## 3 Control Strategy
### Proposed NFIHC  
The NFIHC is an amalgamation of FL and ANN techniques, where the process of FL is controlled by the ANN technique. The FL controller works on mathematical reasoning, i.e., on linguistic rules. The FL controller works in three stages: fuzzification, inference, and defuzzification. During the processes of fuzzification, the numerical inputs are converted into linguistic variables. In order to transform the values into linguistic terms, a set of MFs is developed. The fuzzy rule base and MFs are determined in the inference stage. Lastly, in the stage of defuzzification depending on the input, any one of the values is considered as output. The process of FL is given in Figure 7.  
The Takagi-Sugeno method is considered and receives \(Er\) and \(CE\) as inputs. The E is evaluated by Equation (29). The triangle MFs for both the E and CE are shown in Figures 8 and 9, respectively. The fuzzy variables are denoted by triangular MFs as given in Figures 8 and 9, involving P1, medium positive (P2), P0, Zero (O), N2, medium negative (N1), and N0. The voltage across DC-Link considers values in the range of these linguistic terms, and it is operated in a total of 49 sets of MFs, as exhibited in Table 4.  
\[E_{r}=V^{ref}_{dc}-V^{i}_{dc};\ i=1,2,3,4,5,6 \tag{29}\]The ANN is a self-adaptive advanced control technique; its working mechanism is similar to the human brain. It is preferable due to its self-training, where interconnected neurons are trained according to the task required. The ANN contains three layers, namely IPL to receive data, HDL (between IPL and OPL), possessing specific weights and bias, and OPL, providing the output. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Er**} & \multicolumn{5}{c}{**CE**} \\ \cline{2-9}  & **P2** & **P1** & **P0** & **O** & **N0** & **N1** & **N2** \\ \hline N2 & O & N0 & N1 & N2 & N2 & N2 & N2 \\ N1 & P0 & O & N0 & N1 & N2 & N2 & N2 \\ N0 & P1 & P0 & O & N0 & N1 & N2 & N2 \\ O & P2 & P1 & P0 & O & N0 & N1 & N2 \\ P0 & P2 & P2 & P1 & P0 & O & N0 & N1 \\ P1 & P2 & P2 & P2 & P1 & P0 & O & N0 \\ P2 & P2 & P2 & P2 & P2 & P1 & P0 & O \\ \hline \hline \end{tabular}
\end{table} 
Table 4: MF mapping for capacitor voltage. Figure 8: MF for “Er”. Figure 7: Overview of Fuzzy controller. Figure 9: MF for “CE”. The proposed NFIHC is an efficient self-adaptive controller that utilizes both the superior qualities of FL and ANN controllers. Initially, the given inputs are trained by the MFs of FL and fed as inputs to the ANN. Based on the number of HDL, the NFIHC trains and provides appropriate output. The schematic diagram of NFIHC is illustrated in Figure 10. The MFs are trained through the NFIHC method to produce the desired output. In the proposed WPGS, and BSS connected SHAPF, the reference DC voltage is compared with the actual voltage, and the error is fed to the NFIHC controller. In this paper, the Levenberg-Marquardt algorithm is used to train the ANN. The NFIHC system is mathematically modeled by Equation (30). \[\text{IF }M\text{ is }G\text{ AND }N\text{ is }H,\text{ then }P\text{= }F(M,N) \tag{30}\]  
where  
\(M\), \(N\), and \(P\) are input and output parameters. A total of five layers were considered. At the 1 st, the MFs with input \(M\) are represented as \(\delta_{Gj}(M)\), where \(j\) denotes the MFs used. The weight (\(W\)) of neurons (\(i\)) at the product layer with AND operator is given in Equation (31). \[W_{i}=\delta_{Gj}(M)*\delta_{Hj}(N) \tag{31}\]  
The 3 rd layer works for the normalization of the values received from the 2 nd layer and are expressed in Equation (32). \[W_{i}=\frac{W_{i}}{W_{1}+W_{2}} \tag{32}\]  
In the 4 thdefuzzification layer, the ANN controller adopts self-adaptive property with the inference parameters \((a_{i},b_{i},c_{i})\) as given in Equation (33). \[\overline{W_{i}}F_{i}=\overline{W_{i}}(a_{i}M+b_{i}N+c_{i}) \tag{33}\]  
The summation of inputs is carried out at the 5 th layer to produce the output function \(F\) as given in Equation (34).