In light of the COVID-19 pandemic, many patients have suffered from Acute Respiratory Distress Syndrome (ARDS) in Intensive Care Units (ICUs) around the world. In the medical field, it is known that the so-called artificial ventilation device, which has become the mainstay of treatment of such syndrome, decreases mortality in critically ill COVID-19 patients. Due to the high reliability of this device, there is an emergency need to follow up the progress made on designing a robust controller for improving its performance. From this perspective, this work introduces different control design schemes for obtaining an optimal Fractional-order PID controller (or simply $P{I}^{\rho }{D}^{\mu }$-controller) of the Artificial Ventilation (AV) system through two optimization algorithms: the Bacteria Foraging Optimization (BFO) and the Particle Swarm Optimization (PSO) algorithms. The realization of the controller is accomplished using four approximations: Oustaloup's approximation, the Continued Fractional Expansion (CFE) approximation and the $1^{st}$- and $2^{nd}$-order El-Khazali approximations. The validation of the controller design and the AV system behavior are verified via numerical simulation in order to demonstrate the effectiveness and the potency of all proposed schemes.