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Consider the closed-loop system shown in the figure. What is the critical value of K for stability by the use of the Nyquist stability criterion?

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Concept:

Enclosed:

A point or region is enclosed, if it lies to the right of the path (polar plot direction is from ω = 0 to ω = ∞)

  • If the plot is intersecting the negative real axis, therefore the stability of a system (-1, j0) critical point should not be enclosed by its plot.

 

In this figure, if we take the value K as equal to, then it will be its critical value.

Reason:

By taking the K = 1, the circle center will be -K/2 ie -1/2, and the boundary point will be - k ie - 1.

 

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