A new relaxation algorithm for the time optimal control problem of step motors

The free end-velocity time-optimal control of a bifilar-wound hybrid step motor is considered. The necessary conditions for the optimal control are derived from motor, load, and driver circuit models using Pontryagin´s minimum principle. A reduced-order relaxation method, involving forward/backward integrations, is presented for finding the solution to the nonlinear two-point boundary value problem specified by the necessary conditions, including generation of an initial control. A driver model for the inverse-diode drive circuit is introduced, and the time-optimal controls for the hybrid step motor with drive circuit are found. Example solutions and comparisons to lead angle controls are presented