## 5 Outcomes and Valuation
### Valuation of the Influence of Biodiesel and GPPt on the Dynamics of the System  
In Section 5.1, it was shown that the performance of the SHO-augmented TIDN-FOID controller is better compared to PIDN/TIDN controllers. The system in Section 5.1 included both biodiesel as well as GPP. Now, in order to analyze the impact of biodiesel and GPPt on system dynamics, they are removed from structure-1, keeping the capacities of the areas constant. Thus, the system now has thermal-thermal energy in area-1 and area-2 and hydrothermal energy in area-3 (structure-2). For structure-2, the best values of the TIDN-FOID controller are shown in Table 5, obtained by using the SHO controller. With these values, the responses for with and without both biodiesel and GPPt are contrasted in Figure 7. It can be easily viewed that the system in presence of biodiesel and GPPt have a large number of lessened values of peak_overshoot, peak_undershoot, settling_time, and number of oscillations. Only four responses are provided here.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Resposes**} & **Name of** & \multirow{2}{*}{**C\_O**} & \multirow{2}{*}{**C\_U**} & \multirow{2}{*}{**S\_D**} & **Computational** \\  & **Algorithm** & & & **(In Seconds)** & **Time (In Seconds)** \\ \hline \multirow{4}{*}{\(\Delta f_{3}\) (Figure 6a)} & WOA & 0.0021 & 0.0120 & 60.28 & 380 \\  & PSO & 0.0026 & 0.0122 & 65.31 & 375 \\  & CS & 0.0026 & 0.0121 & 66.39 & 378 \\  & FA & 0.0028 & 0.0124 & 67.64 & 353 \\  & **SHO** & **0.0002** & **0.0120** & **54.92** & **310** \\ \hline \multirow{4}{*}{\(\Delta Ptie_{1-2}\) (Figure 6b)} & WOA & 0.0005 & 0.0042 & 62.32 & 380 \\  & PSO & 0.0008 & 0.0042 & 71.01 & 375 \\ \cline{1-1}  & CS & 0.0009 & 0.0042 & 68.09 & 378 \\ \cline{1-1}  & FA & 0.0009 & 0.0042 & 66.87 & 353 \\ \cline{1-1}  & **SHO** & **0** & **0.0041** & **50.72** & **310** \\ \hline \multirow{4}{*}{\(\Delta Ptie_{1-3}\) (Figure 6c)} & WOA & 0.0005 & 0.0043 & 80.28 & 380 \\  & PSO & 0.0005 & 0.0043 & 78.28 & 375 \\ \cline{1-1}  & CS & 0.0006 & 0.0043 & 80.68 & 378 \\ \cline{1-1}  & FA & 0.0006 & 0.0044 & 67.87 & 353 \\ \cline{1-1}  & **SHO** & **0.0004** & **0.0042** & **56.69** & **310** \\ \hline \hline \end{tabular}
\end{table}
Table 4: P_O, P_U, and S_T for dynamics in Figure 6 in case of structure-1 using a WOA/PSO/CS/FA/SHO-augmented TIDN-FOID subordinate controller on an individual base.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Name of** **Controller**} & \multirow{2}{*}{**Corresponding Gains and** **Parameters**} & \multirow{2}{*}{**Area-1**} & \multirow{2}{*}{**Area-2**} & \multirow{2}{*}{**Area-3**} \\  & & & & \\ \hline \multirow{8}{*}{TIDN-FOID} & \(K_{Pl}\)* & 0.0762 & 0.0274 & 0.0385 \\  & \(K_{li}\)* & 0.3913 & 0.3850 & 0.3913 \\  & \(K_{Di}\)* & 0.7666 & 0.4598 & 0.1361 \\  & \(N_{i}\)* & 66.72 & 84.07 & 95.12 \\  & \(n_{i}\)* & 1.8853 & 3.8440 & 2.5914 \\  & \(K_{Fli}\)* & 0.4189 & 0.8526 & 0.9492 \\  & \(\lambda_{i}\)* & 0.0084 & 0.0058 & 0.0037 \\  & \(K_{Fli}\)* & 0.9043 & 0.8201 & 0.7264 \\  & \(\mu_{i}\)* & 0.0050 & 0.0065 & 0.0032 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Best values of attributes of TIDN-FOID controllers for structure-2 (hydrothermal system), excluding biodiesel and GPPt.