The prep stage is designed to measure parameters for the model of the subject’s physiology. There isn’t a reference to that stage that I can point to for you to read specifically on the prep stage. However, I can explain why the end-tidal PCO2 rises at the end.
With a resting calm subject, in the initial prep the gas exchange in the lungs is set by the subject’s tidal volume, dead space, breathing frequency and the metabolic production of CO2. This stage should be with the subject relaxed. The key factor is the alveolar ventilation, which is tidal volume – dead space. We breathe in and out via the same airways, so the conducting airways constitute a volume that contains expired (used) gas on inspiration. Only after this airways volume (dead space) has been inspired do we get fresh air.
During sequential gas delivery (SGD) the RespirAct controls alveolar ventilation and the gas composition of the fresh air (alveolar air). In doing so it controls arterial PO2 and PCO2. To see how sequential gas delivery works, look at Fisher, J.A., Iscoe, S., and Duffin, J. (2016). Sequential gas delivery provides precise control of alveolar gas exchange. Respir Physiol Neurobiol 225, 60-69.
When the RespirAct initiates SGD it sets the alveolar volume for each breath based on the measured tidal volume and the estimated subject’s dead space. To allow for errors in the dead space estimate the alveolar volume is lowered by a fraction. It is therefore less than the subject’s resting alveolar ventilation before SGD. Hence PCO2 rises because the elimination of CO2 via the lungs is less than it was. To allow the RespirAct to best control PCO2, have the subject increase their tidal volume from what it was during the relaxed phase of prep before SGD. I recommend the kind of slow deep breathing practiced for meditation. Implementing that voluntary control (if possible) after the SGD is established will improve targeting during the sequence.