# Metaheuristic and Heuristic Algorithms-Based Identification Parameters of a Direct Current Motor
## 3 Optimization Algorithms
### Implementation of Metaheuristic Algorithms
Considering the above, each algorithm uses common general parameters, such as limits and iterations; see Table 2. However, they also use parameters that are specific to each method. The summary with the values of all the parameters used in each metaheuristic algorithm is shown in Table 3.  
Simulations were run for 3 s for a constant voltage of 10.5 V. Likewise, a numerical method with a fixed step of 0.001 s was used to adapt to the data acquisition system. In executing the three metaheuristic algorithms, MATLAB was used to model the dynamic system of the DC motor through Simulink, and to obtain the responses of current and angular velocity, Equations (6) and (7) were used, respectively. MATLAB is responsible for executing the heuristic and metaheuristic algorithms; however, to evaluate performance, the Simulink scheme shown in Figure 7 is used, which evaluates the proposed solutions and subsequently returns the current and voltage signals obtained to MATLAB. The parameters calculated for all algorithms are shown in Tables 5 and 6. Two real signals from the M2 Motor were used for this. The current signal was hardware-filtered, and the velocity signal was filtered using a Chebyshev software filter. Both signals are considered real, although there may be variations due to acquisition and filtering. * Figure 11 shows the comparison between the real current of the motor and the one estimated by the Steiglitz-McBride algorithm. In the same way, Figure 12 shows the comparison of the real velocity of the motor against that estimated by the Steiglitz-McBride algorithm. * Figure 13 shows the comparison between the real current of the motor and the one estimated by the GWO algorithm. In the same way, Figure 14 shows the comparison of the real velocity of the motor against that estimated by the GWO algorithm. * Figure 15 shows the comparison between the real current of the motor and the one estimated by the Jaya algorithm. In the same way, Figure 16 shows the comparison of the real velocity of the motor against that estimated by the Jaya algorithm. * Figure 17 shows the comparison between the real current of the motor and the one estimated by the GA algorithm. In the same way, Figure 18 shows the comparison of the real velocity of the motor with that estimated by the GA algorithm. Figure 10: Fitness evolution for Genetic Algorithm. Figure 9: Fitness evolution for Jaya. Figure 11: Real current signal vs. Steiglitz–McBride signal. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Jaya**} & \multicolumn{2}{c}{**GA**} \\ \cline{2-6}
**Parameter** & **Nominal Value** & **Value** & **MSE** & **Value** & **MSE** \\ \hline \(R\) (\(\Omega\)) & 0.921042 & 0.996974 & 08.24\% & 0.817929 & 13.44\% \\ \(L\) (H) & 0.007759 & 0.008941 & 15.04\% & 0.011908 & 89.00\% \\ \(K\) & 0.073472 & 0.000676 & 01.28\% & 0.076071 & 05.75\% \\ \(B\) \(\left(\frac{\text{kg}\cdot\text{m}^{3}}{\text{s}^{2}}\right)\) & 0.000678 & 0.291812 & 01.61\% & 0.000661 & 17.07\% \\ \(J\) (\(\text{kg}\cdot\text{m}^{2}\)) & 0.000136 & 0.000128 & 08.75\% & 0.000135 & 17.67\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison of Jaya and GA algorithms against nominal values. Figure 12: Real velocity signal vs. Steiglitz–McBride signal. \begin{table}
\begin{tabular}{l c c c c c} \hline \hline  & & \multicolumn{2}{c}{**Steiglitz–McBride**} & \multicolumn{2}{c}{**GWO**} \\ \cline{2-6}
**Parameter** & **Nominal Value** & **Value** & **MSE** & **Value** & **MSE** \\ \hline \(R\) (\(\Omega\)) & 0.921042 & 0.914735 & 00.68\% & 0.923696 & 0.42\% \\ \(L\) (H) & 0.007759 & 0.008893 & 14.49\% & 0.007752 & 0.96\% \\ \(K\) & 0.073472 & 0.073547 & 00.10\% & 0.073466 & 0.08\% \\ \(B\) \(\left(\frac{\text{kg}\cdot\text{m}^{3}}{\text{s}^{2}}\right)\) & 0.000678 & 0.000680 & 00.28\% & 0.000677 & 0.16\% \\ \(J\) (\(\text{kg}\cdot\text{m}^{2}\)) & 0.000136 & 0.000135 & 01.03\% & 0.000136 & 0.55\% \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of Steiglitz–McBride and GWO algorithms against nominal values.