$1.(50$ p$)$ Consider the liquid level system given below.O$1-(50$ p$)$ Comober the liquid level sysem given beluw. Dow rate $\{$qu$.$

a$)$ Develop the mathematical model of this system using deviation variables.

b$)$ Develop a transfer function that relates the liquid level in the tank $(h)$ to changes in the inlet

flow rate $(q_1).$