Question

An unknown first order system is excited by a step input of magnitude 4, the output response is shown in the figure, then the static sensitivity of unknown system is

• A. 10
• B. 4
• C. 6
• D. 2

Answer 1

The correct option is D 2

For the first order system
$C\left(t\right)=AK(1-e^{-t/\tau })+C\left(0\right)$

A = step of input applied
K = static sensitivity

C(0) = initial value of C(t) at t = 0 sec

$\text{C(t) at}t=\infty isC\left(\infty \right)=10$

$10=AK(1-0)+2$

$AK=8$

A = 4 given

$\text{Sensitivity}K=\frac{8}{4}=2$