System Identification and Closed-Loop Control of End-Tidal CO $_{\bf 2}$ 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 in mechanically ventilated patients. The predictive capability of the empirical model was evaluated using experimental respiratory data collected from 18 mechanically ventilated human subjects. The model predicted P_ETCO₂ response accurately with a root-mean-squared error of 0.22 ± 0.16 mmHg 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 a proportional-integral (PI) compensator was proposed by systematic analysis of the system root locus. For the 18 mechanically ventilated patient models identified, the PI compensator exhibited acceptable closed-loop response with a settling time of 1.27 ± 0.20 min and a negligible overshoot (0.51 ± 1.17%), in addition to zero steady-state P_ETCO₂ set point tracking. The physiologic implication of the proposed empirical model was analyzed by comparing it with the traditional multicompartmental model widely used in pharmacological modeling.