Q$5$ Consider a process with the following input$-$output relationships:

$\frac{?}{\text{b}\text{a}\text{r}}(y{)}_1=\frac{1}{s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_1+\frac{1}{0\mathrm{.}1s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_2\frac{?}{b}$

$ar(y{)}_2=\frac{-0\mathrm{.}2}{0\mathrm{.}1s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_1+\frac{0\mathrm{.}8}{s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_2$

i$.$ Compute the relative gains for a unit step change in each of the transfer functions.

$[16]$

ii$.$ What is the best recommended pairing?

$[4]$