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 ia turns a shaft, opening a valve. The inductance of the DC motor is negligible, that is, La = 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

the motor constant is Km = 10, and the inertia of the motor shaft and valve is J = 6 × 10-3 kg m2. Determine
(a) The differential equation for h(t) and v(t) and
(b) The transfer function H(s)/V(s).

Transcribed Image Text:

h)[16) ()]dt,