# Iterative Learning Control for Vibration Suppression of a Robotic Arm
## 5 Conclusions  
In this paper, two topics are emphasized. One is the vibration signal analysis, and the other is vibration suppression. Elastic-joint dynamics is introduced to understand the reason for the vibration of the six-axis manipulator and eliminate the vibration through an effective control method. Vibration usually occurs when the arm moves rapidly to a fixed point, and the vibration signal contains a wealth of information. A method of VMD-HHT is proposed to analyze the vibration signals and provide effective information for subsequent vibration control to extract useful information and vibration features from vibration signals. Smooth trajectory planning can suppress part of the residual vibration caused by the system. According to the algorithm of elastic-joint dynamics, a smooth trajectory planning method is first used to eliminate the residual vibration, and then the feedback controller and iterative learning controller are used to control the vibration. In addition, information from past learning is added to the traditional ILC controller, and the method of ILC-VMD is proposed, which uses a signal processing method to separate useless information so that the ILC can learn more quickly how to compensate for the error caused by vibration. Finally, the proposed vibration control algorithm is verified by simulations and experiments, and the results are satisfactory.  
A VH-ILC-EJ controller has been presented for the vibration suppression of a robotic arm. The VMD-HHT method extracts the vibration signal features and feeds the information into the ILC-EJ controller. As demonstrated numerically, the VH-ILC-ET method has better vibration suppression than when only considering the elastic-joint dynamics. Moreover, the VH-ILC-ET method is applied in a laboratory-developed 6-DOF robotic arm. The results show that the ILC method is valid for vibration suppression, and the VMD-HHT improves the error's convergence rates and L2 norm. Overall, the VH-ILC-EJ method is effective in the vibration suppression of a robotic arm. In the future, some new methods will be applied to the robotic arm for vibration suppression.  
Conceptualization, H.-P.H.; methodology, H.-P.H. and J.-L.L.; software, J.-L.L.; validation, J.-L.L.; formal analysis, J.-L.L.; investigation, J.-L.L.; resources, H.-P.H. and C.-Y.L.; data curation, J.-L.L. and C.-Y.L.; writing--original draft preparation, J.-L.L.; writing--review and editing, C.-Y.L.; visualization, J.-L.L.; supervision, H.-P.H.; project administration, H.-P.H.; funding acquisition, H.-P.H. All authors have read and agreed to the published version of the manuscript.  
This work was supported in part by the National Science and Technology Council, Taiwan, under grant number 110-2221-E-002-110-MY3 and in part by Syntec Technology Co., Ltd., under Grant TLIR-S200.  
Not applicable.  
The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Iteration No.**} & \multicolumn{3}{c}{**Joint No. (Unit: rad)**} \\ \cline{2-4}  & & **1** & **2** \\ \hline Maximum & 1 & 0.859 & 0.034 \\ \cline{2-4} Error & 20 & 0.031 & 0.016 \\ \hline L2 norm & 1 & 0.956 & 0.558 \\ \cline{2-4} Error & 20 & 0.501 & 0.398 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Maximum tracking error and L2 norm of the error of an input-based ILC in experiments.