It is desired to control the composition and the level of the mixing tank used to prepare a saline solution at the nominal value by two PID controllers. There are $2$ inlet streams entering the mixing tank. Density of the mixture can be assumed constant through out the mixing process. The dilute inlet stream has a constant composition of $10$ wt$\%$ with a nominal flowrate of $5$kg$/$min$.$ The other concentrated stream has a constant composition which is $80\%$ and has a nominal stream flowrate of $4$kg$/$min$.$ It is desired to keep the level of the cylindrical mixing tank with a crosssectional area of $1$m$2$ at $3$m$.$

a$)$ If the dilute stream is considered to be disturbance to the mixing tank. Draw a block diagram for level and composition control system.

b$)$ Determine all transfer functions that relates level of the tank and the product composition to set point and disturbance variable. It is reasonable to assume that every control element in the control system has unit gains and fast dynamics.

Hint for block diagram