Question

The OLTF of a feedback control system is $G\left(s\right)H\left(s\right)=\frac{-1}{2s(1-20s)}$, the Nyquist plot of the system is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

OLTF is $G\left(s\right)H\left(s\right)=\frac{-1}{2s(1-20s)}$
(or) $G\left(j\omega \right)H\left(j\omega \right)=\frac{-1}{2j\omega (1-20j\omega )}$

$M=|G\left(j\omega \right)H\left(j\omega \right)|=\frac{1}{2\omega \sqrt{1+400{\omega }^2}}$


$\varphi ={180}^o-{90}^o-ta{n}^{-1}\left(\frac{-20\omega }{1}\right)$
$={90}^o+ta{n}^{-1}\left(20\omega \right)$

$At\omega =0;$ $M=\infty$; $\varphi ={90}^o$
$At\omega =0.1;$ $M=2.24$; $\varphi ={153.43}^o$
$At\omega =\infty ;$ $M=0$; $\varphi ={180}^o$

We get the Nyquist plot as,