In the flow-level system shown below the inflow rate through the control valve is Qi(t). The head if the tank is H(t) and it flows out through two outlets by the rate of Q1(t) and Q2(t). The two valves leads the fluid out by resistances R1 and R2(t). Obtain the transfer functions and the corresponding differential equations governing the dynamic behaviors of h(t), qi(t), q1(t),and q2(t).Displaying them as the following three cases.
Case Input L(Input) Output L(Output)
(i) qi(t) Qi(s) q1(t) Q1(s)
(ii) qi(t) Qi(s) q2(t) Q2(s)
(iii) qi(t) Qi(s) h(t) H(s)
Note
Qi(t) = Q_bar + qi(t)
Q1(t) = Q1_bar + q1(t)
Q2(t) = Q2_bar + q2(t)
H(t) = H_bar + h(t)