Gain scheduling controller synthesis for active magnetic bearing based on parameter dependent LMI with convexity condition

This paper proposes a gain scheduling (GS) controller synthesis for active magnetic bearing (AMB) systems. The AMB can be represented as a linear parameter-varying (LPV) system depending on rotor angular velocity. The GS controller for the LPV system is designed based on parameter-dependent Lyapunov function. The purpose of this study is to stabilize rotor attitude of AMB that is influenced by gyro effect. Since the gyro effect corresponds to the rotor angular velocity, it is treated as a scheduling parameter in the GS controller synthesis. The robust stability for the LPV system is theoretically guaranteed by using polytopic representation. The GS controller synthesis is formulated in terms of parameter dependent linear matrix inequality (LMI) conditions. However, it is difficult to solve the synthesis condition because the LMI conditions are not affine but quadratic of the time-varying parameter. In order to guarantee the stability by solving the LMI condition at only vertices of the polytope, Lyapunov matrix in the synthesis condition is restricted to make LMI conditions convex/affine. The restriction for the Lyapunov matrix is derived by considering dynamics of the AMB. Finally, the effectiveness of proposed method is illustrated by simulations.