A process is described by the exact transfer function below:

$G(s)=Y\frac{s}{U}(s)=\frac{6}{(10s+1)(4s+1)(s+1)}$

$($a$)$ Use an appropriate method to approximate the transfer function by a first$-$order$-$plustime$-$delay transfer function. State the method used and write down the FOPTD transfer function.

$($b$)$ For a unit step increase in input $u(t),$ find the expressions for $y(t)$ first from the exact transfer function and then from the FOPTD approximation.

$($c$)$ From the two expressions in part $($b$)$ calculate the responses $y(t)$ at $t=12.$