Nonlinear parametric identification of magnetic bearings

This paper proposes a new electromagnetic force model and its parameter identification method. As a case study, the parameters of the proposed model for an experimental electromagnetic bearing system are obtained using extended Kalman filter (EKF). The experimental setup includes a symmetric rigid rotor which is disturbed by the electromagnet of a magnetic bearing. Experimental results show that the system response to harmonic excitation includes super-harmonic terms which are not shown by the well-known conventional electromagnetic force model. This shortcoming necessitates an investigation to propose a more realistic electromagnetic force model. Based on the observations of the system response, a novel parametric model is presented in the form of a nonlinear Mathieu–Duffing equation with unknown coefficients. Then in the operating frequency range, a random input is synthesized and applied to the experimental system as a persistent excitation and the response of the system is recorded. In order to estimate the states and parameters of the model, the EKF method has been applied to the recorded input–output data. To validate the identification results the outputs of estimated and experimental models are compared in time and frequency domains. The results show a notable improvement in modeling of magnetic force. The proposed model and the method for identifying its parameters are applicable for all magnetic fields.