In this paper, a nonlinear modeling and control method for magnetic bearings is designed, considering the core material nonlinear high flux behavior for the first time. A combination of the generalized Lur'e method and linear matrix inequalities is used during the modeling and control design process. It is common to include a margin of safety in amplifiers and other active magnetic bearing (AMB) components. The nonlinear modeling makes it possible to operate an existing industrial AMB system with larger electric currents and thus achieve a larger maximum load capacity than existing AMB modeling and control practices allow. As a result, existing industrial AMB's can be tuned to become more resilient in dealing with external disturbances. In addition, smaller and lighter AMBs can be designed by using the proposed method, which enables achievement of the same maximum force requirement of present-day larger AMB systems.