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Nyquist stability criterion: coun

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Nyquist stability criterion: coun

(OP)

Nyquist stability criterion: counting turns with vertical asymptote
Help me please to understand this : when I apply Nyquist stability criterion and there's a vertical asymptote in the diagram, how to count the number of times that function encircles the critical point? For example:

$$\frac{1+s^2}{s(1-10s)(1+s/10)}$$

This function has a vertical asymptote in Nyquist diagram in point 10.

Supposing that I have a proportional feedback K such that the critical point in Nyquist diagram becomes (1,0).
(-1/K = 1 so K would be -1).

How should I count the number of turns around (1,0) of G(s) in Nyquist diagram ? (it should be N=-1=nG+-nW+ but I don't understand why, what is the rule with vertical asymptotes?)

where nG+ is the number of unstable poles.
I've attached the Nyquist diagram.

RE: Nyquist stability criterion: coun

s is in your case is an imaginary variable...by way of electronics 101...or engineering maths, good luck, it is not the problem you are describing

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