Consider a lab scale CSTR with a single second order reaction. To the reactor reactants

enter with a flowrate, $F(l\frac{t}{m}in),$ and concentration $C_{\text{A}\text{i}\text{n}}(mo\frac{l}{l}t).$ The output

concentration in terms of component $A$ is $C_A$ and is the output variable.

The CSTR is a constant volume one.

Data: Rate of reaction $r=k{C}_A^2[$moles of A reacted $/$lt$-$min$/$lt$]$

Steady state conditions are:

$\frac{?}{\text{b}\text{a}\text{r}}(F)=1$ liter$/$min; $\frac{?}{\text{b}\text{a}\text{r}}(C_{As})=1mo\frac{l}{?}$ liter; $\frac{?}{\text{b}\text{a}\text{r}}(V)=1$ liter ;$k=1$ liter$/($mol$-$min$)$; $\frac{?}{\text{b}\text{a}\text{r}}(C_{\text{A}\text{t}\text{n}})=2mo\frac{l}{?}$ liter

The Control Valve:

$F^{\text{'}}(s)\{$:$=5\mathrm{.}0\frac{lt}{\text{m}\text{i}\text{n}}\frac{?}{})P^{\text{'}}(s)$

$K_{IT}=0\mathrm{.}75\frac{}{m}A$

I$/$P Transmitter:

$C_{Am}^{\text{'}}(s)=0\mathrm{.}1e^{-2s}(\frac{mA}{\text{m}\text{o}\text{l}}\frac{?}{(\text{l}\text{i}\text{t}\text{e}\text{r})})C_A^{\text{'}}(s)$

$G_c(s)=K_c[m\frac{A}{m}A]$

Temperature$-sensor-$transmitter: $C_{Am}^{\text{'}}(s)$

$G_c(s)=K_c[m\frac{A}{m}A]$

Controller:

$G_c(s)=K_c[m\frac{A}{m}A]$

a$.$ Draw the reactor system schematically showing all inputs and outputs

b$.$ Derive the necessary unsteady$-$state differential equations for modelling the reactor by

making necessary assumptions

c$.$ Linearize the equations and obtain the input$-$output model in Laplace Domain indicate

the load and process Transfer Function find numeric values of gains and time

constants.

d$.$ Suggest control configuration for controlling the output concentration of A for any

changes in input concentration by stating the controlled variable, manipulated variable

and disturbance.

e$.$ Draw the block$-$flow diagram for the design you developed considering inputs and

outputs of all hardware elements with their units.

f$.$ What will be your suggestion for the correct controller type $($P$/$PI$/$PD$/$PID$)?$

g$.$ Find closed loop transfer functions for servo and regulator problems.

h$.$ For a decrease of $0\mathrm{.}10mo\frac{l}{?}$ liter in the inlet concentration of A what is the time

i$.$ Find the open$-$loop response of $C_A(t)$ for a decrease of $0\mathrm{.}10mo\frac{l}{?}$ liter in the inlet

concentration of A$.$

j$.$ Find the offset for open$-$loop and compare it with the one you found in part $"$h$".$

$($Hint: You can use Pad$$ approximation for the delay term $e^{-2s}$ for part $h)$