A transfer function is known to have the form

$()=2++$

$2++$

Use the following facts to do the function identification, that is to find constants a$,$ b$,$ c$,$ d

i$)$ The steady state response to a unit step is $2$

ii$)$ The steady state response to the input $(2)$ is zero

iii$)$ The transient response is critically damped $(=1$