Question:
If the Nyquist plot encircles the point \((-1,0)\) twice in the clockwise direction and the open-loop system has one RHP pole, then the number of closed-loop RHP poles is
If the Nyquist plot encircles the point \((-1,0)\) twice in the clockwise direction and the open-loop system has one RHP pole, then the number of closed-loop RHP poles is
Show Hint
Nyquist stability criterion:
\[
\boxed{
Z=P-N
}
\]
where
\[
\begin{aligned}
P&=\text{Open-loop RHP poles},
N&=\text{Clockwise encirclements of }(-1,0),
Z&=\text{Closed-loop RHP poles}.
\end{aligned}
\]
Updated On: Jul 14, 2026
- \(0\)
- \(1\)
- \(2\)
- \(3\)
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The Correct Option is D
Solution and Explanation
Step 1: Apply the Nyquist stability criterion.
According to the Nyquist criterion,
\[
Z=P-N,
\]
where
\[
\begin{aligned}
P &= \text{Number of open-loop RHP poles},
N &= \text{Net clockwise encirclements of }(-1,0),
Z &= \text{Number of closed-loop RHP poles}.
\end{aligned}
\]
Step 2: Substitute the given values. Given, \[ P=1, \] and the Nyquist plot encircles \((-1,0)\) twice clockwise, so \[ N=-2. \] Therefore, \[ Z=P-N =1-(-2) =3. \] Hence, \[ \boxed{Z=3.} \] Therefore, \[ \boxed{(D)} \] is the correct answer.
Step 2: Substitute the given values. Given, \[ P=1, \] and the Nyquist plot encircles \((-1,0)\) twice clockwise, so \[ N=-2. \] Therefore, \[ Z=P-N =1-(-2) =3. \] Hence, \[ \boxed{Z=3.} \] Therefore, \[ \boxed{(D)} \] is the correct answer.
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