Q$4-$The water level, h$($t$),$ is controlled by an open$-$Joop system as shown in figure below. A dc motor controlled by an armature current $i_a$ turns a shaft, opening a valve the inductance of dc motor is negligible, that is $l_a=0.$ Also the rotation friction of the motor shaft and valve is negligible. That is$,C=0,$ The amount of q in the tank$\text{'}$s water is

$dt{\displaystyle \underset{0\mathrm{.}025q_{1}dt=\frac{d(t)}{20}}{\overset{20}{}}}$

The motor constant is $K_m=10,$ the inertia of the motor shaft and valve is$/=6{10}^{-3}Kg*m^2,$ back emf constant $K_b=0\mathrm{.}0706\frac{V}{ra\frac{d}{s}}$ and the capacitance C of the tank is $2m^2,R_r-1$ DetermineThe transfer function $H\frac{s}{V}(s).(25$marks$)$