# Design of the Input and Output Filter for a Matrix Converter Using Evolutionary Techniques
## 6 Results
### Optimal Solutions
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{x_{1}}\) [\(\mathbf{F}\)] & \(\mathbf{x_{2}}\) [\(\mathbf{H}\)] & \(\mathbf{x_{3}}\) [\(\mathbf{g}\)] \\ \hline \(2.80\times 10^{-6}\) & 0.0062800000000028 & 0.187555316441543 \\ \hline \(2.80\times 10^{-6}\) & 0.0062800000000017 & 0.187555316657591 \\ \hline \(\mathbf{2.80\times 10^{-6}}\) & **0.0062800000000007** & **0.18755531746872 \({}^{a}\) \\ \hline \(2.80\times 10^{-6}\) & 0.0062800000000004 & 0.187555315666788 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000013 & 0.187555317687343 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000008 & 0.187555317484832 \\ \hline \(2.80\times 10^{-6}\) & 0.0062800000000026 & 0.187555315207603 \\ \hline \(2.80\times 10^{-6}\) & 0.0062800000000005 & 0.187555313375193 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000013 & 0.187555317687343 \\ \hline \(2.80\times 10^{-6}\) & 0.0062800000000026 & 0.187555317149325 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000025 & 0.187555316290116 \\ \hline \(2.80\times 10^{-6}\) & 0.006280000000000012 & 0.187555317506824 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000013 & 0.187555315746281 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000026 & 0.187555315616287 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000013 & 0.187555317592858 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000017 & 0.187555316425078 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000012 & 0.187555317506824 \\ \hline \(2.80\times 10^{-6}\) & 0.006280000000000013 & 0.18755531680009 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000022 & 0.18755531655392 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000022 & 0.187555316820297 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000018 & 0.187555316346879 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000013 & 0.187555317471883 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000013 & 0.18755531571449 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000022 & 0.187555315578319 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000026 & 0.187555316660662 \\ \hline \(2.80\times 10^{-6}\) & 0.006280000000000008 & 0.187555314295145 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000038 & 0.18755531713709 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000026 & 0.187555315947656 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000026 & 0.187555316199455 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000012 & 0.187555317592252 \\ \hline \(2.80\times 10^{-6}\) & 0.00628000000000012 & 0.187555317592252 \\ \hline \hline \end{tabular} \({}^{a}\) Selected solution vector for the simulation stage.  
\end{table} 
Table 1: Best individuals obtained for the input filter problem. The statistical analysis of these results is presented in Table 4. As can be seen, the variance and the standard deviation were approximated to zero, which indicated the stability of the algorithm. The convergence graph is presented in Figure 7, including the best, the average, and the worst convergence behavior of the 30 runs. It could be seen that DE converged uniformly to a minimum of the objective function. The values obtained in the design vector in the 30 runs were the same, and based on the convergence of the algorithm, it was concluded that the values found were optimal for the problem posed. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Objective Function (dB)** \\ \hline Best & \(-\)33.4705013527862 \\ \hline Worst & \(-\)33.4705013527862 \\ \hline Average & \(-\)33.4705013527862 \\ \hline Standard deviation & \(1.519204271928768\times 10^{-14}\) \\ \hline Variance & \(5.2357\times 10^{-29}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Table of the results from the statistical analysis. Figure 6: Convergence graph of the objective function for the input filter. Figure 7: Convergence graph of the objective function for the output filter. taking into account only the design restrictions and part of a fixed value of some of the parameters to obtain the others.