## 4 Experiments and Analysis
### The Simulation Experiment  
To verify the effectiveness of the high stiffness constant damping control algorithm, a comparative experiment was conducted between the traditional three-loop feedback controller and the CDHS controller using a typical excitation signal for fast track applications in orbit. The joint servo system was set to a sinusoidal signal with a frequency of 0.05 Hz and an amplitude of 0.1 rad, while the load inertia signal was set to a sinusoidal signal with a frequency of 0.01 Hz and an amplitude of 100 kg\(\cdot\)m\({}^{2}\).  
The position command tracking curve and position tracking error curve obtained using the traditional three-loop feedback controller are presented in Figures 6 and 7, respectively. The curves indicate the occurrence of flexible vibration when the algorithm is used to control the flexible joint to track the sinusoidal position command signal, particularly at the peak and trough of the signal. Notably, the algorithm fails to adapt to changes in joint stiffness. Additionally, the position tracking error curve reveals that the error in joint position at different times, such as 30 s and 50 s, is inconsistent. This indicates that the command tracking error is not solely dependent on the joint position but is also influenced by the load inertia, with the maximum error being \(\pm\)1.5\({}^{\circ}\).  
position tracking error is also similar to a sinusoidal waveform, and the tracking error peak appears at the peak and trough commutation moments of the position command.  
Figures 10 and 11 depict the flexible deformation curves of the joint reducer under the traditional three-loop feedback controller and CDHS controller, respectively. The curves indicate that the joint harmonic reducer is significantly affected by changes in load inertia under the three-loop feedback controller, resulting in noticeable fluctuations and a maximum deformation of \(\pm 0.05^{\circ}\). Conversely, the maximum deformation of the joint harmonic reducer under the CDHS controller is only \(\pm 0.004^{\circ}\), which is not comparable to the three-loop feedback controller; rather, it is reduced by an order of magnitude. This demonstrates the CDHS controller's ability to achieve smooth transmission of the reducer under variable load conditions.  
Figure 6: Joint position command tracking curve using traditional three-loop feedback controller.  
Figure 7: Joint position tracking error curve using traditional three-loop feedback controller.  
Table 2 shows the statistics on the joint position tracking error and flexible deformation of the reducer as key indicators for evaluating the performance of the controller. The results show a big improvement in both indicators with the CDHS controller compared to the three-loop feedback controller. Specifically, the joint tracking error is reduced by 73.1% and the flexible deformation of the reducer is reduced by 97.9%. These results indicate that the CDHS controller improves the control accuracy and robustness of the joint system, particularly under variable load conditions.  
Figure 8: Joint position command tracking curve using CDHS controller.  
Figure 9: Joint position tracking error curve using CDHS controller.