This paper describes a generalized nonlinear model of active magnetic bearings, for arbitrary number, size and position of pole-pairs, including the coordinate coupling between the vertical and horizontal directions, the nonlinearility of the power amplifier and the effect of finite permeability of the ferromagnetic bearing material. As an example, a practical magnetic bearing with four pole-pairs is examined. The predicted force from the model is quite consistent with experimental results. For the PD controller implemented for a horizontal rotor, the expectation of the equilibrium of the rotor also agrees quite well with the measurement.

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