Q$3.$

The liquid level in the second tank for a noninteracting tank system is controlled by

manipulating the inlet flow rate of the first tank.

All of the resistances are linear and $R_1=0\mathrm{.}05,R_2=0\mathrm{.}1$min.$\frac{m}{m^3}$; the cross$-$sectional

areas of the tanks are constant and $A_1=5,A_2=3.$

a$.$ Derive the transfer function between inlet volumetric flow rate and height of liquid

level in second tank, find natural period and damping factor.

b$.$ The transfer function of measuring device with its transmitter and the transfer

function control valve are $1,$ show the effect of $P$ controller by considering $i)$ order

of response, ii$)$ speed of response, iii$)$ ultimate value iv$)$ offset for the unit step change is set point.

Please write your answer by step step and clearly. I'll remember to evaluate your answer.