$G(s)=\frac{1}{(s+4)(s+1)}$

$C(s)=K(\frac{Ts+1}{\text{p}\text{r}\text{o}\text{p}\text{T}\text{s}+1})$

Consider the controller $($C$($s$))$ and plant $($G$($s$))$ given above. For each of the conditions below, please find suitable $K,$prop and $T$ values.

a$)$ The oscillations in the closed$-$loop system response decay faster than $e^{-5t}$

b$)$ The step response of the closed$-$loop system presents $5\%$ error

Find the parameters by deriving them on paper manually! You can get help from MATLAB in finding the solution