A jacketed stirred tank is used to cool a process stream by flowing cooling water through the

jacket as shown below. Assume constant volumes, densities, heat capacities. Simulate the

temperature control loop with Simulink and trend the response of the transmitter and controller

outputs for $200$ minutes to: a step change of $+10\backslash$deg C in process fluid temperature at time $=40$

minutes, a step change of $-5\backslash$deg C in coolant temperature at time $=80$ minutes, a step change of

$+0\mathrm{.}02$ m$^3/$min in process fluid flow at time $=120$ minutes. Use a real PID controller tuned for

quarter decay ratio response, a linear characteristics control valve with constant pressure drop,

a first$-$order lag temperature transmitter with a $0\mathrm{.}6$ min time constant and a $2070\backslash$deg C range, a

first$-$order lag control valve with a $0\mathrm{.}1$ min time constant and a $0\mathrm{.}00\mathrm{.}8$ m$^3/$min range. The

ultimate gain and period of the loop with a proportional controller were determined by a closed

loop step test to be: $-75\%$CO$/\%$TO and $8$ min, respectively. Process parameters are given below.

Properly label your Simulink block diagram and trend.

I. Process constants:

U $=$ overall heat transfer coefficient

U $=200$ kJ$/$min$-$m$^2-\backslash$deg C

A $=$ heat transfer surface area $=4$ m$^2$

V $=$ stirred tank volume $=5\mathrm{.}0$ m$^3$

Vc $=$ coolant jacket volume $=1\mathrm{.}1$ m$^3$

$\backslash$rho $=$ process fluid density $=800$ kg$/$m$^3$

$\backslash$rho c $=$ coolant density $=1000$ kg$/$m$^3$

cp $=$ process fluid heat capacity $=3\mathrm{.}8$ kJ$/$kg$-\backslash$deg C

cpc $=$ coolant heat capacity $=4\mathrm{.}2$ kJ$/$kg$-\backslash$deg C

II$.$ Design conditions:

v $=$ process fluid flow rate $=0\mathrm{.}1$ m$^3/$min

vc $=$ coolant flow rate $=0\mathrm{.}2$ m$^3/$min

Ti $=$ process fluid inlet temperature $=70\backslash$deg C

Tic $=$ coolant inlet temperature $=25\backslash$deg C