System identification and closed-loop control of end-tidal CO2 partial pressure in mechanically ventilated patients

This paper presents a systematic approach to system identification and closed-loop control of end-tidal carbon dioxide partial pressure (P_ETCO₂) in mechanically ventilated patients. An empirical model consisting of a linear dynamic system followed by an affine transform is proposed to derive a low-order and high-fidelity representation that can reproduce the positive and inversely proportional dynamic input-output relationship between P_ETCO₂ and minute ventilation (MV) in mechanically ventilated patients. The predictive capacity of the empirical model was evaluated using experimental respiratory data collected from eighteen mechanically ventilated human subjects. The model predicted P_ETCO₂ response accurately with a root-mean-squared error (RMSE) of 0.22+/-0.16mmHg and a coefficient of determination (r²) of 0.81+/-0.18 (mean+/- SD) when a second-order rational transfer function was used as its linear dynamic component. Using the proposed model, a closed-loop control method for P_ETCO₂ based on the proportional-integral (PI) compensator was proposed by the systematic analysis of the system root locus. For the eighteen mechanically ventilated patient models identified, the PI compensator exhibited acceptable closed-loop response with a settling time of 1.27+/-0.20min and a negligible overshoot (0.51+/-1.17%), in addition to zero steady-state P_ETCO₂ set point tracking.