Estimation of Modeling Error in Magnetic Levitation System

Abstract

Magnetic levitation systems are suitably applicable to transfer systems in an ultra clean room because of their contactless construction. In a levitation system by magnetic attraction forces, the attraction force has nonlinear characteristics with respect to magnetizing current and the gap length between the magnet and the levitated vehicle. Since it is usually equipped only with position sensors to measure the gap length, an observer is adopted to know the velocity of the vehicle. One of the problems of the system which contains the observer is the modeling error which has an undesirable influence on a decoupling control method and, as a result, causes instability of the system. Electrical causes of modeling errors are due to a change of the gain in a current amplifier, the influence of leakage flux and a linearizing error in a magnetic circuit. Mechanical causes are due to the changes of the mass and the moments of inertia by changes of materials on the vehicle. The modeling error by these causes can be formulated as the error between the real attraction force and the reference input for it. In this paper, the electrical and the mechanical changes mentioned above are formulated as the change of the parameters of the system, and then the changing parameters are identified by the observer whose coefficients contain the control input variable. This method can be applied to the case where a constant disturbance, either known or unknown, exits. Appropriateness of the proposed theory is confirmed by simulation and also experiments, using a system which has 4 magnets for levitation and a linear motor for transfer of the vehicle.