## 4 Experimental Verification
### Tracking Performance  
In this section, three different input signals are used to compare the tracking performance of the proposed composite control method and the traditional composite control method:  
1. Tracking performance under a single-frequency signal: We input a 100 Hz sinusoidal signal as the reference trajectory for the FSM, and Figure 14 shows the tracking results. From Figure 14a-c, it can be seen that the proposed composite control method exhibits higher tracking accuracy and smaller tracking errors. Compared with the traditional composite control method, the NME is reduced by 78.6%, and the NRMSE is decreased by 86.16%. Additionally, Figure 14d shows that the proposed composite control method maintains high linearity, indicating its superiority over the traditional composite control method in tracking a single-frequency signal and proving its good tracking performance. 2. Tracking performance under a decreasing signal: A signal with a frequency of 100 Hz and decreasing amplitude is generated to verify the performance of the proposed composite control method, with the tracking results shown in Figure 15. The experimental results demonstrate that the proposed composite control method achieves better tracking performance compared with the traditional composite control method. Specifically, the NME and NRMSE values are reduced by 62.11% and 60.54%, respectively. 3. Tracking performance under a multi-frequency signal: We construct a multi-frequency signal \(v(t)=50-35.3\sin(40\pi t)-19.6\sin(120\pi t)-19.6\sin(200\pi t)\) containing fre  
Figure 13: Hysteresis curves at different frequencies. quency components of 20 Hz, 60 Hz, and 100 Hz to verify the tracking ability of both methods for complex signals. The results shown in Figure 16 indicate that the proposed composite control method has better tracking ability. Numerically, compared with the traditional composite control method, the NME and NRMSE values are reduced by 48.66% and 43.14%, respectively. The tracking errors of both methods under the three test signals are detailed in Table 4.  
Figure 14: Compensation results of proposed composite control method and traditional composite control method for single-frequency input signal: (**a**) tracking curves; (**b**) enlarged view of tracking curves; (**c**) tracking errors; (**d**) hysteresis curves. Figure 15: Compensation results of proposed composite control method and traditional composite control method for single-frequency decreasing input signal: (**a**) tracking curves; (**b**) tracking errors. From the aforementioned experimental results, it is evident that the proposed composite control method exhibits superior tracking performance compared with the traditional composite control method. This further validates the effectiveness and feasibility of introducing a rate correction term into the feedforward compensator. In addition, to test the tracking ability of the proposed method for dual-axis spiral scanning signals, a spiral scanning motion [2] simultaneously conducted along the \(x\)- and \(y\)-axes within a range of \(-1\) to \(1\) mrad is employed. The tracking results shown in Figure 17 demonstrate that the proposed composite control method tracks the expected motion of dual-axis spiral scanning very well. Although the proposed composite control method is designed as shown in Figure 6, in practical applications, a second-order filter needs to be connected in series after the rate correction term. The purpose of doing so is to suppress the peak of the amplitude-frequency characteristic curve across the entire closed-loop bandwidth range and minimize the impact on the system phase within the range of interest. The expression for this filter is \(N(s)=1/\left(3.23\times 10^{-7}s^{2}+9.1\times 10^{-4}s+1\right)\), and the discretization operation is employed during the specific experimental process.