Question

In the Nyquist plot of the open-loop transfer function \[ G(s)H(s) = \frac{3s+5}{s-1} \] corresponding to the feedback loop shown in the figure, the infinite semi-circular arc of the Nyquist contour in the \(s\)-plane is mapped into a point at: \begin{center} \includegraphics[width=0.5\textwidth]{05.jpeg} \end{center}

• A. \(G(s)H(s) = \infty\)
• B. \(G(s)H(s) = 0\)
• C. \(G(s)H(s) = 3\)
• D. \(G(s)H(s) = -5\)

Hint:

For Nyquist plots, the high-frequency asymptote is obtained by dividing the leading coefficients of numerator and denominator.

Answer 1

The Correct Option is C

Step 1: Behavior along infinite semicircle.
On Nyquist contour, for large \(|s| \to \infty\): \[ G(s)H(s) = \frac{3s+5}{s-1} \approx \frac{3s}{s} = 3. \]

Step 2: Mapping to a point.
The infinite arc in \(s\)-plane is mapped to constant point \(3\) in the GH-plane.

Final Answer: \[ \boxed{3} \]