Force control of a linear variable reluctance motor with magnetically coupled phases

The problem of force control is addressed for a type of three-phase linear variable reluctance motor that exhibits strong magnetic coupling between its phases. The force produced is a quadratic function of phase currents with coefficient matrix proportional to the spatial derivatives of inductance. The magnetic coupling leads to a non-diagonal inductance matrix, so all possible products of phase currents are involved in the production of force. Constrained optimization is used to determine phase currents that produce a desired force with minimum power dissipation. The new optimal force controller is shown to be related to an existing force controller that applies to classical synchronous reluctance motors.