A test rig was built to perform fatigue tests on thick-walled cylinders made of fibre reinforced plastic (FRP). During the fatigue test, the rotational speed of an FRP cylinder is periodically varied until it fails. The FRP cylinder is connected to a drive spindle that accelerates and decelerates it using a permanent magnet synchronous machine (PMSM). To avoid excessive wear, the rotor is supported by active magnetic bearings (AMB). After the fatigue test was finished with the first cylinder, a new cylinder was attached to the test stand. With this new specimen, previously uncritical radial vibrations became more severe. For high accelerations, these vibrations led to instability of the rotor. However, high accelerations are desirable to perform the fatigue tests in the shortest possible time. Hence, the AMB control should be made insensitive to these vibrations. Since the vibrations depend on the acceleration of the rotor, it is reasonable to assume that they are induced by the PMSM. To reduce the vibrations, these excitations from the PMSM are included in the model-based controller parametrization process for the radial AMB, in which the parameters are adjusted via optimization. With the adjusted control, the amplitude of the vibration was significantly reduced and higher accelerations were possible. The described parameter tuning process can easily be adapted to different AMB systems with disturbances and changes in the system.