# What is the correct derivation of the magnetic levitation system dynamics?

From MurrayWiki

The equations in the slides form the lecture did not match the physical system. The equations should have been

\aligned

m \ddot z &= mg - k_m (k_A u)^2 / z^2 \\ v_{ir} &= k_T z + v_0

\endaligned

</amsmath>where is the distance of the ball from the magnet (so positive z is down). The linearization of this equation around an equilibrium point gives a transfer function of

P(s) = \frac{-k}{s^2-r^2} \qquad k,r > 0

</amsmath>which corresponds to the plots that were shown. The computations requried for the plots can be found in L9_2_maglev.m.

--Richard Murray 08:01, 23 November 2006 (PST)