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Previously, a generalized bias current linearization was presented for the control of radial magnetic bearings. However, a numerically intensive procedure was required to obtain bias linearization currents. The present work develops an analytical solution to the generalized bias linearization problem in which solutions are indexed by a small number of parameters. The formulation also permits the analytical computation of bias linearization currents for faulted-coil cases. A limitation of the solution presented is that it only applies to stators with an even number of evenly spaces poles of equal area.