using pole placement techniques, to modify the system dynamics and achieve the desired damping performance in the vertical degree of freedom. The designed controller operates over a bandwidth ranging approximately from 0.08 Hz to 3 Hz. The proposed control strategy has been implemented on the Virgo DSP and tested on the Virgo Power Recycling tower. The robustness of the control system has been assessed through a frequencydomain analysis of the stability margins, together with a detailed noise budget of the sensing elements. Finally, the residual mirror displacement has been estimated through the projection of seismic noise along the suspension chain. All simulations and analyses were developed in Python, providing a flexible and reproducible framework for different suspension parameters and control configurations.