Optimal solutions to the inverse problem in quadratic magnetic actuators

The formulation of current-to-force relationships for magnetic actuators proceeds in a fairly straightforward fashion from Maxwell's equations for magnetostatic problems. However, the inverse problem of determining a set of currents to realize a desired force is less well understood. Historically, this problem has been relatively neglected because actuators were built in symmetric geometries where a viable solution could be intuited. Recently, calls for both optimal actuator performance and fault tolerance have necessitated the formulation of general solution methodologies for magnetic actuators. This dissertation explores such formulations for magnetic actuators whose current-to-force relationships are homogeneous quadratics. Two inverse strategies are considered: a generalized bias linearization approach that yields solutions which are easily implemented and fault-tolerant; and a direct optimal approach that realizes low power loss. The examples of the class of actuators addressed are radial magnetic bearings and the magnetic stereotaxis system.