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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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Solution Preview

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 ...

Solution Summary

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.

See Also This Related BrainMass Solution

PI controller design equation

The plant is given as P(s)=(P/(0.3-s))*e^(-0.1s). The only uncertainty is in p E [0.2, 0.6].

Derive the fastest PI controller G9(s)=k(1+(1/T_i*S)) such that the closed-loop system is stable and |S| < 6dB for all w and p. Use frequencies between 0.01 and 100 rad/s and the nominal plant with p=0.6.

Indicate clearly both the (universal) sensitivity bound for the nominal design and the final nominal L(jw) on the logarithmic complex plane of the EdS Chart. Check stability by sketching the NYquist plot of the final design. Report the designed controller in the notes' space of the EdS Chart.

Please leave out the sensitivity part. Just help me design a PI controller. Forget about the fastest.

(See attached files for full problem description)

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