Simulations for the Locking and Alignment Strategy of the DRMI Configuration of the Advanced Virgo Plus Detector

The Advanced Virgo Plus project aims to increase the sensitivity of the Virgo gravitational-wave detector, given the forthcoming O4 Observing Run. One of the major upgrades is the addition of the Signal Recycling Mirror in the optical layout. This additional mirror will provide a broadband improvement to the sensitivity curve of the instrument, but poses significant challenges in the acquisition and operation of the detector's working point. The process which brings the main optical components from the uncontrolled state to the final working point, which ensures the best detector sensitivity, is called lock acquisition: the lock acquisition is made by moving through increasingly more complex configurations toward the full control of all the interferometer's longitudinal degrees of freedom. This paper will focus on the control of the Dual-Recycled Michelson Interferometer (DRMI, the central part of the Virgo interferometer), presenting a comprehensive study of the optical simulations used in the design and the commissioning of this configuration. Treated topics include: the characterization of optical fields, powers, and error signals for the controls; the development of a trigger logic to be used for the lock acquisition; the study of the alignment sensing and control system. The interdependence between the three items has also been studied. Moreover, the validity of the studied techniques will be assessed by a comparison with experimental data.