Anyone here proficient with Control Systems Theory?

[hypn0tik]

If so, I was hoping someone would be able to help me out with finding a linear state model.

 

[henryay]

I took that class last semester, I doubt I remember anything. =)

Which book are you using?

 

[hypn0tik]

Originally posted by: henryay
I took that class last semester, I doubt I remember anything. =)

Which book are you using?

We're not using a textbook. Some Prof. made notes and we get to print those out and use them as our 'textbook'.

Edit: The lectures are good, but neither the notes or the lecture covered the problem I'm having.

 

[henryay]

Do you mean a linear state space model? I think I can help with that.

 

[hypn0tik]

Originally posted by: henryay
Do you mean a linear state space model? I think I can help with that.

That's exactly what I mean.

The differential equation is the following:

My" + M'y' + Ky = u
(u is the input and y is the output)

So, I let the state variable:

X = [x1] = [y] (Note: supposed to be a single column matrix)
......[x2] = [y']

Then:
X' = [x2]
.......[u/M - Kx1/M - M'x2/M]

= f(x,u)

The equilibrium point can be found by setting f(x,u) = 0
=> x2 = 0
and
u -Kx1 = 0

Select the point (x1,x2,u) = (0,0,0)

I'm having trouble finding the Jacobian df/dx.

I got something along the lies of:

df/dx = [0 ...........1]
.........= [-k/M... -M'/M]

I'm unsure as to whether that is correct. M is not a constant so when I different with respect to x1 and x2 do I treat it as a constant or as a variable?

 

[hypn0tik]

Any idea henryay (or anyone else for that matter)?

 

[henryay]

M is a constant there. I have an example of to linearize an equation like that. Then, you can turn that into a space space model. I could scan a copy if you PM me your e-mail.

 

[hypn0tik]

Originally posted by: henryay
M is a constant there. I have an example of to linearize an equation like that. Then, you can turn that into a space space model. I could scan a copy if you PM me your e-mail.

You don't know how awesome that would be. Thanks a million!

YGPM