Question

Figure shows the polar plot of a system. The transfer function of the system is

• A. $5(1+0.1s)$
• B. $(1+0.5s)$
• C. $5(1+10s)$
• D. $5(1+s)$

Answer 1

The correct option is A $5(1+0.1s)$

$T\left(s\right)=5(1+0.1s)$
$T\left(j\omega \right)=5(1+0.1j\omega )$
$\angle T\left(j\omega \right)=ta{n}^{-1}0.1\omega$

At $\omega =10,\angle T\left(j\omega \right)=ta{n}^{-1}\left(1\right)={45}^o$
At $\omega =0,\angle T\left(j\omega \right)=ta{n}^{-1}\left(0\right)=0^o$