Time-Optimal Control of Hybrid Step Motor

This thesis on step motors is prepared with the objectives of finding the time-optimal controls, which include the free end-velocity time-optimal control and the zero end-velocity time-optimal control, for the bifilar-wound hybrid step motor. The necessary conditions for the optimal controls are derived from a motor, load, and driver circuit model using Pontryagin\u27s Minimum Principle. A new reduced-order relaxation method, involving forward/backward integrations, for finding the solution to the nonlinear two-point boundary value problem specified by the necessary conditions, including generation of an initial control, is presented. A drive circuit model for the inverse-diode-clamped drive circuit is introduced and the time-optimal controls for the hybrid step motor with drive circuit are found. Example solutions are presented and comparisons to lead-angle controls are made. The major contribution of this work is the development of reduced-order time-optimal control problems for the hybrid step motor with the drive circuit model and a numerical method for solving these problems. In addition, initial guess solutions for the relaxation method have been found so that the method converges and converges quickly for arbitrary bifilar-wound hybrid step motors and load models, and for different length moves