AbstractThrough proper design, it is possible to build an electromagnetic bearing system, using a ferromagnetic rotor, such that there exists an equilibrium position in the magnetostatic field which is unstable only in the axial direction. In order to achieve axial stability, a regulator may be employed to vary the current in the coils whenever the rotor is displaced from the equilibrium position. The idea is to vary the current in such a way that the resultant change in the magnetic, field produces a restoring force to the rotor.This study is devoted to an investigation of the relative merits of various control laws which could be implemented by the regulator. The rotor is to be maintained in the vicinity of the equilibrium point even if an external force is present which enters the system as an unknown but bounded function of the system state and time.Recent magnetic suspension systems have been designed using a regulator based on linear state variable feedback. It is shown here that asymptotic stability cannot be maintained for the system in the presence of an external force if linear feedback control is used. The effect of an unknown but bounded external force on the system is vividly demonstrated by using qualitative methods to find the boundary of the set reachable under this force. Linear state variable feedback can maintain partial controllability of the system to some neighbourhood of the equilibrium point provided a simple inequality relationship between the feedback parameters and the bounds on the external force is maintained. Finally, it is shown that a game theoretic approach may be used for a nonlinear regulator design which will result in an asymptotically stable system in the presence of an unknown but bounded external force.