An optimal and feedback control routines were developed in this thesis to control simulations of a respiratory system with a muscle and lung compartments. The optimal model was used to find the alveolar ventilation and the Van der Pol constants (𝛼, 𝜔, and 𝛆) that could be used in the body during the steady-state of exercise for each workload. Then, the feedback control model was used to simulate the transient exercise states. The alveolar ventilation was calculated in the feedback control model using a proportional (mean) and a derivative (rate) control. Then, the Van der Pol constants were found from the alveolar ventilation found in the optimal routine. In addition, simulations were done in the steady-state for 3 %, 5 %, and 6 % carbon dioxide inhalation. Once the controller constants had been found, the transient-state of the feedback model showed great promise as the partial pressure of arterial carbon dioxide did not become more than 3.8 % greater then the value that is maintained in the body. The carbon dioxide inhalation tests came within 3 % of the experimental values given by Reynolds (1972). The results from this thesis show that using a Van der Pol oscillator as the breather in the model seems to keep the partial pressure of arterial CO₂ around the value that is maintained in the body for aerobic exercise and CO₂ inhalation. / Master of Science