I want to know Block Diagram for "rlocus(G)" and how they calculate the overshoot of the graph.

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지완 이 2023-12-14

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回答： Paul 2023-12-15

the Plat :

Controller :

I want K(s) and G(s) in forward path. and H(s) = 1 in feedback path.

F(s) = 1, C(s) = K(s)

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).

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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Answer 1

Paul 2023-12-15

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https://ww2.mathworks.cn/matlabcentral/answers/2060847-i-want-to-know-block-diagram-for-rlocus-g-and-how-they-calculate-the-overshoot-of-the-graph#answer_1371967

(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).

You could try to compute the inverse Laplace transform of the output explicitly. You might also be interested in step and stepplot and stepinfo for r(t) being a step input.