In digital valves, stepper motors are often used as the electro-to-mechanical interface. To sustain both high speed of response and good quantitative accuracy, a special algorithm has been designed to control the stepper motor to produce a continuous rotary displacement. Since in this algorithm the current to each coil is cyclic as the rotor tooth advances, several cycles can be used to achieve the desired angular displacement of the motor. This process can result in a reduction or “scaling down” of magnetic nonlinearities such as hysteresis and saturation. This cyclic algorithm has been defined as “stage control” because the algorithm need only be developed for one stage and then repeated when applied to subsequent stages. Critical to the development and understanding of the algorithm is an accurate model of the electromagnetic saturation and hysteresis which exist between the input current and output torque. In this paper, a special mathematical formulation is developed to simulate magnetic saturation and hysteresis which can be applied to a more generic situation. The mathematical formulation derived is one in which hysteresis and saturation parameters are established; an error rate of both saturation and hysteresis is defined from this. Since the error rates are easily determined experimentally or through manufacturers’ specifications, the parameters can be found from these mathematical formulations. The parameters can then be used to predict the hysteresis and saturation characteristics. Special experiments are designed to obtain the input-output characteristics of a stepper motor/valve system under single and multistage control. The model follows the experimental results reasonably well and can be used with confidence to model any system with hysteresis and saturation. The model also predicts very well the effects of using stage control in reducing hysteresis and saturation in a practical valve.

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