  In this article, a systematic and comprehensive approach based on finite
element analysis and analytical modelling for studying static pull-in phenomena
in hybrid levitation micro-actuators is presented. A finite element model of
electromagnetic levitation micro-actuators based on the Lagrangian formalism is
formulated and developed as a result of recent progress in the analytical
calculation of mutual inductance between filament loops. In particular, the
developed finite element model allows us to calculate accurately and
efficiently a distribution of induced eddy current within a levitated
micro-object. At the same time, this fact provides a reason for formulating the
analytical model in which the distribution of the induced eddy current can be
approximated by one circuit represented by a circular filament. In turn, both
developed models predict the static pull-in parameters of hybrid levitation
micro-actuators without needs for solving nonlinear differential equations. The
results of modelling obtained by means of the developed quasi-finite element
and analytical model are verified by the comparison with experimental results.
