# modeling transfer function of ping pong ball levitation in a tube as a damper

I am building a control system to levitate a ping pong ball at a given height in a clear plastic tube using an arduino and implementing PID control.

I have to come up with a transfer function... I am using an air pump with pulse width modulation that controls the air speed, the pump is attached to the side of the bottom of the tube, and one end is closed and the other is open in the tube.

I was wondering if my idea would be correct, since one end of the tube is sealed and the other end is open, and the tube is a diameter that just barely fits around the ping pong ball, would I be correct in saying that to develop the transfer function for this system I could model it as a damper?

I was thinking it could be modeled as a damper or piston because the air forms a pocket beneath the ping pong ball and little air escapes around it?

I was looking up Bernoulli principle of lift, but not sure if a damper/piston would be the correct way in modeling this behavior?

If anyone could please shed some light on this I would be truly grateful!

or would it be easier to have both ends of the tube open? Not sure how the math would complicate for the transfer function in either case

Thank You!

• I know very little about PID control, but I do know that a ping pong ball will levitate in a stable state above the top of the tube with a little airflow due to the Coanda effect. Granted, that won't help you learn about PID, but it is one way to levitate the ping pong ball... – Kevin Vermeer Mar 3 '12 at 22:05

• +$\infty$. – tyblu Mar 4 '12 at 1:22