Developing artificial breathing machines is crucial in respiratory care, especially for people whose lungs are working poorly. This paper looks at building a mathematical model and computer simulation of a device that tries to mimic normal breathing. The model integrates important lung characteristics such as compliance and resistance to the dynamics of real patient breathing. The initial round of verification tests attempts to validate the system’s response to an ideal input, which allows an assessment baseline for future evaluations. In an effort to improve set-point stability and minimize the effect of disturbances, a PID and FOPID controller were employed on the airflow and pressure control system. In addition, the parameters of PID and FOPID controllers are tuned using PSO and Genetic Algorithms. Results from the assessment indicate that PSO performs better with less error proportional to the power of the simpler PID controllers while explaining more of the system variance. On the other hand, the addition of fractional order terms to FOPID controllers arms them with greater precision and flexibility, and that is where GA is the most effective. FOPID controllers immensely surpass PID controllers, verifying the results, and demonstrating the potential of more advanced controllers for modeling and controlling the respiratory system.