Respiratory modules are used to assist patients who are unable to breathe sufficiently on their own. The aim of this paper is to develop a control method that achieves exact tracking of a time-varying target pressure, invariant to patient-hose-leak parameters. This is achieved by an online hose calibration that enables compensation for the pressure drop over the hose. Stability of the closed-loop system is analyzed and the performance improvement compared to state-of-practice feedforward and linear feedback control strategies is demonstrated by a simulation case study.