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When analyzing a control system via Bode, Nyquist and Root-Locus, are we using open or closed loop information? I'm not being able to understand when the poles of the open loop are used and when the one of the closed loop are. I think that what interests us is the information about closed loop, as that determines whether the final system is stable or not, but I'm pretty confused with this issue.

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The root locus is a way to see how the poles of your system vary from their open loop locations to their closed loop locations.

If the closed loop system is $$ C(s) = \frac{O(s)}{1+KO(s)} $$ where $O(s)$ is your open loop system and $K$ is the constant gain in the feedback path around the open loop system, then the root locus looks at how the poles of $C(s)$ vary from those of $O(s)$ (when $K=0$) to something else for $K>0$.

This picture

Root locus plot

from this answer shows an example.

Nyquist and Bode plots are applied to any transfer function, as others have said, whether open or closed loop.

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It looks like you are considering these analysis like part of a universal streamline desing process. These analysis techniques are simply tools that helps you understand the behaviour of your system, being open or closed loops, it doesn't matter. Both type of systems can be stable or unstable depending on the value of their poles.

Closing the loop on a open-loop system is a modification you make to your system just like any other modification. After that modification, you get a new system with a different transferr function that can be stable or unstable, independently of the previous system.

Hope I was clear enough.

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The bode plot is just a plot showing the frequency representation of your system. Any transfer function has one, hence you can use it to see the response of both closed or open loop. Nyquist and the root locus are mainly used to see the properties of the closed loop system. The root locus shows the position of the poles of the c.l. system as the gain of your controller changes. While nyquist diagram contains the same information of the bode plot. But instead of splotting two real graphs of the amplitude and the phase of the complex function the nyquist plot shows the same function in the complex plane

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