The water level ht in a tank is controlled by an open-loop

Question

The water level h(t) in a tank is controlled by an open-loop system, as shown in Figure P2.47. A DC motor controlled by an armature current i_a turns a shaft, opening a valve. The inductance of the DC motor is negligible, that is, L_a = 0. Also, the rotational friction of the motor shaft and valve is negligible, that is, b = 0. The height of the water in the tank is

a

the motor constant is K_m = 10, and the inertia of the motor shaft and valve is J = 6 X 10^-3 kg m². Determine (a) the differential equation for h(t) and v(t) and (b) the transfer function H(s)IV(s).