Question

Taking \( N \) as positive for clockwise encirclement, otherwise negative, the number of encirclements \( N \) of \( (-1, 0) \) in the Nyquist plot of \( G(s) = \frac{3}{s-1} \) is \(\underline{\hspace{2cm}}\).
 

Hint:

In Nyquist plots, the number of encirclements of \( (-1, 0) \) depends on the poles to the right of the imaginary axis.

Answer 1

Correct Answer: -1

The transfer function is \( G(s) = \frac{3}{s - 1} \). This is a simple first-order system with a pole at \( s = 1 \). In the Nyquist plot, the number of encirclements of \( (-1, 0) \) is determined by the number of poles to the right of the imaginary axis. Since the pole at \( s = 1 \) is to the right of the imaginary axis, it will contribute one encirclement in the positive direction. Therefore, the number of encirclements is:
\[ N = 1 \] Thus, the value of \( N \) is \( 1 \).