The liquid ventilator have a peristaltic pump to deliver oxygenated PFC liquid to and from lungs of newborn. This paper is about the learning control of the pump. The problem is to track a reference signal of N ramps in spite of large measurement noise. The presented algorithm slowly learns the initial conditions of the controller for each desired ramp. Thus, few information are memorized to track repetitive sequence. The implementation is based on the use of as many PI controllers as ramps. An analysis of the control scheme and experimental results with the prototype of a total liquid ventilation system are presented.