GATE 2020 EE – Question 34
Consider a negative unity feedback system with forward path transfer function $G(s)=\dfrac{K}{(s+a)(s-b)(s+c)}$, where $K,a,b,c$ are positive real numbers. For a Nyquist path enclosing the entire imaginary axis and right half of the $s$-plane in the clockwise direction, the Nyquist plot of $(1+G(s))$, encircles the origin of the $(1+G(s))$-plane once in the clockwise direction and never passes through this origin for a certain value of $K$. Then, the number of poles of $\dfrac{G(s)}{1+G(s)}$ lying in the open right half of the $s$-plane is ________.
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Correct answer: 2
Explanation
$G(s)$ has one open-loop pole in the right half plane ($s=b$), so $P=1$. One clockwise encirclement gives $N=1$, so the number of closed-loop poles in the right half plane is $Z=N+P=1+1=2$.