Self Scheduled H Controllers for Magnetic Bearings

In this paper we present a design procedure for disturbance attenuation with internal stability of a rotor supported by mag netic bearings over the whole interval of the rotor operating speeds The nonlinear gyroscopic equations can be simpli ed to a set of linear time varying di erential equations owing to the linear dependence of the rotor speed in the plant dynam ics For rotors operating in high speeds even small unbalanced masses can create large synchronous disturbances To alleviate the forces produced due to imbalance the controller automati cally balances the rotor for each operating speed The proposed methodology addresses both the gyroscopic compensation prob lem due to change of the rotor speed as well as the automatic balancing problem The approach is based on the recently de veloped theory of self scheduled H controllers Owing to the linear dependence of the equations on the rotor speed the com putation of the controller can be done very e ciently using con vex optimization and Linear Matrix Inequalities LMIs