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I have a 'simplified' equation of the magnetically suspended ball.

a = g - (i/h * M)

where

a - actual acceleration of the ball.

h - distance from the magnet.

g - gravitational acceleration, to keep it simple let g = 10

M - mass of the ball 0.05 kg

i - current through the coil = how strong the magnet is.

I need to make a simulation where controller's input 'u' is distance of the ball from magnet and 'y' from the controller is current 'i' of the magnet. The output y directly puts current into the coil (its just processing simulation with a falling ball). To keep it simple, no observer is required.

My suggested solution:

state x consists of [x1, x2, x3] = [h, v, i]

h - dist. from magnet

v - velocity of the ball

i - current

so steady state x0 = [10,0,5]

But I do not know how to make matrixes A and B to build model:

x_dot = Ax + Bu

I started to compute matrix A as a Jacobian matrix but can not compute 3rd raw of the matrix. Maybe jacobian is not necessary.

could anybody help me please? Thx.