modeling transfer function of ping pong ball levitation in a tube as a damper
I would not try to guess all the effects.  There are probably some non-obvious things going on, and you can't know all the parameters.

I would measure the step response.  Find two pump settings that both result in the ball being within the measurable range within the tube.  Then have the controller suddenly switch from one setting to the other open loop.  Meanwhile measure what the ball does over time.  That is the step response.  You can take the derivative of that and get the impulse response.  From the impulse response you can predict the motion of the ball for any history of pump settings, assuming this is a linear system.  It is probably linear enough over the small range of settings to keep the ball within its normal range.

You can use this as a simulation base to find the parameters for old fashioned PID control.  Or you can use the impulse response directly to do a convolution control.  You have to low pass filter the control input enough so that convolution kernel doesn't go negative unless your pump is actually reversible and can suck the ball back down.