This paper describes an original methodology to operate a new nonlinear vibrating membrane pump, actuated by a moving magnet actuator without the use of a motion sensor, in the scope of cardiac assistance. A nonlinear mathematical model of the system is established and used to parametrize a nonlinear position observer that uses the coils current as an input and which output is a feedback to a stroke controller. Actuator’s parameters are identified by a recursive least square algorithm and direct measurements. Finally, a numerical experiment illustrates the implementation of the algorithm and its possible applications.