Identification of a solid-core magnetic bearing using incommensurate fractional-order models

Due to the effects of eddy current, solid-core magnetic bearings (MBs) show fractional-order characteristics. In this paper, a practical strategy for incommensurate fractional-order system identification is adopted to model a solid-core MB. The model structures are firstly determined by selecting the number of terms of the numerator and denominator in sequence, and then the derivative orders are derived based on a passive search within a given range. By using a weighed least squares method, the coefficients of derivative operators are calculated. Besides, a modified error criterion is proposed by combining the mean square error with a maximal phase error. The results show that the new error criterion is better for deriving a model with smaller phase errors, and the identified fractional-order models are more precise and simpler than the integer-order models.