Inductive and resistive load current draw - PSU
Sorry, but brushless motor is a complex load. It has electronic commutator which switches the input voltage to the winding or windings which currently are best to keep the motor running. The load is not pure inductance, there are controlled switches in series and the controller itself. If your current limiter causes voltage drops they can disturb the controller. Your system can oscillate. If you have an oscilloscope, check does the voltage stay stable. Anything written without having your system is only guessing.

If you have a big inductor, say the secondary winding of a few voltage output AC mains transformer, you can check what pure inductive load causes. 

WARNING: removing the DC from the coil by disconnecting a wire causes a disastrous high voltage peak. It can be for ex. 15000 volts and punches the insulation of the transformer. Or something which happens to have contact with the transformer get a fatal shock. Be sure that the wires do not get disconnected nor make bad contact as long as there's power on in the system. If you happen to be a beginner do not try this!