Active magnetic bearings (AMBs) have found a wide range of high-speed rotating machinery applications in energy storage, electric power generation, machine tool operation, heart pumps and hybrid vehicles. Compared with conventional mechanical bearings, AMBs need feedback control to support and constrain the rotor and demand additional electronic devices.When AMBs are used to support flexible rotors, their nonlinear characteristics and complex dynamics of flexible rotors cause problems with stabilization and disturbance rejection. Proportionalintegral-derivative (PID) controllers are the most popular control method for AMB applications.They are easy to implement and reasonable control performance can be achieved. However, it is difficult for PID controllers to deliver robust and near optimal performance for complex dynamic systems. In recent years, robust control techniques such as µ-synthesis have also been applied to AMB applications. The µ-synthesis is able to better handle the uncertainties in complex systems and to achieve reliable performance. However, it requires plant and uncertainty models to generate the most suitable solution, which makes this control design not as practical as PID controllers.