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I need help in understanding the connection between Nyquist plot and root locus plot.

Let's say I have a Nyquist plot, what can I infer about the root locus plot? and vise versa.

Given the root locus plot, can I draw the Nyquist plot?

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  • $\begingroup$ We used Nyquist plot to determine if an Op-amp with negative feedback stable is. This is a specific application, but Nyquist plot represents the stability of any system supplied with feedback. Here is a link math.stackexchange.com/questions/2472050/… $\endgroup$ – Sam Farjamirad Sep 8 '18 at 19:33
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A root locus plot shows how the poles of the transfer function change, when some parameter of the system changes. The parameter is often the loop gain of the system, but it could be anything.

A Nyquist plot shows how the response of the system changes with frequency, for one fixed value of the parameter and one fixed set of pole positions.

So, you can't draw a root locus plot from just one Nyquist plot. Well, you can, but it would just be a plot showing the positions of the poles of that response curve, which isn't very interesting.

Given a root locus plot, in principle you could draw many Nyquist plots for different values of the parameter, but in practice the curves on the root locus plot are unlikely to be labeled to show how the parameter changes along each curve, so you can't extract the data you need (i.e. the positions of all the poles for one value of the parameter) just from the plot.

To summarize: a root locus plot and a Nyquist plot are two different ways of looking at the same underlying information (i.e. the system transfer function) but they show different things, and they are useful for different purposes.

You might say that a root locus plot is more useful for designing a system (for example it tells you what values of the parameter will give a stable or unstable system response) while a Nyquist plot is more useful for analysing a system where the parameter value has already been chosen (for example it tells you about the phase and gain stability margins of the system at different frequencies).

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