Question

The system and its response to the unit step input is shown below.



The value of K is

• A. 1.22
• B. 1.72
• C. 1.09
• D. 1.42

Answer 1

The correct option is D 1.42

(d)

$M_p=25.4$ %

${}_e^{-\xi \pi /\sqrt{1-{\xi }^2}}=0.254$

$e^{-\pi }\cot \theta =0.254$

$-\pi \cot \theta =In\left(0.254\right)$

$\cot \theta =0.436$

$\xi =\cos \theta =0.4$

$t_p=3$

$\Rightarrow \frac{\pi }{{\omega }_n\sqrt{1-{0.4}^2}}=3$

$${\omega }_n=1.14rad/\sec$$

$\frac{C\left(s\right)}{R\left(s\right)}=\frac{K/T}{s^2+\frac{s}{T}+\frac{K}{T}}$

${\omega }_n=\sqrt{\frac{K}{T}}\Rightarrow {\omega }_n^2=\frac{K}{T}$

$K={\omega }_n^{2}T$

$T=\frac{1}{2\xi {\omega }_n}=\frac{1}{2\times 0.4\times 1.14}=1.09$

$K={\omega }_n^{2}T={1.14}^2\times 1.09=1.42$