Shifting state space variables by constant value
5 views (last 30 days)
Show older comments
Hi,
I have a discrete time state space model for which I want to shift the state variables by a constant value. The actual model is as follows,
x(k+1) = Ax(k) + Bu(k)
It is a 4-state system. The goal is to change state variables and input to the following variable.
z(k) = x(k) - c
v(k) = u(k) - c
Where c is a constant. My question here is, how shall this change of variable be implemented to change the state space equation accordingly. Is the following change going to work? I could not see similarity transform working here.
z(k+1) = Az(k)+ Ac + Bv(k) + Bc
Am I missing anything here? Please advise of your thoughts.
Thank you.
0 Comments
Answers (1)
Azzi Abdelmalek
on 22 Jul 2014
Edited: Azzi Abdelmalek
on 22 Jul 2014
You gave an incomplete state space equation. What about the output?
y[k]=e.x[k]+d u[k] ,
The output should also change
y[k]=e.(z[k]+c])+d.(v[k]+c)
The states change but not the output
4 Comments
Azzi Abdelmalek
on 23 Jul 2014
Nothing happens to x[k+1],
x(k+1) = Ax(k) + Bu(k)
In your case you have considered another state z[k], you have the choice to work with x or z, just do not forget to change the equations
See Also
Categories
Find more on Array Geometries and Analysis in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!