Here I show several issues that we have encountered in the quad magnetic levitation system. It would be great if you can give
some suggestions and comments (Poor haixing is crying for help)

The current setup is shown by the figure below (I took the photo this morning):

Basically, we have one heavy load which is rigidly connected to a plane that we try to levitate. On corners of the
plane, there are four push-fit permanent magnets. Those magnets are attracted by four other magnets which are
mounted on the four control coils (the DC force is to counteract the DC gravity). By sensing the position of the plane
with four OSEMs (there are four flags attached on the plane), we try to apply feedback control and levitate the plane.
We have made an analog circuit to realize the feedback, but it is not successful. There are the following main issues
that need to be solved:

(1) DC magnetic force is imbalanced, and we found that one pair has a stronger DC force than others. This should
be able to solved simply by replacing them with magnets have comparable strength to others.

(2) The OSEM not only senses the vertical motion, but also the translational motion. One possible fast solution is to
cover the photodiode and only leave a very thin vertical slit so that a small translational motion is not sensed.
Maybe this is too crappy. If you have better ideas, please let me know. Koji suggested to use reflective sensing
instead of OSEM, which can also solve the issue that flags sometimes touche the hole edge of the OSEM and
screw up the sensing.

(3) Cross coupling among different degrees of freedom. Basically, even if the OSEM only senses the vertical motion,
the motion of four flags, which are rigidly connected to the plane, are not independent. In the ideal case, we only
need to control pith, yaw and vertical motion, which only has three degrees of freedom, while we have four sensing outputs
from four OSEMs. This means that we need to work out the right control matrix. Right now, we are in some kind of dilemma.
In order to obtain the control matrix, we first have to get the sensing matrix or calibrate the cross coupling; however, this is
impossible if the system is unstable. This is very different from the case of quad suspension control used in LIGO,
in which the test mass is stable suspended and it is relatively easy to measure the cross coupling by driving the test mass
with coils. Rana suggested to include a mechanical spring between the fixed plane and levitated plane, so that
we can have a stable system to start with. I tried this method today, but I did not figure out a nice way to place the spring,
as we got a hole right in the middle of the fixed plane to let the coil connectors go though. As a first trial, I plan to
replace the stop rubber band (to prevent the plane from getting stuck onto the magnets) shown in the figure with mechanical
springs. In this case, the levitated plane is held by four springs instead of one. This is not as good as one, because
of imbalance among the four, but we can use this setup, at least, to calibrate the cross coupling. Let me know if you come
up better solution.

After those issues are solved, we can then implement Jamie's Cymac digital control, which is now under construction,
to achieve levitation.