Nowadays Active Magnetic Bearing (AMB) are being studied as a solution in many applications where reduced friction, high-speed operation, high reliability, and vibrations exemption are required. To achieve these benefits, AMBs require a complex actuation system, which includes position sensors, power electronics and advanced control dedicated to AMBs operation. All these features are also dependent of the AMBs coil arrangement. Among several solutions, Wheatstone Bridge winding configuration is considered in this paper. In terms of current control, Finite Control Set Model Predictive Control (FCS-MPC) is proposed in this paper, in order to generate the required forces with a fast dynamic response and improve the system robustness. Moreover, the AMB coils inductance is estimated in a predictive fashion, enabling rotor position estimation without including additional sensing coils or position sensors. In fact, the link between coil inductance variation and rotor position can be obtained by means of finite element simulation and analytical modelling. However, the position controller is critical for the system operation and nonlinear high bandwidth controllers are often investigated for AMB systems. For this reason, a Lyapunov Function Control (LFC) is proposed in this paper and compared through simulation with a classical linear controller implementation.