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I am trying to understand how to draw nyquist plot.

Lets say the transfer function is

Subbing in jω for s,

***Note: should be (jw)^4 , (jw)^3, (jw)^2

Then separating the Real and Imaginary part,

So when

w = 0, in the nyquist plot it is infinity

w = infinity, it is 0

Imaginary intercept is 1.25

For real intercept I am not sure. Since imaginary part is 0 only when w is infinity, i plug in infinity for w in real part. Would the real intercept be infinity or 0? It would be infinity/infinity but numerator is lower order than higher order so would it be 0 instead?

In any case, how am i supposed to plot the rough nyquist plot or at least be able to determine the stability using these 4 points?

In Matlab the Nyquist plot comes out like this

Lets say the transfer function is

Subbing in jω for s,

Then separating the Real and Imaginary part,

So when

w = 0, in the nyquist plot it is infinity

w = infinity, it is 0

Imaginary intercept is 1.25

For real intercept I am not sure. Since imaginary part is 0 only when w is infinity, i plug in infinity for w in real part. Would the real intercept be infinity or 0? It would be infinity/infinity but numerator is lower order than higher order so would it be 0 instead?

In any case, how am i supposed to plot the rough nyquist plot or at least be able to determine the stability using these 4 points?

In Matlab the Nyquist plot comes out like this

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