$"$In the figures, both the PI diagram and the block diagram for a control loop regulating the level H in a tank by controlling the outlet flow Qu can be seen. Variations in the inlet flow Qi occur as disturbances to the system. The signals shown in the block diagram are deviations from steady$-$state values."

$($styrer it is means controls$)$

"The tank is cylindrical with a cross$-$sectional area of $4$ m$2$ and a total height of $5$ m$.$ The level transmitter has a measurement range of $05$ m$,$ meaning it converts H $=05$ m to PV $=0->100\%."$

"The time constant of the level transmitter is $2$ seconds."

"The control valve converts the control signal y $(0->100\%)$ into flow Qu $(0->0\mathrm{.}1$m$3/$s$).$ The time constant of the control valve is $10$ seconds. The controller is a proportional controller with gain Kc$.$ The bias offset is $50\%($not shown in the block diagram$)."$

A$)$ Set up a model for the tank$\text{'}$s contents and explain, based on the PI diagram at the top, why the 'Process' block $($in the bottom block diagram$)$ has the signals, units, constants, and transfer functions it has!

B$)$ How much does the level H $($m$)$ increase after a $1\%$ setpoint $($SP$)$ step?

C$)$ If the setpoint $($SP$)$ is increased in a step of $1\%,$ what steady$-$state error $($offset$)$ occurs on the level H $($m$)?$

D$)$ Is the found 'offset' $($above$)$ what you would expect? Explain!

E$)$ rite down the transfer function h$($s$)/$qi$($s$)($for fixed Qu$,$ i$.$e$.,$ qu$($s$)=0).$