Net Encirclements of $(-1, j0)$:
The point $-1$ is inside both the outer loop (CW) and the inner loop (CCW).
Contribution from Outer Loop: $+1$ (CW)
Contribution from Inner Loop: $-1$ (CCW)
Total Encirclements ($N$):
$$N = 1 - 1 = 0$$
2. Determining Open-Loop Poles ($P_{OL}$)
We use the Principle of Argument for the origin $(0, j0)$ to find the number of open-loop poles in the Right Half Plane (RHP).
Formula: $N_{origin} = Z_{OL} - P_{OL}$
Given: The open-loop transfer function has one zero in the RHP ($Z_{OL} = 1$).
From Plot: The entire Nyquist plot lies to the left of the origin (in the 2nd and 3rd quadrants) and does not encircle the origin. Thus, $N_{origin} = 0$.
Calculation:
$$0 = 1 - P_{OL}$$
$$P_{OL} = 1$$
(There is 1 open-loop pole in the RHP).
3. Calculating Closed-Loop Poles ($Z_{CL}$)
Now, we apply the Nyquist Stability Criterion again for the critical point $(-1, j0)$:
$$N = Z_{CL} - P_{OL}$$
Substitute the values we found ($N = 0$ and $P_{OL} = 1$):
$$0 = Z_{CL} - 1$$
$$Z_{CL} = 1$$
Conclusion
The number of closed-loop poles in the right-half plane is 1.
Correct Option: B. 1
