Q$17.$ The system below is to be compensated with PID compensator $C(s)=\frac{K_d{s}^2+K_{p}s+K_i}{s}$

$[8$ Marks$]$

$($Hint: the critical gain $Kcr=8)$

$Kcr=8$

$kP=0\mathrm{.}6(8)=4\mathrm{.}8$

$Kd=4\mathrm{.}8$

$\frac{kd{s}^2+kps+ki}{s(s+1{)}^3+Kd{s}^2+kps}$

$s^3+s^2(3+4\mathrm{.}8)+s(kp+3)+$