[Solved] How do you use rlocus with multiple feedback loops?

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Joseph Patrick 2021-4-19

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编辑： Joseph Patrick 2021-4-20

So I have this control loop and I want to plot the root locus with the gain variable Kt but I how do you do this as rlocus expects a single feedback loop, not two where one is affected by the gain and the other is not?

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Paul 2021-4-19

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Start with the correct characteristic equation:

1 + D(s)*G(s)*I(s) + D(s)*G(s)*Kt = 0 (not sure why the picture shows the last term divided by I(s) ).

Let L(s) be the "loop transfer function" that should be used to plot the root locus with respect to Kt. What is the CE written in terms of L(s) and Kt? Can the actual CE be manipulated into that form?

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Paul 2021-4-20

Correct.

So now you have to decide ...

if the nominal value of Kt is given and you want to know how the closed loop poles migrate based on scaling that nominal value, in which case:

L(s) = Kt*D(s)*G(s)/(1 + D(s)*G(s)*I(s))

as shown in the first line in the preceding comment, or if you want to know how the closed loop poles migrate as a function of Kt itself, in which case:

L(s) = D(s)*G(s) /(1 + D(s)*G(s)*I(s))

as in the second line in the preceding comment.

Joseph Patrick 2021-4-20