Consider the liquid level control system with the plant transfer function G$($s$).($a$)$ Design a proportional controller so that the damping ratio is zeta $=0\mathrm{.}6.($b$)$ Design a PI controller so that the rise time is less than $1$ sec$.($c$)$ Design a PD controller so that the rise time is less than $0\mathrm{.}7$ sec$.$ Design a PID controller so that the settling time is less than $1\mathrm{.}8$ sec$.$