A unity feedback control system shown in Fig. BQ$1$ has the open loop transfer function as

$G(s)=\frac{K}{s^2+3s+2}$

and $G_c(s)=K_{d}s+K_p$ is a Proportional$-$Derivative Controller with $K_d$ and $K_p$ are positive constants. It is observed that the response is bounded and stable for all positive values of $K_d$ and $K_p$ such that $K_d{K}_p.$

Figure BQ$1$

i$.$ Determine $K$ values if gain $K_p=1$ and $K_d=0$ such that the damping ratio $$ is $0\mathrm{.}7.$ Also obtain the Rise Time $t_r,$ peak time $t_p,$ and settling time $t_s$ for a unit step input.

$[$PO$3/$CO$2/$C$4](6$ marks$)$