## 5 Experimental Verification
### Experimental Results
#### 5.3.5 Disturbance Rejecting Testing  
In order to verify the anti-disturbance performance of the proposed controller, a periodic multi-frequency disturbance, as shown in Figure 10, was set up during the experiment to simulate the impact of a periodic disturbance, such as spindle vibration and cutting force, on the machining process of the piezoelectric-driven FTS system. The amplitude of the set disturbance signal is much larger than the actual disturbance to the system during the machining process, which is enough to represent the actual disturbance.  
\begin{table}
\begin{tabular}{c c c} \hline
**Controller** & **ASMC** & **ILC-ASMC** \\ \hline \(e_{max}\) (nm) & 987.91 & 268.87 \\ Percentage error & 4.94\% & 1.34\% \\ \hline \(e_{rms}\) (nm) & 338.77 & 120.76 \\ Percentage error & 1.69\% & 0.60\% \\ \hline \end{tabular}
\end{table}
Table 2: Controller performance comparison under 1N load.  
Figure 8: ILC-ASMC tracking error distribution at the 2 nd, 4 th, 6 th, 8 th, and 10 th iterations.  
In Figure 11, after the 10 th iteration, the trajectory output by the system can already approximately track the desired trajectory. It can be seen that the trajectory tracking control goal has been successfully achieved with high-precision control accuracy, strong anti-interference ability, and excellent dynamic response performance. It shows that the ILC-ASMC control strategy proposed in this article is feasible and effective.  
Figure 10: Experimental input disturbance.  
Figure 9: ASMC and ILC-ASMC tracking results of sinusoidal trajectory at 40 Hz with 1N.  
As shown in Figure 12, it intuitively reflects the trend of the position tracking error decreasing with the iteration number. In the presence of external disturbance, the tracking error of the piezoelectric-driven FTS system based on the exponential convergence ILC-ASMC control strategy has oscillation in the initial iteration. After 10 iterations, the post-tracking error is small enough, indicating that the composite control has good anti-disturbance and convergence properties. Experiments have proven that the improved iterative learning algorithm has a faster convergence speed and shows stronger robustness and stability.  
Figure 11: ILC-ASMC tracking results of sinusoidal trajectory at 40 Hz with input disturbance.  
Figure 12: Tracking error changes with the iteration number.  
Considering the above experimental results, the control method proposed in this paper effectively improves the tracking accuracy during the machining process and enhances the system's resistance to external disturbances compared to traditional fast tool servo control methods. This improves the processing quality of the fast tool servo system in micro-nano array structures represented by microlenses. In addition, it is worth noting that due to the optimization of the control method, the response speed and stability of the system have been improved, which has improved the processing efficiency, shortened the processing cycle, and saved the energy consumption of the fast tool servo system in the processing process to a certain extent. It has likewise improved energy utilization, is more energy-saving, and has realized green processing. In summary, the proposed control method not only enhances the machining quality and precision of fast tool servo systems but also improves processing efficiency and provides important support for the improvement of actual processing processes.