This example shows how to model a two-pole variable reluctance actuator. Initially the rotor is held at 45 degrees by the rotational spring, and then at 0.1 seconds the motor is activated. The rotor is pulled towards zero degrees so as to minimize the magnetic circuit reluctance. The reluctance depends nonlinearly on rotor angle and current, saturating at higher flux values. When saturated, the current-flux relationship is defined by a quadratic function. Torque is then determined by differentiating flux with respect to rotor angle and integrating over the current.
The approach used in this model can be used to incorporate flux as a function of current and rotor angle for any motor as calculated by a finite element magnetic package. Here the underlying equations are approximated by the quadratic function, and a small number of data points are used to calculate the coefficients. An alternative would be to use the 2-D lookup table in the Simscape™ Physical Signals sublibrary. Two tables are required, one for the flux and a second derived table of the local derivatives of the flux as a function of rotor angle and current.
Plot "Flux vs. Current and Rotor Angle" shows the dependency of magnetic flux on both current and rotor angle. As the motor is activated, the current increases from 0 to 2 amperes before the rotor has a chance to turn. The linear and nonlinear flux-current relationships can be seen on the plot. The current remains nearly constant as the rotor oscillates about 0 degrees. The plot shows how flux varies with rotor angle.