## 5 Experimental Results
### PMSM Motion Control Experiment  
This study used 1.5 kW commercialized PMSM packs for the motion control experiment, as shown in Figure 7. The PMSM has a rated speed and torque of 2000 rpm and 7.16 Nm, respectively. In addition, the PMSM is coupled to a 23-bit absolute optical encoder that can measure the rotating angular position of the PMSM. This study identified the moment of inertia and the friction parameters of the PMSM through a constant speed experiment and estimation experiment [28]. Table 1 shows the identification results. Figure 8 shows the experimental results of 11 cycles of the helical path. The vertical axis is the RMS of the contour error, and the horizontal axis is the cycle number of the helical path. Since the PMSM does not significantly suffer from external disturbances, for the results of the PMSM-PPIC, the AVG of the RMS variation is 0.129 rad with an SD of \(6.1811\times 10^{-5}\) rad; hence, the ratio between the SD and AVG is 0.48%. Accordingly, the RMS contour error of the PMSM-PPIC is almost unchanged in each cycle of the helical path. Similarly, the RMS contour error is almost unchanged because the PMSM-DC does not perform cycle learning. The AVG of the RMS variation is 0.0012 rad with an SD of \(8.4230\times 10^{-6}\) rad so that the ratio of the SD and AVG is 0.69%. Nevertheless, compared with the PMSM-PPIC, the contour errors of the PMSM-DC were significantly reduced, and the AVG of the RMS variation achieves a rate of reduction of 90.48%. The PCB-ILCC can further reduce the RMS contour errors through cycle learning. Figure 8 shows that, after using the PCB-ILCC, the RMS contour error starts to converge at the fourth cycle; the RMS contour error is reduced from 0.0012 rad (the first cycle) to \(5.2681\times 10^{-4}\) rad (the elevent \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **X-Axis** & **Y-Axis** & **Z-Axis** \\ \hline Moment of inertia (kg\(\cdot\)m\({}^{2}\)) & 0.0016 & 0.0015 & 0.0015 \\ Viscous friction coefficient (Nm/rad/s) & 0.0074 & 0.0071 & 0.0064 \\ Static friction torque (Nm) & 0.1037 & 0.1043 & 0.1079 \\ Coulomb friction torque (Nm) & 0.0890 & 0.0916 & 0.0929 \\ Stribeck velocity (rad/s) & 0.2588 & 0.3146 & 0.3406 \\ Stribeck shape factor & 1.5302 & 1.7817 & 1.5339 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: PMSM parameters of the testbench. Figure 7: Testbench with PMSM packs used in the motion control experiment. Figure 9 shows the magnitude of the CEVs in the last cycle (the eleventh cycle) of Figure 8. Figure 10 compares the different control structures in the AVG, RMS, and MAX errors. The experimental results show that, compared with the PMSM-PPIC, the PMSM-DC significantly reduces contour errors, and the PCB-ILCC can further reduce contour errors. The AVG, RMS, and MAX errors for the PMSM-PPIC are 0.0117, 0.0129, and 0.0314 rad, respectively. As the PMSM-PPIC is susceptible to the influence of PMSM motion dynamics and friction disturbances, the contour errors using the PMSM-PPIC vary considerably. However, because the PMSM-DC and PCB-ILCC use the PMSM driving control developed in this study, which can not only compensate for the PMSM motion dynamics and friction disturbances but can also provide robust performance to PMSM motions, the PMSM-DC and PCB-ILCC have robust control results and small contour errors compared with the PMSM-PPIC. For the PMSM-DC, the AVG error is reduced to 0.0011 rad at a rate of reduction of 90.74%, the RMS error is reduced to 0.0012 rad at a rate of reduction of 90.50%, and the MAX error is reduced to 0.0031 rad at a rate of reduction of 90.18%. Although the PMSM-DC can mitigate the adverse influence of external disturbances, few contour errors remain. Since external disturbances can repeatedly act on the PMSM while performing cycle motions along the helical path, the PCB-ILCC helps reduce contour errors. Compared with the PMSM-PPIC, the rate of reduction of the AVG, RMS, and MAX errors are 96.27%, 95.92%, and 94.76%, respectively.