The dynamic forces of nonlaminated magnetic thrust bearings are highly impaired by the magnetic skin effect inside the solid core. As the modification of the core design only offers limited room for improvement at a high financial cost, control-based measures are desired. Currently, advanced control topologies try to overcome the problem with complex controllers and observers but hardly maintain the direct physical reference to essential bearing parameters like stiffness and damping, required for a simple bearing operation. This is one major reason why most of them are not established sustainably and the common decentralized and cascaded position control with subordinated current control remains the industry standard. The inability to cope with the skin effect and the accompanying loss of stability, dynamic and bandwidth is merely tolerated. Here we propose a new model-based control scheme based on a pre-calculated fractional-order flux estimator. It allows us to compensate the skin effect within the inner control loop by means of a simple IIR-filter-cascade in the feedback path and maintains all physical references and the simplicity of the standard topology. We show that it is possible to stably implement the known high-fidelity eddy current models, based on the diffusion equation, as real-time application on a microprocessor. Unlike other voltage-based flux estimators, our approach is based on the measured coil current as a more reliable true feedback signal. We conclude with a proof of concept of our new digital flux control, which significantly improved bearing stiffness and damping and at least quadrupled the bandwidth of the axial position control over the industry standard.