Gain scheduled control for active magnetic bearing system considering gyroscopic effect

Abstract

This paper proposes gain scheduled (GS) control for an active magnetic bearing (AMB) system. The system levitates and supports a rotor without contact. The AMB is unstable and strongly nonlinear due to characteristics of the magnetic levitation. Furthermore, gyroscopic effect occurs corresponding to the rotational speed and the moment of inertia of the rotor. Thus, the AMB system tends to be unstable by the gyroscopic effect. The rotational speed is not fixed but variable in actual operation. It is treated as a time-varying parameter. The moment of inertia does not changed in operation but different by situations. It is treated as an uncertain time-invariant parameter. The robust stability for the uncertain parameters in the rotational speed and the moment of inertia is guaranteed by using polytopic representation. Linear fractional transformation (LFT) is applied to design the GS controller via parameter dependent Lyapunov function. The problem of designing the GS controller can be formulated as solving a finite set of linear matrix inequality (LMI) conditions. The effectiveness of the proposed method is illustrated by simulations.