The figure shows a reactor, in

which a batch process is used to hydrogenate $(\text{'}$harden$\text{'})$ fish oil into a solid fat."

"The process $($absorption of hydrogen at the oil's double bonds$)$ must occur at $190$ldegC

and $3$ bar. Hydrogen is supplied $($as shown$)$ via a distribution pipe. The oil is sprayed by a

stirrer into a conductor pipe in the gas phase. This creates good contact between the liquid

and gas phases and good agitation in the liquid phase. The process is slightly exothermic,

and the heat of reaction is removed with cooling water. If the control air to the valves fails,

the contents of the tank must not be allowed to solidify. After starting the process, the

continuous regulators shown must ensure constant pressure and temperature as mentioned.

The following information is provided:

The PC regulator is a proportional regulator with a gain of $2\mathrm{.}5.$

The pressure transmitter has a measuring range of $1\mathrm{.}5-4$ bar $($corresponding to $0\%-$

$100\%).$

The hydrogen valve is linear and should be $50\%$ open when the tank pressure is at the

setpoint of $3$ bar.

Answer the following:

A$)$ What valve characteristics $($ATO$/$ATC$)$ would you suggest for each of the regulators?

B$)$ What regulator action $($Direct$/$Inverse$)$ does your choice imply?

C$)$ Calculate the setpoint in $\%$ and draw the regulator characteristic for PC$.$

D$)$ How wide is the proportional band?"