Date of Award

Winter 1979

Project Type


Program or Major


Degree Name

Doctor of Philosophy


Stepping motors have become an increasingly popular electromechanical interface device, due to their increased reliability and lower costs over the D.C. Servo motor. The inherent open loop mode of stepping motor operation results, under certain circumstances, in a failure mode in which the output of the stepper no longer follows the input commands. In the past, it has been difficult for the designer to define the failure modes and it has not been obvious how to avoid them.

It is the intent of this dissertation to present a mathematical model for a class of stepping motors, the permanent magnet stepping motors. Analysis reveals that a second order nonlinear model adequately describes the major failure modes for stepping motors. The phase plane, a plot of motor velocity versus position, is used to graphically display the computer solutions of the mathematical model. This method offers the advantage of organizing the solutions in a very compact format and brings order to an otherwise complex problem. By using the phase plane approach, one cannot only predict when the motor will fail, but optimum step sequences can be readily obtained by graphical means.

The second order model is based on the assumption that the current rise time in the motor windings is insignificant compared to the on-time of the windings. A more complex model which includes these effects is developed. This results in a third order nonlinear model, for which the phase plane is no longer adequate to display the solutions. It is then necessary to use a phase space or a three-dimensional plot. It is shown, however, that for step sequences, one can project the three space onto the phase plane to show the effects of the driver electronics. Most of the same organizational advantages apply to the projected three space as was found for the phase plane.