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Nyquist Design

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I am completely lost with Nyquist. I am sure it's a plot of G(s), but when I put the plot in my calculator, it looks nothing like a traditional nyquist plot.

I have a pole at the origin, that is not in the rhp is it? I have a zero in the rhp. So, the number of encirclements is N=#p-#z= so that's -1? There are -1 ccw encirclements? Help!

I'm trying to design a lag compensator with kv=2, pm>=50, PM>0 for all w<=wc (where wc is the corner frequency).

Please help me to understand how to do the nyquist plot for G(s)=2((-s/.142)+1)/(s* ((s/.35)+1) ((s/.0362)+1) ))

I'm lost, please help.

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The solution is provided in an attachment and includes diagrams and short explanations describing how to manually draw a nyquist diagram. A reference is also given.

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Please refer to the attached file.

G(s)=2((-s/.142)+1)/(s* ((s/.35)+1) ((s/.0362)+1) ))

Matlab code:

num=2*[(-1/0.142) 1];
den1=conv([1 0],[(1/0.0362) 1]);
den=conv([(1/0.35) 1],den1);

Transfer function of the system:
-14.08 s + 2
78.93 s^3 + 30.48 s^2 + s

Root locus of the system:

There are three poles and a right hand pole zero.

Nyquist diagram of the ...

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