The reboiler of a distillation column is a process known to exhibit first$-$order plus time delay

dynamics. In this process, the inlet mass flow rate of steam to the reboiler $(l\frac{b}{m}in)$ is manipulated to

control the temperature $(F)$ of in the reboiler. Consider the following feedback control system, set

to proportional mode:

The transfer functions for each instrument are shown below, with all time constants and time delays

in minutes:

$G_v(s)=0\mathrm{.}52$

$G_p(s)=\frac{0\mathrm{.}27e^{-3s}}{3\mathrm{.}6s+1}$

$G_d(s)=\frac{e^{-3s}}{3\mathrm{.}6s+1}$

$G_m(s)=\frac{1}{0\mathrm{.}18s+1}$

a$.$ What is the open$-$loop transfer function, $G_{OL},$ for this system?