# Metaheuristic and Heuristic Algorithms-Based Identification Parameters of a Direct Current Motor
## 6 Conclusions  
This work performed a parametric estimation of a DC motor using a heuristic algorithm (Steiglitz-McBride) and three metaheuristic algorithms (Jaya, GWO, and GA). The MSE and standard deviation were used as statistical indicators to evaluate the performance of each algorithm as well as other values of the dynamic response, such as settling time,overshoot, and steady-state error. In this way, this work determined which algorithm provides a parametric estimation closer to the nominal parameters and real DC motor signals. The comparison between metaheuristic and heuristic algorithms is limited to parametric estimation in direct current motors. As the No Free Lunch theorem states, no algorithm is best for all applications. Another limitation is the selection of hyperparameters, because there is no way to guarantee the optimal selection of these parameters in metaheuristic algorithms. There are algorithms for selecting hyperparameters, but they do not guarantee optimal selection. Therefore, the maximum performance of a metaheuristic algorithm may not be found.  
According to the aforementioned aspects, the two best-performing algorithms were Steiglitz-McBride and GWO. GWO was the best parametric estimator for this application, having the lowest MSE of all algorithms for the nominal parameters. Likewise, this algorithm had the closest responses to the real ones, with the best overshoot and settling time approximation. However, Steiglitz-McBride also obtained good results as a parametric estimator, even better than Jaya and GA, but with the lowest computational cost of all and a less variable parametric estimation.  
Although GWO is a better parametric estimator, it does not mean that it is better than the Steiglitz-McBride algorithm, since implementing the mathematical model in a metaheuristic algorithm can be simpler. However, the search parameters required by metaheuristic algorithms are obtained after many tests, which generate a high computational cost. Although the Steiglitz-McBride is mathematically more complex, if appropriately implemented, it may require fewer tests and fewer corrections within the algorithm, resulting in a lower computational cost.  
In this work, the heuristic algorithm produced fewer problems during tests, with lower computational cost and low variation in estimates. However, if a more precise parametric estimation is required, it is recommended to use GWO. Considering these aspects, the heuristic algorithm has more advantages in the parametric estimation of DC motors. The performance of the algorithms presented in this paper may change if different error functions are used, as well as other search parameters. In addition, performance depends on the final application of the algorithm.  
Conceptualization, L.A.M.-S., E.A.D.-R., M.C.-F. and J.R.-R.; methodology, M.C.-F., D.M.M. and E.A.D.-R.; writing--original draft preparation, L.A.M.-S., M.C.-F. and J.R.-R.; writing--review and editing, D.M.M., E.A.D.-R. and L.A.M.-S.; supervision, L.A.M.-S. and M.C.-F. All authors have read and agreed to the published version of the manuscript.  
No funding was received to conduct this study.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors thank the Polytechnic University of Queretaro (UPQ) for the support.  
The authors declare that they have no conflicts of interest. The datasets generated during and/or analyzed during the current study are available from the corresponding authors on reasonable request.