An adaptive squeeze film damper is one whose properties can be continuously adapted to minimize the amplitude of vibration of the rotor in any working condition. This paper concerns an adaptive squeeze film damper with a magnetorheological fluid (MR): a change of its apparent viscosity and stiffness is obtained by applying a magnetic field through the fluid. Electric coils generate the magnetic field and hence simply varying the electric current intensity in the coils can vary the damping effect of the device. The device has been manufactured and preliminary tests have been carried out showing its susceptibility to be automatically controlled. The paper is focused on the study of the control chain of the rotor whirling orbit amplitude in the neighborhood of its critical speed. The rotor is modeled as a flexible shaft supported at the ends with the rotor mass concentrated in the middle and with the damper journal mass close to one support. The damper reaction force is linearized so that the system dynamic equilibrium is described by a set of linear differential equations. Models with different combinations of springs and dashpots in series and parallel have been also considered and compared so as to have a better representation of the magnetorheological fluid behavior. Models of the power supply and of the measurement system are also taken into account. A regulator classical synthesis is then performed to limit the shaft orbit amplitude keeping the damper journal displacement well within the range of the film thickness. Finally simulation results are presented and discussed to show the validity of the proposed solution.