Continuously stirred tanks have an extensive use in chemical processes. They are often supplied

with some sort of heat exchange system. If the tank is used for a chemical or biochemical reaction it

is often important to keep a certain temperature to obtain desired productivity. A continuously

stirred tank with a common type of heat exchange system is shown in the Figure below. The tank is

surrounded with a heating$/$cooling layer in which a liquid flow through to heat or chill the liquid in

the tank.

A$.$ Determine the important signals of the system. Suggest a control strategy based on feedback

and draw the block diagram.

B$.$ To be able to construct and evaluate different controllers it is necessary to have a process

model. Determine a dynamical model for this system. Assume that the volumes in the tank and

in the heat exchange system are constant.

C$.$ Linearize the model at the equilibrium point: $T_t=50\mathrm{.}0C,T_c=75\mathrm{.}0C.)$

D$.$ The parameters of the model are as follows.