## 4 Experimental Study
We utilized MATLAB's Data Statistics Tool, which can access experimental data from the window of the figure to compute the various errors. Despite these practical challenges, the trends observed in the experiments largely align with those seen in the simulations. The Syn-TDE-PID strategy exhibited AATEs of \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Errors** & **Syn-TDE-PID** & **Syn-TDE-SMC** & **Syn-TDE-NFTSMC** \\ \hline \(e_{s_{1}}\) (mm) & 0.24 & 0.134 & 0.06 \\ \(e_{s_{2}}\) (mm) & 0.32 & 0.19 & 0.15 \\ \(e_{c_{1}}\) (mm) & 0.77 & 0.21 & 0.2 \\ \(e_{c_{2}}\) (mm) & 0.91 & 0.49 & 0.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The absolute average synchronization errors (AASE) and cross-coupling errors (AACE) of the control schemes used in the experimental study, computed by MATLAB. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**AAEE** & **Syn-TDE-PID** & **Syn-TDE-SMC** & **Syn-TDE-NFTSMC** \\ \hline \(e_{est_{1}}\) (Nm) & 0.03 & 0.01 & 0.017 \\ \(e_{est_{2}}\) (Nm) & 0.002 & 0.0006 & 0.0006 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The absolute average estimation errors (AAEE) of the Syn-TDE-NFTSMC scheme computed by MATLAB. Figure 9: The control input signals of the control schemes of Joint 1 and Joint 2 in the experimental study. 0.7 mm and 0.8 mm for Joint 1 and Joint 2, respectively. In comparison, the Syn-TDE-SMC and Syn-TDE-NFTSMC strategies demonstrated notable improvements, with errors of 0.127 mm and 0.129 mm for both joints. These experimental results further confirm that the control scheme outperformed the other existing approaches in terms of synchronization and control performance, achieving a reduction of up to 81% in maximum tracking error relative to the Syn-TDE-PID controller for Joint 1. The experimental results demonstrate that the Syn-TDE-NFTSMC controller is the most effective in reducing tracking errors in real-world applications, followed closely by Syn-TDE-SMC. In the experimental setup, the trends observed in the simulation remain consistent, although the AASEs and AACEs are higher. Regarding synchronization errors, the Syn-TDE-PID controller shows the highest AASEs, with values of 0.24 mm and 0.32 mm for Joint 1 and Joint 2, respectively. In contrast, Syn-TDE-SMC and Syn-TDE-NFTSMC show smaller AASEs, with Syn-TDE-SMC having values of 0.134 mm and 0.19 mm, while Syn-TDE-NFTSMC delivers the best performance, with AASEs of 0.06 mm and 0.15 mm. The same trend is observed for AACEs, as shown in Table 6, where Syn-TDE-NFTSMC outperforms the other controllers. These results indicate that Syn-TDE-NFTSMC provides the most effective performance overall, minimizing both synchronization and cross-coupling errors in both simulation and experimental scenarios. Table 7 presents the AAEE of the Syn-TDE-PID, Syn-TDE-SMC, and Syn-TDE-NFTSMC controllers in the experimental setup. In the simulation, the AAEE values remain identical across all three controllers, measuring 0.0177 Nm for Joint 1 and 0.0172 Nm for Joint 2. However, the experimental results show some variation compared to the simulation. Syn-TDE-PID exhibits the highest estimation error at 0.03 Nm, whereas Syn-TDE-SMC and Syn-TDE-NFTSMC achieve significantly lower errors of 0.01 Nm and 0.017 Nm, respectively, for Joint 1. A similar trend is observed for Joint 2 across all three control schemes. This indicates that, in the experimental study, Syn-TDE-SMC and Syn-TDE-NFTSMC provide more accurate estimation compared to Syn-TDE-PID. In summary, the results demonstrate that the newly developed control scheme Syn-TDE-NFTSMC surpassed the performance of existing control schemes, as confirmed by comprehensive simulations and experimental validation on a 2-DOF CKCM. As expected, the experimental results show slightly higher tracking errors than those of the simulation, primarily due to experimental conditions and real-world factors, such as sensor noise, environmental disturbances, actuator backlash, and mechanical compliance.