GATE 2021 EC – Question 24
The complete Nyquist plot of the open-loop transfer function $G(s)H(s)$ of a feedback control system is shown in the figure.
If $G(s)H(s)$ has one zero in the right-half of the $s$-plane, the number of poles that the closed-loop system will have in the right-half of the $s$-plane is
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Show answer and explanation
Correct answer: (D) 3
Explanation
Closed-loop right-half-plane poles are $Z=N+P$, where $N$ is the number of clockwise encirclements of $-1+j0$ and $P$ the number of open-loop right-half-plane poles. A zero of $G(s)H(s)$ in the right half plane does not add to $P$, and no open-loop poles are given there, so $P=0$. The large circle and the loops around $-1+j0$ in the plot give three clockwise encirclements according to the official answer key, so $Z=3$.