## 3 Results  
A total of 1000 cases of systems with random \(m\), \(k\), and \(c\) values were tested. Two neural network models were proposed to automate the tuning of PID parameters. The results indicated that the PID parameter tuning was completed in less than 1.6 attempts in every method, because these methods generated the acceptable PID parameters of the system as outputs after identifying the system from the response. An example of a response graph that changed as the tuning was repeated is shown in Figure 6.  
Figure 5: Flowchart of the tuning process using neural networks. According to the learning method classified by the type of network, number of sampling data, and whether response characteristics were included as inputs, the LSTM networks showed better performance in the results of both the first and second neural networks (Tables 2 and 3). The relative error between real model parameters and predicted model parameters from the first neural network was between 14.5% and 37.6% (Table 2). The accuracy of the first neural network also affected the performance of the second neural network. When the relative error of the first neural network was low, the final results were also good. LSTM networks showed approximately 98% (~980 success per 1000 cases) success in tuning (Table 3). However, ANN with 21 and 11 sampling data without response characteristics showed poor performance. The performances of the LSTM network and ANN were similar when the input data included the response characteristics; however, there was a significant difference in the performances when the input data did not include the response characteristics. The performance of the LSTM network was 53% better than that of ANN when the input data did not include the response characteristics. Based on the input features, both the methods with inputs including the number of sampling data and response characteristics showed approximately 98% success in tuning; however, when the input did not include response characteristics, the ANN showed unacceptable performance. Therefore, an LSTM network with an input sampling data size of 11 was recommended, because when the input was minimal, only 1 s of the response data was sufficient for tuning the PID parameter. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{4}{c}{**Relative Error (\%)**} \\ \cline{2-5}  & **Mass** & **Spring** & **Damper** & **Average** \\ \hline A-21-RC & 4.37 & 9.90 & 29.3 & 14.5 \\ A-11-RC & 4.07 & 12.2 & 36.8 & 17.6 \\ A-21 & 32.5 & 30.0 & 26.6 & 29.7 \\ A-11 & 34.3 & 52.3 & 26.1 & 37.6 \\ \hline L-21-RC & 5.81 & 13.4 & 26.5 & 15.2 \\ L-11-RC & 6.50 & 25.0 & 15.3 & 15.6 \\ L-21 & 15.3 & 17.9 & 17.6 & 16.9 \\ L-11 & 10.0 & 25.7 & 34.6 & 23.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The relative error between real model parameter and predicted model parameter from the first neural network for model identification after training 10 million data. Figure 6: Response graphs with the changes as tuning was repeated when \(m=187.77\) kg, \(k=318.47\) N/m, and \(c=88.65\) N-s/m. The advantages of using a neural network to identify the system are quick tuning of PID parameters and creation of learning data. Except for the reinforcement learning method, all other learning methods require optimal PID parameters to predict the subsequent parameters from the response. The methods using AI demonstrate high accuracy after learning multiple cases of predicting the optimal parameters and the response corresponding to each system with different \(m\), \(k\), and \(c\) values. Therefore, researchers must be able to identify multiple cases for predicting the optimal PID parameters for multiple cases of response of the random system to create learning data. However, there was no need to identify the optimal PID values for multiple cases of response from multiple cases of systems when one AI system identified the system from the response and another AI system identified the optimal PID parameters for the system.