This is my version of a levitation circuit found surfing in internet. It is essentially  an analog feedback system. The feedback signal is obtained by  converting  the magnetic field intensity near the electromagnet  in a voltage by means of  an hall sensor ( SS495 or SS496). My version of this circuit is based on the  LM311D  voltage comparator opamp. I used this circuit ( prototype ) to explain  the feedback concept in the systems to my students ( V A INF  a.s. 11/12). It uses  an LED and a buzzer to monitor the  electromagnet driving. This helps to locate the  point where to put the  magnet and/or metal object to levitate.

Here is the circuit: 

 

Here the post with video on the circuit test.