## 4 Experiments and Analysis
### Physical Experiment  
In order to further validate the effectiveness of the control strategy, a physical test platform was constructed, as shown in Figure 12. The platform was used to simulate  
Figure 11: The flexible deformation of harmonic reducer using CDHS controller.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Controller Method** & **Maximum Error\({}^{\circ}\)** & **Average Error\({}^{\circ}\)** & **Error Reduction Rate** & **Maximum Deformation Rate** & **Average Deformation Deformation Deformation Deformation Rate** & **Flexible Vibration Rate** & **Flexible Vibration** \\ \hline Three-loop & \(\pm\)1.5 & 0.606 & 1 & \(\pm\)0.05 & 0.019 & 1 & Exist \\ CDHS & \(\pm\)0.5 & 0.163 & 73.1\% & \(\pm\)0.004 & 0.0004 & 97.9\% & None \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of key indicators resulting from three-loop and CDHS controllers.  
Figure 10: The flexible deformation of harmonic reducer using three-loop feedback controller.  
flexible joints controlling the displacement of large inertia target loads, with an inertia of about 100 kg\(\cdot\)m\({}^{2}\). The joint driver utilized Altera's FPGA A3 PE300 as the core computing unit, which allowed for efficient operation of the algorithm through the parallel computing capability of the FPGA. The host computer sent continuous position commands with a period of 16 ms to the joint driver through the CAN bus. The joint driver then controlled the compliant joint to drive the simulated load to track the position command. The photoelectric encoder located between the joint and the load recorded the position response curve of the joint output.  
The joint position control performance of the three-loop feedback controller and the CDHS controller was compared on a physical test platform. The controllers were configured with the same control parameters and tested on the joint's range of motion from \(-135^{\circ}\) to \(-125^{\circ}\), with varying speeds. The highest speed was reached at 40 s, followed by a gradual reduction in speed until the joint stopped. The joint driver recorded the position tracking curves and error curves for both controllers. Figures 13-16 show the results for different controller and speed configurations.  
Figure 14: Physical joint position tracking error curve using three-loop feedback controller.  
Figure 12: Flexible joint experiment platform.  
Figure 13: Physical joint position command tracking curve using three-loop feedback controller.  
The position tracking curve indicates that the tracking error of the three-loop feedback controller is larger than that of the CDHS controller. When the three-loop feedback controller is in operation, the average errors in the high-speed and low-speed sections are 0.7\({}^{\circ}\) and 0.5\({}^{\circ}\), respectively. In contrast, the CDHS controller operating in the high-speed and low-speed sections has average errors of 0.08\({}^{\circ}\) and 0.05\({}^{\circ}\), respectively. The position command tracking errors of the CDHS controller in the high-speed section and low-speed section are reduced by 88.6% and 90%, respectively, compared to the three-loop feedback controller.