Hybrid foil–magnetic bearings (HFMBs) are contactless-type bearing systems composed of foil bearings (FBs) on the inner side and active magnetic bearings (AMBs) on the outer side. This configuration provides advantages such as low drag torque, a high DN value (bearing inner diameter multiplied by rotating speed), and high supporting efficiency. However, subsynchronous rotor vibration and modelling uncertainties pose significant challenges to the rotor–HFMB system, which are addressed in this paper. This paper introduces a state-space model for the rotor–HFMB system and analyses the nonlinear hardening stiffness of FBs and the electromagnetic force of AMBs. We propose bounded functions for FBs based on foil structures and the series supporting relationship to effectively limit the resulting modelling uncertainties. To stabilise the system, we design sliding mode, high-gain, and high-frequency controllers through a backstepping method. Moreover, we establish the stability of the resultant closed-loop system. Additionally, we validate our results through simulation studies on the rotordynamics of the rotor–HFMB system and analyse its performance under the designed robust controllers. We evaluate the steady-state error, convergence rate, and system input during transient and steady-state conditions in the X and Y directions.
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