Consider the liquid level control system with plant transfer function $()=7$

$2+8+7$ and unity

feedback Design a proportional controller so the damping ratio is $=0\mathrm{.}707.$

b$)$ Design a PI controller so the settling time is less than $4$ sec$.$

c$)$ Design a PD controller so the rise time is less than $1$ sec$.(0-100\%).$

d$)$ Design a PID controller so the settling time is less than $2$ sec