Adaptive Displacement Constraint Control with Tan-Type Time-Varying Barrier Lyapunov Functions for Active Magnetic Bearings

In this paper, barrier Lyapunov function-based adaptive backstepping control strategy is proposed for rotor displacement regulation in active magnetic bearing (AMB) systems with non-stationary parameters and uncertainties. The switched-parameter nonlinear dynamics of AMBs are modeled to describe time-varying geometric or material characteristics and external disturbances. Time-varying displacement constraints are systematically enforced through tan-type barrier Lyapunov functions (t-BLF), allowing dynamic adjustment of position limitations according to operational phases. Parameter uncertainties and abrupt variations are compensated by an adaptive law, ensuring bounded estimation. Theoretical verification confirms the ultimately bounded stability of the closed-loop system with constrained state trajectories. Simulation results validate the effectiveness of the proposed method in maintaining safe rotor operation under time-varying constraints.