THE ANALYSIS AND SIMULATION OF HYBRID STEPPING MOTORS USING THE PHASE PLANE APPROACH

Stepping motors have become very popular electromechanical interface devices because they are easy to interface to digital control logic. The most popular stepping motor currently used is the hybrid design stepping motor. It incorporates an efficient magnetic structure to obtain a high output torque, while maintaining a position resolution of fifty parts per million. All stepping motors are nonlinear devices and, therefore, control strategies have been difficult to develop and implement. A second order, nonlinear model was developed by Gauthier to describe the permanent magnet stepping motor. The results of this model are displayed using the phase plane and considerable insight into the motor\u27s performance and operating characteristics are obtained. In this work the model is modified to describe the hybrid stepping motor by including inductance, magnetic saturation, hysteresis and eddy current losses. This yields a sixth order, nonlinear model, the solution of which requires a six dimension space to display the results. The six dimension solution can be projected back into the two dimension phase plane. A strong understanding of the implications of this projection is necessary to properly interpret the results. Once this understanding is obtained, many of the operating and dynamic characteristics of the hybrid stepping motor can be understood and explained. In addition, the techniques that were developed for designing sequences or control strategies for the permanent magnet stepping motor can now be applied to the hybrid stepping motor. The hybrid motor can also be operated as a synchronous device. The model that was developed to describe its performance when being stepped can be used to predict the operating modes when the motor is driven by a synchronous AC source. The solution of the equations is again projected back into a two dimension space where many of the dynamic characteristics are easily seen. Both the stepping and synchronously driven models are then used to investigate the characteristics and cause of mid-frequency resonance in the hybrid motor. This instability phenomenon is shown to be caused by amplitude and frequency modulation effects in the stepping motor