Adaptive control of an active magnetic bearing with external disturbance

•Both adaptive back-stepping control (ABC) and adaptive observed-based back-stepping control (AOBC) are applied to an active magnetic bearing (AMB) system.•ABC is based on full state feedback from AMB.•AOBC is constructed on position feedback from the AMB only.•An unknown external disturbance is estimated by the adaptive laws of two adaptive controllers respectively.•Adaptive and adaptive observed-based back-stepping control (ABC and AOBC) are applied to an active magnetic bearing (AMB).•The stability and robustness of two control systems are verified through simulations and Lyapunov approach.

Adaptive back stepping control (ABC) is originally applied to a linearized model of an active magnetic bearing (AMB) system. Our control goal is to regulate the deviation of the magnetic bearing from its equilibrium position in the presence of an external disturbance and system uncertainties. Two types of ABC methods are developed on the AMB system. One is based on full state feedback, for which displacement, velocity, and current states are assumed available. The other one is adaptive observer based back stepping controller (AOBC) where only displacement output is measurable. An observer is designed for AOBC to estimate velocity and current states of AMB. Lyapunov approach proves the stabilities of both regular ABC and AOBC. Simulation results demonstrate the effectiveness and robustness of two controllers.