Electromagnetic levitation device
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Length: 0min 51sec (51 seconds)
Published: Tue Nov 22 2016
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I was curious and found a paper with model + control methods
I would use the Gilbert Model given on this page: https://en.wikipedia.org/wiki/Force_between_magnets
And then just apply F = Ma and tau = J*omega_dot + omega x J*omega.
At that point you can linearize the equations of motion and apply your favorite linear control scheme.
Edit: I missed probably the most important piece, which is using some version of Faraday's Law to relate the magnetic force to the current through those wire coils. That's actually the only way to get a control input here.
Actually, we did control a similar system with one big coil only at university control lab.I remember we used state space representation with feedforward gain and the equations found by newton’s laws of motion and electrical differential equations.there should be 4 states of the system and you can implement state feedback controller K matrix.
It depends on how detailed you would like to go. In this example other answers should give you necessary precision. But if you want to dig deeper then you have to switch to a FEM analysis of magnetic interaction which is not so fun. And then a suitable model order reduction for control would be needed. Then you are back to the familiar realm.