The device compares a voltage representative of the supply voltage of the electromagnet with two distinct inrush thresholds and a drop-out threshold. As soon as this voltage reaches one of the inrush thresholds, the device commands switching to an inrush phase of preset duration. The first inrush threshold is representative of a voltage of about 40 to 50% of the rated supply voltage of the electromagnet, whereas the second inrush threshold is representative of 70 to 85% of this voltage. The same control device can thus be used with both an under-voltage release and a shunt release or for a circuit breaker closing electromagnet.