• control
• low-frequency
• Superattenuator
• vertical

Gravitational waves (GWs) detectors have been upgraded over time to increase their sensitivity, and studies are going on toward reaching the limits imposed by their infrastructure, with Virgo_Next, and A#. Next generation detectors, Einstein Telescope and Cosmic Explorer, are under design, while candidate sites to host them are being carefully evaluated.
Increasing sensitivity can have significant implications in scientific research, such as the possibility of detecting GWs produced by high-redshift compact object coalescences, increasing the signal-to-noise ratio for spinning neutron stars and stochastic background.
Lowering the minimum detectable frequency allows also to detect binary neutron star systems well before the coalescence, enabling early warnings to telescopes for multimessenger observations.
Seismic noise poses a critical challenge for detecting GW at very low frequencies (below 10 Hz) since vibrations are anyway transmitted to the mirrors, making it essential to isolate them. To optimally operate the detector it is also very important to minimize the mirrors' Root-Main-Square (RMS) residual motion.
Over the years, the INFN Pisa group's efforts led to the development of the VIRGO's Super-Attenuator (SA), which provides passive seismic isolation for frequencies above 4 Hz, successfully reaching design performance. However, seismic noise is amplified at its natural frequencies in the range of [0.1,3] Hz, increasing the RMS motion with respect to the ground one.
This thesis aims at developing a control system capable of damping the SA resonances and reducing the mirror's RMS residual motion, focusing on the vertical degree of freedom (d.o.f.).
For this purpose, I first developed a comprehensive mathematical model for the SA chain, crucial for designing effective control systems in modern control theory.
I implemented a Python simulation of the system's temporal evolution by employing state-variable models and ARMA techniques, which allow us to describe the system dynamics by a list of first-order differential equations. Then, using the state-space design, I computed its transfer function, yielding a system's description in terms of its poles and zeros. It was then possible to produce a set of matrices that contains all the information about the system's dynamic.
I have compared the modelled transfer function with real-world data. Specifically, I retrieved the Virgo measurement of the vertical transfer function for the Signal Recycling (SR) chain. Then, I proceeded to design a full-state feedback in Python, employing pole placement techniques to manipulate system dynamics and achieve the desired performance.
This research contributes to the advancement of GWs detection technology by addressing fundamental challenges in seismic noise mitigation and control system design. It represents an essential step toward reducing the overall RMS motion, in view of the more complex work on the horizontal d.o.f. along the beam direction, however beyond the scope of this thesis. Currently all GWs interferometers have low frequency noise that exceeds by orders of magnitude the expected one. Through a combination of theoretical modelling, simulation, and practical control strategies, the goal is to contribute to reaching the design sensitivity in current and future detectors.