I want to know Block Diagram for "rlocus(G)" and how they calculate the overshoot of the graph.
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the Plat : ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1569412/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1569412/image.png)
Controller : ![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1569417/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1569417/image.png)
I want K(s) and G(s) in forward path. and H(s) = 1 in feedback path.
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1569422/image.png)
- If I use "rlocus(G);", does it fit for the architecture I intended?
And from the graph, I can see overshoot.
As long as I know, I can get overshoot from
*100%, (where,
: peak time).
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1569427/image.png)
![](https://www.mathworks.com/matlabcentral/answers/uploaded_files/1569432/image.png)
and I can get C(t) from Inverse Laplace Tranform of C(s) = Closed Loop Transfer Function(CLTF) * R(s).
and CLTF = K(s)G(s)/(1+K(s)G(s)).
2. the overshoot I get from the root-locus graph is from CLTF = K(s)G(s)/(1+K(s)G(s)) ?
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Paul
am 15 Dez. 2023
(1) Yes, rlocus(G) fits the architecture you have.
If "I can see overshoot" means that you're clicking on a branch on the root locus plot and looking at the overshoot in the data tip that pops up, then
(2) yes, that's the overshoot for K(s)*G(s)/(1 + K(s)*G(s)) where K(s) = Kp, and Kp takes on the gain value in the data tip. However, that's only true in this case becasue CLTF is a second order system. In general, that datatip is showing the response information as if the closed loop system had ONLY the selected poles (for a conjugate pair) or only the selected pole (for a real pole).
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