The complete Nyquist plot of the open-loop transfer function G(s)H(s) of a feedback control system ...

Given:

$$Z_{OL}=1$$

where $Z_{OL}$ is the number of RHP zeros of $G(s)H(s)$.

From the Nyquist plot, applying the argument principle to the origin gives the number of RHP poles of the open-loop transfer function. Then applying the Nyquist criterion to $(-1,j0)$ gives the number of RHP closed-loop poles.

For Open Loop

N = P - Z

Or, 2 = P - 1  (because open loop zero = closed loop pole)

Or, P = 3

Now for Closed Loop,

N = P-Z

or, 0 = 3-Z

or, Z = 3

*(N = number of encircles, P = # open loop poles, and Z = closed loop poles)

The resulting number is

$$\boxed{{\displaystyle Z_{CL}=3}}$$

So the answer is:

$$\boxed{{\displaystyle \text{(d) }3}}$$

Final answer: (d) 3