Rigorous development processes aim to be effective in developing critical systems, especially if failures can have catastrophic consequences for humans and the environment. Such processes generally rely on formal methods, which can guarantee, thanks to their mathematical foundation, model preciseness, and properties assurance. However, they are rarely adopted in practice. In this paper, we report our experience in using the Abstract State Machine formal method and the ASMETA framework in developing a prototype of the control software of the MVM (Mechanical Ventilator Milano), a mechanical lung ventilator that has been designed, successfully certified, and deployed during the COVID-19 pandemic. Due to time constraints and lack of skills, no formal method was applied for the MVM project. However, we here want to assess the feasibility of developing (part of) the ventilator by using a formal method-based approach. Our development process starts from a high-level formal specification of the system to describe the MVM main operation modes. Then, through a sequence of refined models, all the other requirements are captured, up to a level in which a C++ implementation of a prototype of the MVM controller is automatically generated from the model, and tested. Along the process, at each refinement level, different model validation and verification activities are performed, and each refined model is proved to be a correct refinement of the previous level. By means of the MVM case study, we evaluate the effectiveness and usability of our formal approach.