How to derive the state-space model in which the second derivative of the output of the system is needed?
57 views (last 30 days)
Show older comments
Dear all:
My transfer function is:
Y/U = (a1s+a0)/(b4s^4+b3s^3+b2s^2+b1s); s is the laplace symbol, U is the single input, and Y is the single output.
Now I want a state-space model where I can have the second derivative of Y, which is dotdot(y) (dotdot is second derivative with respect to time).
Any help is appreciated!
0 Comments
Accepted Answer
Sebastian Castro
on 11 Aug 2015
If the above is the TF for Y, then the second derivative of Y is just Ys^2, so the TF would be:
Ys^2/U = (a1s^3+a0s^2)/(b4s^4+b3s^3+b2s^2+b1s);
In MATLAB terms, you could either mathematically rework these into a state-space, or if you're lazy like me, make both the transfer functions and then convert to State-Space. NOTE: This requires Control System Toolbox.
Y = tf([a1 a0],[b4 b3 b2 b1 0]);
Ydd = Y*tf('s')^2;
G = [Y;Ydd];
Gss = ss(G);
... and there you have it, a state-space with 2 outputs: The first being Y, the second being Y doubel dot. Hope this helped.
- Sebastian
6 Comments
Sebastian Castro
on 11 Aug 2015
Oh yes, I thought you wanted both Y and Ydotdot.
In that case, just do G = ss(Ydd);
More Answers (0)
See Also
Categories
Find more on Dynamic System Models in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!