Q$7$ Consider a process whose input$-$output relationships are given by:

$\frac{?}{\text{b}\text{a}\text{r}}(y{)}_1=\frac{0\mathrm{.}5e^{-1\mathrm{.}5s}}{s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_1+\frac{e^{-0\mathrm{.}5s}}{2s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_2\frac{?}{b}$

$ar(y{)}_2=\frac{2e^{-10s}}{0\mathrm{.}5s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_1+\frac{1}{s+1}\frac{?}{\text{b}\text{a}\text{r}}(m{)}_2$

Find the expressions for the ideal decouplers and indicate how they can be simplified on practical considerations.

$[15]$