Uncertain model and μ-synthesis of a magnetic bearing

This paper deals with modeling, uncertain structure and μ-synthesis of magnetic bearings. The dynamics of magnetic bearing systems are characterized by their instability and complex dynamics of rotor and electromagnets, hence they should have a robustness for stability and performance against model uncertainties. First we derive a nominal mathematical model of the plant under some assumption, then consider the gap between the real physical system, and the obtained nominal design model. This gap has complex structure which is expressed by the structured uncertainties that includes linearization error, parametric uncertainties, unmodeled dynamics, and gyroscopic effect. Then we set the interconnection structure which contains the above structurally represented uncertainties. Next we design a robust controller which achieves robust performance condition using the structured singular value μ. Finally, we evaluate the proposed interconnection structure and verify robustness of stability and performance of the designed μ controller by several numerical simulations.