In this paper, the dynamics associated with rotor-stator touchdowns involving full circular rub are considered. The expected range of phase shifts occurring in various measurable signals are examined from a theoretical standpoint, with the aim of developing model-free control algorithms that can limit contact force magnitudes during touchdown with auxiliary bearings and ensure contact-free rotor levitation can be restored following persistent contact. Two different strategies are proposed according to whether touchdown planes can be considered collocated with the magnetic bearings or not. Requirements for successful operation, in terms of available sub-models and measurement information are explained and verified through experimental tests on a multi-mode flexible rotor test rig.