# Robot Joint Vibration Suppression Method Based on Improved ADRC
## 5 Conclusions  
This article proposes a novel vibration suppression strategy, which successfully extracts vibration disturbance signals by accurately measuring the angle error values of robot joints, conducting in-depth analysis of the reducer model, and redesigning the ESO. These disturbance signals are then introduced into the speed loop controller of the PMSM, effectively reducing the fluctuation of the robot joint angle error values. The experimental results have verified the feasibility and effectiveness of this method, significantly reducing the vibration level of the robot and providing a new type of technical support for precise control of the robot.  
As an advanced control method that does not rely on an accurate system model and can actively estimate and compensate for disturbances, ADRC demonstrates unique theoretical value and application potential in the field of robot vibration suppression. In response to the challenge of precisely modeling the complex disturbances in robot systems, such as nonlinearity, flexibility deformation, and external interferences, this article employs a unified framework of \"total disturbance\". Through the ESO, the unmodeled dynamics, nonlinear coupling effects, and external disturbances are regarded as external state variables of the system and are estimated and dynamically compensated for in  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Algorithm** & **Vector Control** & **ADRC** \\ \hline Robot trajectory speed & 300 mm/s & 400 mm/s \\ Fluctuations during trajectory deceleration & \(\pm\)11 mm/s & \(\pm\)4 mm/s \\ Joint PMSM speed fluctuation & \(\pm\)12 rpm & \(\pm\)5 rpm \\ Joint angle error \(\theta_{el}(t)\) & \(\pm\)28 arcseconds & \(\pm\)13 arcseconds \\ Amplitude & 0.322 mm & 0.311 mm \\ Vibration velocity & 8.32 mm/s & 6.86 mm/s \\ Vibration acceleration & 1.19 m/s\({}^{2}\) & 0.52 m/s\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of control results for robots running at 300 mm/s speed.  
real time. The core advantage of this approach is breaking through the dependence of traditional control methods on high-precision dynamic models. Even in the presence of parametric uncertainties and time-varying characteristics in the system, the ESO can still effectively track the changes in disturbances, thereby significantly enhancing the robustness of vibration suppression. Experimental and theoretical studies have shown that ADRC is widely applicable to nonlinear and time-varying robot systems and provides an effective solution for vibration suppression across different speed scenarios.  
The adjustment of the ADRC parameters used in this study is rather difficult. A great deal of effort was spent on the experiment to adjust the ADRC parameters. Currently, these parameters are attempted to be adjusted based on the author's personal practical experience, which is also the difficulty in the promotion of ADRC theory.  
The next research work of this paper will focus on the combination of artificial intelligence and ADRC, adopting a machine learning algorithm to enable the robot joint to automatically find the optimal parameters of ADRC.  
G.W. Conceptualization, data curation, validation, writing--original draft. S.F. Funding acquisition, investigation, visualization. Q.X.: Writing--review and editing. All authors have read and agreed to the published version of the manuscript.  
This research was funded in part by the special fund of Jiangsu Province for the transformation of scientific and technological achievements under Grant No. BA2023048.  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare that they have no known competing financial interests or personal relationships that may have appeared to influence the work reported in this study.