So far, the sensitivity of gravitational-wave (GW) detectors, in the low-frequency and mid-frequency regions of its bandwidth, has been limited by technical noises. The re-injection of sensing and control noises can be one of the main limitations. After the end of the third observing run O3, in preparation for the fourth observing run O4, an upgrade phase started among all the km-scale GW detectors, namely LIGO, Virgo and KAGRA, with the aim of improving their sensitivity. In particular, for the case of Advanced Virgo, one of the most significant upgrades is the installation of a signal recycling (SR) mirror, introducing the SR cavity. The main target of this SR mirror is to shape the sensitivity curve of the detector. The installation of a SR mirror adds an extra optical cavity and, thus, extra DoFs (longitudinal and angular), that should be controlled to keep its working point, ultimately increasing the complexity of the whole control strategy. In order to have an accurate description of the interferometer, we have implemented a multiple-input multiple-output (MIMO) model in the frequency domain. The target of this paper, after showing the Advanced Virgo configuration for the next observing run, is to describe the control scheme used for the main longitudinal degrees of freedom using a MIMO approach. In particular, we detail a useful matrix representation for the modeled system. Finally, we use the implemented model to project the sensing and control noises on the sensitivity curve. Following the obtained results, we propose noise subtraction filters to achieve the low control noise target in the low-frequency region of the sensitivity curve. Additionally, using this model, we have implemented the core of a noise budget tool, which will allow to estimate the contribution of all the known sources of noise on the measured sensitivity.