Portable Oxygen Concentrators (POCs) are devices that produce oxygen-enriched air, by selectively filtering nitrogen out of ambient air with a cyclic process called Pressure Swing Adsorption (PSA). The current control method is to adjust the timings of the process by means of lookup tables, such that the POC operates as efficient as possible. The aim of this thesis is to determine whether Model Predictive Control (MPC) is a viable alternative to control the POC, and is able to cope with the constraints and variations of the system. First, a high-fidelity model has been made of the POC, used for simulation of the device and controller design. Comparisons with other suitable models of POCs have shown that the dynamics inside the POC have been modeled correctly. Because this model is too complex to serve as a predictive model, a simplified batch model has been created for that purpose. This hybrid automaton consists of 13 linear models, and encompasses the cycle-to-cycle dynamics of the plant. Finally, a switched linear MPC strategy has been designed and implemented on the high-fidelity model. Simulations show that this control strategy is suited to control the POC, although further research is needed to cope with system degradation.