Fault tolerance of magnetic bearings by generalized bias current linearization

The mathematical basis for bias linearization of quadratic magnetic actuators, as typified by magnetic bearings, is developed. The approach generalizes prior ad hoc methods of linearizing the relationship between actuator force and electromagnet current, obviating the earlier assumptions of stator symmetry. This relationship is fundamentally quadratic in the regime where the magnetic material is unsaturated and flux is essentially proportional to magnet current. Growing from the properties of a fundamental representation for the current-force relationships in magnetic bearings, conditions are determined under which linearization may be possible. A numerical optimization problem is posed whose solution provides a linearization scheme which maximizes the available force capacity of the actuator. A corollary result is a method for obtaining coil-fault tolerance in magnetic bearings without adding coils to existing actuators. Several paper examples are presented to illustrate linearization of asymmetric actuators, actuators with failed coils, and force/moment actuators.>