# Metaheuristic and Heuristic Algorithms-Based Identification Parameters of a Direct Current Motor
## 5 Discussion  
Table 7 shows the computation performance of each algorithm. In this way, the computation times are compared among themselves to see whether they influence each algorithm's performance, since in works such as ref. [47], it has been reported that the increase in iterations negatively affects the optimization of the solutions. This is contrary to what occurs in our research, where the increased iterations and, consequently, high computational cost improved the parametric estimates. Even though parameterization is an offline process, the response times of the algorithms are too high for the response time expected in a control system. Thus, this type of algorithm is usually avoided in processes that require a high response speed. As can be seen in Table 7, the Steiglitz-McBride heuristic algorithm has a lower computational cost compared to the metaheuristic algorithms. This is because the algorithm itself works through pure mathematics and is in charge of finding a unique solution. However, among the metaheuristic algorithms, a similar computational cost was observed, with a time variation of 10.7 min. GWO has been used to estimate the parameters of a DC motor by applying an Integral Squared Error (ISE) object function [3]. It is reported that a smaller number of iterations could be detrimental, as it causes stagnation and local optima problems. Because of this, the authors decided to implement 500 iterations per test and few search agents compared to iterations. The use of 500 iterations in our research significantly increased the computation \begin{table}
\begin{tabular}{l c} \hline \hline
**Algorithms** & **Average Time (min)** \\ \hline Steiglitz–McBride & 0.102 \\ GWO & 49.53 \\ Jaya & 51.16 \\ GA & 60.23 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Computation time. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Algorithms**} \\ \cline{2-5}
**Parameters** & **Steiglitz–McBride** & **GWO** & **Jaya** & **GA** \\ \hline R & 0.0023 & 0.0040 & 0.0086 & 0.1340 \\ L & \(6.49\times 10^{-5}\) & \(9.22\times 10^{-5}\) & \(8.69\times 10^{-4}\) & 0.0114 \\ K & \(4.53\times 10^{-5}\) & \(7.24\times 10^{-5}\) & 0  
time. GWO has also been used as a parameter tuner for a PID controller [48], where 50 iterations and 30 search agents were applied. Taking into account the above, the configuration we decided to use in our research consisted of a smaller number of iterations and a larger number of search agents to reduce the computational cost and achieve a low error compared to the literature. This represented an estimation with an average error rate of 1.73%, which was 55% lower than that shown in [3]. The algorithm with the highest average MSE percentage was the GA algorithm, which was 28.59%. Among all the algorithms, the algorithm that showed the lowest average percentage error was the GWO, with 0.43%. However, the average MSE percentage for Steiglitz-McBride, which is not a metaheuristic algorithm, was lower than Jaya and GA; see Tables 5 and 6. Although GWO generated the best parametric estimation in this research, the Steiglitz-McBride algorithm could work as another alternative when the application requires low computational cost and a low standard deviation in the estimation of each parameter; see Table 8. For example, in [49], it has been shown that the Steiglitz-McBride algorithm is useful in the parametric estimation of electrical machines such as DC motors, brush DC, and brushless AC and gear machines. Also, it is frequently used as an optimizer. The current signals estimated by GWO and Steiglitz-McBride were very similar to the nominal ones. For this reason, a comparison of the real and estimated signals obtained by the algorithms was performed with the following indicators: settling time, overshoot, and steady-state error. The stabilization times of the current signals were as follows: 1.107 s in the real signal, 1.118 s in Steiglitz-McBride, 1.103 s in GWO, and 1.167 s in GA.