This paper presents an axisymmetric formulation of the circuit-coupled finite element method embedded in closed loop control system. The controller checks the current of the coil of the magnetic system after each time step and controls the applied voltage to reach the steady state faster. The results of the voltage driven finite element model are compared with the results from the analytical model. The control parameters for the proportional-integral-derivative controller were estimated using the step response of the system. Furthermore, the results of the closed loop system simulation show why the model accuracy is important in the controller design.