# 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
Specifically, when using the vector control algorithm, the fluctuation range of \(\theta_{e1}(t)\) is plus or minus 25 arcseconds, as shown in Figure 14a. After applying the ADRC algorithm, the fluctuation range of \(\theta_{e1}(t)\) was significantly reduced to plus or minus 9 arcseconds, as shown in Figure 14b. This comparison result demonstrates the superiority of the ADRC algorithm in reducing angle error fluctuations. The vibration data are listed in Table 2 for further analysis and research. Figure 17 shows the angle error \(\theta_{e1}(t)\) waveform exhibited by the robot joints under the condition that the robot trajectory running speed is set to 300 mm/s. The data are summarized in Table 3.  
Figure 15: Velocity waveform of 300 mm/s trajectory. (**a**) Robot trajectory waveform using vector control algorithm. (**b**) Local diagram of trajectory waveform using vector control algorithm. (**c**) Robot trajectory waveform using ADRC algorithm. (**d**) Local waveform of trajectory using ADRC algorithm. Figure 16: PMSM velocity waveform of robot moving at a speed of 300 mm/s. (**a**) PMSM speed waveform using vector control algorithm. (**b**) PMSM speed waveform using ADRC algorithm. The red line is the reference speed and the black line is the actual speed. Figure 17: Waveform of robot moving at a speed of 300 mm/s. (**a**) Angle error value using vector control algorithm. (**b**) Angle error value using ADRC algorithm. Through the optimization of the ADRC algorithm and the summarization of the experimental data, the following results can be obtained: The fluctuation values of the robot trajectory speed, joint speed, and joint angle error can be reduced to a maximum of 20.0%, 53.3%, and 35.3% of their original values, respectively. The vibration indicators of robot joints, such as the amplitude, vibration velocity, and vibration acceleration, can be reduced to a maximum of 30.9%, 23.4%, and 24.6% of their original values, respectively. Compared with the traditional FOC algorithm, ADRC exhibits significant advantages. In the field of robot vibration suppression, traditional control methods and emerging algorithms each have their own characteristics. Theories such as input shaping algorithms, model predictive control, modeling based on the finite element method, and online gravity compensation all require the establishment of precise mathematical models. However, in robot control, the presence of nonlinear factors and time-varying disturbances within the system suppresses the effectiveness of precise model-based control. The ADRC vibration suppression method, by employing the ESO to regard internal nonlinear variations and external disturbances as a \"total disturbance\" and compensate for it in real time, does not rely on high-precision models. Nevertheless, adjusting the parameters of ADRC is relatively challenging and depends on experience or trial-and-error methods. When the application scenarios of robots vary, parameters need to be adjusted online, and currently, there is a lack of a systematic adaptive mechanism. This is also a difficulty in promoting ADRC theory. The next step of this research will be dedicated to the integration of artificial intelligence with ADRC, adopting machine learning algorithms to enable robot joints to automatically search for the optimal parameters of ADRC.