Question

Which of the following is the transfer function of a system having the Nyquist plot shown in figure below?

• A. $\frac{K}{s(s+2{)}^2(s+5)}$
• B. $\frac{K}{s^2(s+2)(s+5)}$
• C. $\frac{K(s+1)}{s^2(s+2)(s+5)}$
• D. $\frac{K(s+1)(s+3)}{s^2(s+2)(s+5)}$

Answer 1

The correct option is B $\frac{K}{s^2(s+2)(s+5)}$

$\because$ Curve starts form $-{180}^{\circ }$ $\Rightarrow$ type 2 system and curve ends at $-{360}^{\circ }.$

$\Rightarrow Differencebetweennumberofpolesandnumberofzeros=\frac{{360}^{\circ }}{{90}^{\circ }}=4$

$\because$ only option (b) is satisfying these two properties.

$\therefore$ option (b) is correct.