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In medical practice, critical care ventilation provides a vital life support function for patients that have difficulty or are unable to breath for themselves. For the machines that provide this function, control engineering plays a key role in providing safe and accurate delivery of gas to the patient. This tutorial presents an overview of the modeling and control techniques practiced by engineers in critical care ventilation. The lung and the ventilator system are modeled. Flow control, mix control, volume based ventilation controls, pressure based ventilation, adaptive PBV control solution, exhalation pressure control, triggering, disconnect and occlusion, higher level controls, volume assured pressure support, flow regulated CPAP, proportional assist ventilation and oxygen saturation (SpO2) controls in the flow ventilator control system are discussed.