Time-optimal acceleration control and point-to-point of step motors

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