Question

A first order system and its response to a unit step input are shown in figure below. The system parameters are
a=____
​​​​​​k=____

• A. $2,10$
• B. $5,10$
• C. $5,5$
• D. $5,4$

Answer 1

The correct option is B $5,10$

$\because$ Time constant =0.2 sec (from figure)
$=\frac{1}{a}\left(\text{from}G\right(s)=\frac{k}{a(1+\frac{s}{a})})$

$\because \frac{1}{a}=0.2$

$\Rightarrow a=5$

$\because$ Final value $={lim}_{s\to 0}sC\left(s\right)$

$={lim}_{s\to 0}s\frac{k}{s+a}.\frac{1}{s}=\frac{k}{2}=2$

(from figure)

$\because \frac{k}{a}=2$

$\Rightarrow k=2\times 5=10$