View source for What is the correct derivation of the magnetic levitation system dynamics?

The equations in the slides form the lecture did not match the physical system.  The equations should have been
<center><amsmath>
\aligned
  m \ddot z &= mg - k_m (k_A u)^2 / z^2 \\
  v_{ir} &= k_T z + v_0
\endaligned
</amsmath></center>
where <math>z</math> 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 
<center><amsmath>
P(s) = \frac{-k}{s^2-r^2} \qquad k,r > 0
</amsmath></center>
which corresponds to the plots that were shown.   The computations requried for the plots can be found in {{cds101 matlab|L9_2_maglev.m}}.

--[[User:Murray|Richard Murray]] 08:01, 23 November 2006 (PST)

[[Category:CDS 101/110 FAQ - Lecture 9-2]]