# Robot Joint Vibration Suppression Method Based on Improved ADRC
## 4 Comparison and Analysis of Experimental Results
### Experimental Setup and Methods
#### 4.1.2 Experimental Results and Analysis  
The vibration of robot motion trajectory is usually caused by the velocity fluctuation of one of the joints. During the experiment, six joints of the robot were made to work together to move along a straight path, and the following data were recorded for comparison and reference:  
1. Robot trajectory jitter waveform. 2. Velocity waveform of robot joint module PMSM. 3. \(\theta_{e1}(t)\) data waveform. 4. The vibration peak data read by the vibrometer. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Item** & **Parameters** & **Unit** \\ \hline Rated speed & 1500 & rpm \\ Rated current & 19.4 & A \\ Rated torque & 3.32 & N\textasci{}m \\ Phase resistance & 0.25 & ohms \\ Phase inductance & 4.9 & mH \\ Back electromotive force & 13.6 & Vrms/krpm \\ Encoder resolution & 20 & bit \\ Harmonic reducer transmission ratio & 1:81 & \\ Rated torque of harmonic reducer & 107 & N\textasci{}m \\ Peak torque of harmonic reducer & 169 & N\textasci{}m \\ Positioning accuracy & 25 & arcseconds \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Joint parameter. Figure 11: Laser tracker and vibrometer. Figure 10: Collaborative robot for testing. The rationality of vibration suppression is verified by controlling the fluctuation value of \(\theta_{\epsilon 1}(t)\) through these four related data. It was found that the velocity fluctuation of the second joint was significantly higher than that of the other five joints. Therefore, this experiment will focus on comparing and analyzing the vibration data of the second joint. In order to investigate the influence of different trajectory velocities on vibration, two trajectory velocities were selected to compare the effects of adding the ADRC algorithm, namely 50 mm/s and 300 mm/s. Experimental results of 50 mm/s  
Figure 12 shows the speed fluctuation of the robot trajectory running at a speed of 50 mm/s. The horizontal axis in the figure represents the time coordinate in seconds, and the vertical axis represents the velocity value of the trajectory captured by the laser tracker in millimeters per second. Figure 12: Cont. As shown in Figure 12a,b, when using the vector control algorithm, the maximum trajectory velocity fluctuation occurs during the transition of the robot from uniform speed to deceleration, with a trajectory fluctuation value of plus or minus 20 mm/s. Figure 12c,d show the significant improvement in trajectory fluctuations of the robot joint module after applying the ADRC algorithm, with the fluctuation amplitude successfully reduced to plus or minus 5 mm/s. These data clearly reflect the effectiveness of the ADRC algorithm in improving robot motion stability. Figure 13 shows the PMSM velocity waveform of the second joint when the robot trajectory speed is set to 50 mm/s. The red line in the waveform corresponds to the speed setting value of the PMSM, while the green line reflects the actual speed value of the PMSM. When the robot performs linear motion at a speed of 50 mm/s, if the vector control algorithm is used, the speed fluctuation range of the PMSM is plus or minus 11 revolutions per minute, as shown in Figure 13a. After applying the ADRC algorithm, the speed fluctuation significantly decreased to plus or minus 5 revolutions per minute, as shown in Figure 13b. Figure 12: Velocity waveform of 50 mm/s trajectory. (**a**) Trajectory waveform using vector control algorithm. (**b**) Local waveform diagram of trajectory using vector control algorithm. (**c**) Robot trajectory waveform using ADRC algorithm. (**d**) Local waveform of trajectory using ADRC algorithm. Figure 13: PMSM velocity waveform of robot moving at a speed of 50 mm/s. (**a**) PMSM speed waveform using vector control algorithm. (**b**) PMSM speed waveform using ADRC algorithm. Figure 14 shows the angle error \(\theta_{e1}(t)\) waveform exhibited by the second joint of the robot under the condition that the robot trajectory running speed is set to 50 mm/s.