Stroke-dependent magnetic hysteresis modeling in proportional solenoids using parametric Gaussian-mixture Preisach distribution

The experimental-based modeling of stroke-dependent magneto-static hysteresis in proportional solenoids is proposed. Using the set of quasi-static measurements with the fixed solenoid anchor, this over the whole stroke range, the Discrete Dynamic Preisach (DDP) hysteresis model has been identified for the assumed two-components Gaussian mixture of Preisach distribution. While the first mixture component keeps the fixed parameters corresponding to the maximal stroke configuration, i.e. with maximal air gap, the identified parameters of second mixture component yield as clearly stroke-dependent. The observed dependency is described by fitting the low-order polynomial curves. The derived and identified hysteresis model of the flux linkage as function of both coil current and solenoid stroke is evaluated on the measured dynamic curves. Here, the solenoid anchor is not longer fixed and moves under the prestress conditions while been excited by the coil current. The obtained model provides a sensorless flux linkage prediction and can be used for simulation, control, and diagnosis purposes in several applications, e.g. proportional valves.