Adaptive Displacement Constraint Control With Predefined Performance for Active Magnetic Bearings

This manuscript presents an adaptive funnel controller applying to the active magnetic bearing for position constraint control with prescriptive tracking performance. To better depict the actual active magnetic bearing dynamics, a nonlinear active magnetic bearing model with switched parameters instead of the existing fixed parameters is constructed considering the inherent properties of uncertainties and nonstationarities of active magnetic bearings. Then, by designing the funnel control scheme and adaptive laws based on Lyapunov stability theory and backstepping technique, the rotor displacement is constrained to not exceed the prescribed funnel boundary in view of safety concerns. Moreover, the funnel boundary integrated into the proposed controller is in line with the rotor displacement characteristics of active magnetic bearing systems under different speeds during real operation process. The boundness of the position tracking error is confirmed via Lyapunov synthesis. Eventually, the effectiveness of the proposed controller is verified by simulated and experimental examples. Note to Practitioners-The motivation of this manuscript is to investigate a control strategy with potential application for the displacement control of active magnetic bearings. In most of the existing displacement control schemes for active magnetic bearings, the constraint and limitation of displacement is not taken into account. However, considering the high-speed rotation and active controllability of active magnetic bearings, it is necessary to preset the performance indicators of rotor displacement including convergence speed, overshoot, and constraint limit, which can not only avoid serious safety accidents, but also give full play to the active control advantages of active magnetic bearings in different actual situations. Therefore, this manuscript suggests an adaptive funnel control strategy for prescriptive performance. Moreover, this manuscript solves the modeling and control problems for active magnetic bearings subject to nonlinearity, uncertainty, and external disturbances, which are difficult to be tackled in practical applications. The stability and convergence of the proposed controller are analyzed mathematically, and the practical experimental results reveal that the proposed controller has the potential and possibility to be applied in practice.