A nonlinear adaptive control method integrated with finite element approximation and its application to 6 DOF magnetic levitation system

Abstract

This paper proposes a nonlinear adaptive control method integrated with finite element approximation to obtain the model of the magnetic levitation system of 6 degrees of freedom. Since a magnetically levitated stage is free from friction, it is useful not only to position precisely, but also to measure small force applying to the stage. However, inherent nonlinear characteristics of electromagnetic force make it difficult to measure force correctly. Therefore in this study, with the aim to overcome this difficulty, a control method is proposed to obtain the model of the magnetic levitation system by adopting the manner of model reference adaptive control integrated with finite element approximation for the nonlinear characteristics of electromagnetic force. The controller can compensate the nonlinear characteristics by adjusting PD feedback gains using the obtained model. The parameters of inertia and the center of gravity are also identified to be reflected on a linear reference model. By compensating the nonlinear characteristics of electromagnetic force, the magnetic levitation system behaves as a linear system, which facilitates the position control and the force measurement. The efficiency of this method is shown in an experiment of improving the tracking trajectory control performance.