Cascaded Displacement--Flux Density Control of the Thrust Magnetic Bearings Based on an Effective Inductance-Based Eddy Current Compensation Model

Due to the inherent nonlinear characteristics and stability limitations, magnetic bearings can’t be applied in high-precision systems directly such as precision reconnaissance satellites and high-speed rotating machinery. Flux density control has the potential to significantly enhance control precision of magnetic bearings. However, there is a scarcity of appropriate Hall sensors capable of effectively capturing the real-time flux density within the air gaps of magnetic bearings. This study focuses on the thrust magnetic bearing (TMB) and proposes a cascaded control strategy based on magnetic flux density feedback. First, the fractional-order reluctance model is approximated using a rationalization method based on continued fraction expansion. Then, the magnetic flux density observer is designed that integrates displacement and current signals based on Maxwell’s stress tensor theory and in conjunction with an effective inductance eddy current compensation model. To analyze the inner-loop dynamic performance conveniently, the magnetic flux loop is reconstructed. Finally, a cascaded displacement–flux density control loop for the magnetic thrust bearing was ultimately developed and validated through simulation and experimental testing. The results demonstrate that the proposed control strategy effectively compensates for magnetic flux delay caused by eddy current effects. Compared with conventional current control methods, the proposed control system significantly increases the closed-loop bandwidth, reduces the resonance peak, and improves the phase margin, which enables stable control over a wide range of parameters and demonstrates excellent dynamic performance and robustness.