## 5 Outcomes and Valuation
### Suggestion of Pix  
The leading performance index (_Pix_) among the integral squared error (_PIxISE_), integral absolute error (_PIxIAE_), integral time squared error (_PIxITSE_), and integral time absolute error (_PIxITAE_) is acquired by facilitating structure-1, excluding these _PIx_ on individual terms via the TIDN-FOID controller. The finest values of the TIDN-FOID controller's attributes are accomplished via the SHO algorithmic procedure. The expression of _PIxITSE_, _PIxIAE_, and _PIxITAE_ are shown in Equations (31)-(33), respectively, while the expression of _PIISE_ was shown by Equation (5):  
\[PIx_{ITSE}=\int_{0}^{T}\Bigl{\{}\left(\Delta f_{1}\right)^{2}+\left(\Delta f_{ 2}\right)^{2}+\left(\Delta f_{3}\right)^{2}+\left(\Delta P_{tie_{1-2}}\right)^ {2}+\left(\Delta P_{tie_{2-3}}\right)^{2}+\left(\Delta P_{tie_{1-3}}\right)^{2} \Bigr{\}}t\;d \tag{31}\]  
\[PIx_{IAE}=\int_{0}^{T}\bigl{\{}\left|\Delta f_{1}\right|+\left|\Delta f_{2} \right|+\left|\Delta f_{3}\right|+\left|\Delta P_{tie_{1-2}}\right|+\left| \Delta P_{tie_{2-3}}\right|+\left|\Delta P_{tie_{1-3}}\right|\bigr{\}}\;dt \tag{32}\]  
\[PIx_{ITAE}=\int_{0}^{T}\bigl{\{}\left|\Delta f_{1}\right|+\left|\Delta f_{2} \right|+\left|\Delta f_{3}\right|+\left|\Delta P_{tie_{1-2}}\right|+\left| \Delta P_{tie_{2-3}}\right|+\left|\Delta P_{tie_{1-3}}\right|\bigr{\}}t\;dt \tag{33}\]  
Using the best values obtained for TIDN-FOID controller in individual circumstances, the potent outcomes are distinguished in Figure 5a-c. In addition, the conforming C_O_ and C_U, besides S_D_ standards, are shown in Table 3. An extensive understanding of the outcomes shows that outcomes using _PIISE_, as per _Pi_, have a healthier presentation with reference to diminished C_O, C_U, and S_D_ oscillations. Additionally, the standards of _PIx_ are _PIxISE_ = 0.0007218, _PIxITSE_ = 0.001793, _PIxIAE_ = 0.1467, and _PIxITAE_ = 1.3210, showing that _PIxISE_ improves the scheme. The merging features for structure-1 via dissimilar _PIx_ are shown in Figure 5d. It can be seen that merging features via ISE as _PIx_ converges quicker in fewer repetitions when more _PIx_s are added. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Resposes**} & **Name of** & \multirow{2}{*}{**C\_O**} & **C\_U** & **S\_D (In Seconds)** \\  & **Controller** & & & \\ \hline \(\Delta f_{1}\) & PIDN & 0.0008 & 0.0176 & 118.10 \\ (Figure 4a) & TIDN & 0.0006 & 0.0161 & 98.72 \\  & TIDN-FOID & **0.0004** & **0.0153** & **62.36** \\ \hline \(\Delta f_{2}\) & PIDN & 0.0007 & 0.0110 & 111.50 \\ (Figure 4b) & TIDN & 0.0005 & 0.0103 & 89.71 \\  & TIDN-FOID & **0.0003** & **0.0093** & **57.44** \\ \hline \(\Delta\)_Ptie_2-3 & PIDN & 0.0024 & 0.0007 & 119.30 \\ (Figure 4c) & TIDN & 0.0022 & 0.0006 & 100.81 \\  & TIDN-FOID & **0.0021** & **0.0004** & **57.37** \\ \hline \(\Delta\)_Ptie_1-3 & PIDN & 0.0002 & 0.0051 & 109.11 \\ (Figure 4d) & TIDN & 0.0001 & 0.0045 & 88.27 \\  & TIDN-FOID & **0.00004** & **0.0042** & **56.69** \\ \hline \hline \end{tabular} _ Bold signifies best values._  
\end{table} 
Table 2: C_O, C_U, and S_D for consequences in Figure 4 in circumstance of structure-1 using SHO-augmented PIDN/TIDN/TIDN-FOID subordinate controllers.