- #1
rasco
- 8
- 0
Hi,
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.
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.