## 6 Conclusions  
This paper presents the application of active disturbance rejection control (ADRC) to the control of permanent magnet synchronous motors (PMSMs). It proposes a compound control method that integrates active disturbance rejection with radial basis function (RBF) neural networks and feedforward control. The active disturbance rejection controller is incorporated into the servo system of the PMSM, achieving position control through a second-order nonlinear active disturbance rejection controller. Additionally, the radial basis neural network adaptively compensates for and adjusts the extended state observer within the controller, enhancing the system's capability to withstand load disturbances and improving the positioning accuracy. The simulation and experimental results show that the RBF-ADRC controller outperforms the conventional ADRC controller in terms of positioning, load convergence, and error management. The performance comparison tables (Tables 5 and 6) clearly illustrate these differences. Furthermore, the FRBF-ADRC controller surpasses the RBF-ADRC controller in terms of its overall performance. Figure 18: Step signal position curve in the experiment. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Signal Setting** & **ADRC** & **RBF-ADRC** & **FRBF-ADRC** \\ \hline Step signal rapidity & 0.0429 s & 0.0339 s & 0.0189 s \\ Sudden load convergence & poor & mezzo & good \\ Given the sinusoidal signal & 0.0196 rad & 0.0173 rad & 0.0043 rad \\ error \(\mid\)Emax\(\mid\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: A comparison of simulations for ADRC, RBF-ADRC, and FRBF-ADRC controllers. This study has successfully achieved high precision and stability in controlling a permanent magnet synchronous motor by integrating a radial basis function (RBF) neural network with feedforward control and an active disturbance rejection control (ADRC) strategy. Notably, the FRBF-ADRC controller enhances the motor's ability to resist interference and improves its dynamic response speed under disturbances, such as load changes and fluctuations in the position curve. Secondly, the performance of the neural network parameter adjustment involved in this paper is affected by the training data. If the training data are not sufficient or there is a deviation, this may lead to a decrease in the control performance. In addition, there is still a lot of room for improvement in the parameter tuning of the active disturbance rejection controller and its immunity under multiple operating conditions. Finally, because of the limitations of this study, the following directions are worthy of more in-depth study, as follows:  
1. To improve the learning ability and generalization ability of neural network controllers, the structure and parameters of the RBF neural network are worth further study and optimization, or a more advanced neural network could be used for the research;
2. In terms of the improvement in the auto disturbance rejection controller, an auto disturbance rejection controller with linear and nonlinear switching could be introduced, combining a switching controller, the neural network method, and feedforward control to maximize the advantages of auto disturbance rejection;
3. The active disturbance rejection controller could be combined with advanced methods other than neural networks from the perspective of a composite control strategy, such as active disturbance rejection control and deep learning, particle swarm optimization, etc. Conceptualization, Q.Z., H.G. and Y.Z. ; Methodology, Q.Z. ; Software, W.L. ; Formal analysis, W.L. and Y.C. ; Investigation, W.L. and K.X. ; Resources, W.L. ; Data curation, W.L. ; Writing--original draft, W.L. ; Writing--review & editing, Q.Z., W.L., Y.C., K.X., H.G. and Y.Z. ; Supervision, Q.Z., Y.C., K.X., H.G. and Y.Z. ; Funding acquisition, Q.Z. All authors have read and agreed to the published version of the manuscript.