A unit feedback digital control system at a sampling interval of \(0.05 \mathrm{sec}\). If the plant transfer function is given by

\[
G(z)=\frac{z+0.8}{(z-1)(z-0.8)}
\]

design the controller \(D(s)\) using root locus methods so that the closed-loop system satisfies the following time domain specification:

\[
\begin{aligned}
\text { Settling time } & \leq 0.4 \text { sec } \\
\text { Damping ratio } & \geq 0.7 \\
\text { Steady-state error } & =\text { Zero }(\text { step input). }
\end{aligned}
\]