Research on Fractional-Order Modeling of Nonlaminated Electromagnetic Bearings Considering Eddy Current Effects

Eddy current effects are evident in nonlaminated electromagnetic bearings; their nonlinear characteristics are complicated due to magnetic saturation, edge effect, and magnetic leakage. The resultant phenomena of phase lag and gain decay lead to significant amounts of error between the traditional model and the real system. This article analyzes the relationship between the effective reluctance of the magnetic circuit, eddy currents, and related nonlinear factors. Then, an analytical model for a nonlaminated electromagnetic bearing is presented. A fractional-order term is induced in the effective reluctance due to eddy currents and related nonlinear factors, turning the analytical model to fractional order. In addition, for the problem that the coefficients are difficult to obtain, the system identification of a nonlaminated electromagnetic bearing is carried out in this article, and an improved quantum particle swarm algorithm based on gain-phase weighting is proposed to realize the optimal parameter identification. The experimental results show that the identified fractional model can fit the real frequency-domain response well, and the amplitude error does not exceed 0.15 dB, which shows the accuracy of the modeling method and provides a preliminary guarantee for the precise and stable control of the nonlaminated electromagnetic bearing.