Question

For a system having transfer function $G\left(s\right)=\frac{-s+1}{s+1}$, a unit step input is applied at time $t=0$. The value of the response of the system of $t=1.5$ sec(rounded off to three decimal places ) is .

Answer 1

$G\left(s\right)=\frac{-s+1}{s+1}$

System output,
$Y\left(s\right)=G\left(s\right).\frac{1}{s}=\frac{-s+1}{s+1}.\frac{1}{s}$
$=\frac{1}{s}-\frac{2}{s+1}$
$y\left(t\right)=u\left(t\right)-2e^{-t}u\left(t\right)$
$y\left(1.5\right)=1-2e^{-1.5}$
$=1-0.446=0.554$