In this example, we are going to look at the difference in response of an injector considering eddy currents or not considering them.
The system will be feed with a 18 V DC supply the switch will be controlled via MATLAB/Simulink feeding intermittently the injector with the DC source. The Circuit used in JMAG for that purpose is presented in Fig. 1.
The switch is controlled so via an hysteresis band control. The switch will try to maintain the current in a band around the reference. This is achieved in the circuit illustrated in Fig. 2.
The reference is also controlled so that once the injector has been switched on, the reference is maintained until the mover reaches its end position. At that moment the reference is lowered to maintain the mover in position. Finally to be put back to 0 after a defined amount of time as shown in Fig. 2.
Eddy current comparison
The same model is used twice once considering eddy current and once not.
Looking at the position of the mover over time in Fig. 3, we can see that the injector with eddy currents takes more time to reach the end value as well as falling back to the initial state. This is due to the fact that the forces created on the mover are smaller when you consider eddy currents, as shown in Fig. 4. The Rate of variation of the force is also much lower. This is to be expected as the eddy currents are created to oppose the variation of the magnetic field.
In Fig. 5, we can also see that the current drawn by the two cases are different. The eddy currents forces the injector to draw up 30 % more current. This shows that the injector will also use more power.
In conclusion eddy currents can affect the response of a system quite significantly. This means that having the possibility to take them in account in our control system in MATLAB/Simulink will allow foe better fidelity in the model.