## 3 Model Development
### Dynamic State Model Development
#### 3.3.3 Closed Loop Control Scheme and Controller Tuning  
The control scheme should help the operator achieve the desired objectives. For our case, the carbon capture plant should be able to capture a specific amount of CO\({}_{2}\) from the feed flue gas. The outlet stream should have a constant fraction according to the purity requirements set by the methanol reactor that follows the CC stage. The product quality might be difficult to measure online thus inferential control could be a solution through controlling other easily measured variables such as the condenser temperature, saving the cost of an online CO\({}_{2}\) analyzer that could be replaced with an inexpensive thermocouple [41]. To achieve the above-mentioned objectives, several factors have to be taken into consideration, such as:  
* The capture rate of the absorber is to be controlled using a PI controller, measuring the amount of CO\({}_{2}\) captured from the inlet gas stream and manipulating the lean amine flowrate accordingly
* The pressure of the exiting flue gas is controlled by manipulating the flow rate of the exiting gas stream
* The absorber sump level is controlled by measuring the liquid level and manipulating the rich amine flow rate exiting at the bottom of the absorber
* The CO\({}_{2}\) stream temperature is controlled by manipulating the condenser duty
* The stripper output pressure is being controlled by a control valve manipulating the exit CO\({}_{2}\) stream flowrate
* The stripper pump level is controlled in a similar fashion to the absorber sump level
* The stripper operating temperature was controlled through manipulating the reboiler duty (steam flowrate) thus ensuring a stable lean loading  
A control scheme was initially installed to control the absorber temperature through manipulating the washing section flowrate, but the results showed low power of control where the correcting variable had a negligible impact on the controlled variable. By controlling the capture rate and the operating conditions of both columns, the CO\({}_{2}\) flowrate, purity, pressure, and temperature were controlled and monitored throughout the dynamic scenarios. The default values for the pressure controllers respond reasonably well, but the other controllers did not show desirable and quick correctional behavior. Open-loop \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Unit**} & \multirow{2}{*}{**Controller**} & \multirow{2}{*}{\begin{tabular}{c} **Process** \\ **Controlled** \\ **Variable (PV)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Manipulated Variable** \\ **(OP)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Gain** \\ **(\%/\%)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Integral** \\ **Time (min)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Derivative** \\ **Time (min)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Controller** \\ **Action** \\ \end{tabular} } \\ \hline \multirow{2}{*}{Absorber} & Absorber PC & Outlet pressure & Clean flue gas flow rate & 20 & 12 & 0 & Direct \\  & Absorber LC & Liquid Level & Rich amine flow rate & 10 & 60 & 0 & Direct \\ \hline \multirow{2}{*}{Stripper} & Stripper PC & Outlet pressure & CO\({}_{2}\) stream flow rate & 20 & 12 & 0 & Direct \\  & Stripper LC & Liquid level & Lean amine flow rate & 10 & 60 & 0 & Direct \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Summary of the unit default controllers. dynamic tuning was conducted to determine the suitable values for each controller, the control was tuned to handle both the set point and load disturbance. The test enables us to estimate the open-loop gain, dead time, and time constant, which were then used to calculate the tuning parameters using Ziegler-Nichols, giving approximate values of gain and integral time.