Basic of Maglav system

This is a simple form of a magnetic train system.

Magnetic levitation is defined as equilibrium of a body without any contact in the solid surface by the result of magnetic field. Trains working based on this technology is called as maglev trains. Recently, our focuses are to making accurate and high speed travelling system so all attentions comes to magnetic levitation systems. In last decade Japan and china developed maglev train system for public transport. Its main advantage is its frictionless path. The basic open loop maglev system is nonlinear so they developed an excellent control platform for controlling and evaluating.
Force relation:
By Newton’s law force (F)=ma

So the total force acting on the bogie = mass of bogie*gravitational force –electromagnetic force
M(d2y/dt2) = mg-F

By the Newton’s law of centre of gravity and Kirchhoff’s magnetic circuit law

F(i, x) = -µo AN2/2 (i/x)2