# Research on Bandwidth Improvement of Fine Tracking Control System in Space Laser Communication
## 3 Results
### Dynamic Target Tracking Experiment  
Based on the experimental platform of the fine tracking control system, this paper conducted a dynamic target tracking experiment to verify the impact of feedforward control on the system's tracking performance. Disturbance signals with an amplitude of \(\pm 400\)\(\upmu\)rad and a frequency range of 1 Hz to 200 Hz were generated with the disturbance FSM. Miss distance data were collected with the CCD camera. Subsequently, the PZT FSM was controlled to track the target for the purpose of suppressing disturbances.  
In this dynamic target tracking experiment, we also compared three control methods: single-PID feedback control, the compound control which combines P-I model feedforward control and PID feedback control, and the compound control which combines P-I rate-dependent model feedforward control and PID feedback control.  
First, this paper tested the nonlinearity of the input and output of the PZT FSM for the above three control methods, and the results are shown in Figure 17.  
Figure 16: The optical path of the experimental platform.  
Figure 15: Experiment platform.  
After calculating the nonlinearity, it was found that when the input signal frequency is 1 Hz, the nonlinearity finally decreases from 11.17% to 5.75%. When the input signal frequency is 30 Hz, the nonlinearity finally decreases from 31.66% to 6.13%. When the input signal frequency is 50 Hz, the nonlinearity finally decreases from 41.57% to 7.21%. It can be observed that feedforward control effectively reduces the nonlinearity of the PZT FSM while enhancing the response speed of the fine tracking system.  
Next, this paper collected the tracking errors of the three control methods using the CCD camera and compared them with the disturbance signals. The comparison results are shown in Figure 18.  
The test data at each frequency were transformed into the frequency domain and analyzed to determine the system's error suppression bandwidth for the three control methods. The results are shown in Figure 19.  
According to the experimental results, the error suppression bandwidth of the single-PID feedback control system is approximately 40.3 Hz. When adding feedforward compensation based on the P-I model, the error suppression bandwidth is approximately 47.2 Hz. When adding feedforward compensation based on the P-I rate-dependent model, the error suppression bandwidth is approximately 57 Hz. This represents an improvement of about 41.71%. The comparison of experimental results and simulation results is shown in Table 3. Due to the influence of experimental conditions and other factors, the system's error suppression bandwidth in the experimental test is lower compared to the simulation results. However, the relative improvement effect is consistent with the simulation results.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Control Methods**} & **Simulation** & **Experimental** \\  & **Results** & **Results** \\ \hline PID & 48.7 Hz & 40.3 Hz \\ PI + PID & 57.5 Hz & 47.2 Hz \\ (R-D)PI + PID & 69.6 Hz & 57 Hz \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparison of simulation results and experimental results of error suppression bandwidth of the fine tracking system.  
Figure 17: The results of nonlinear testing. (**a**) 1 Hz, (**b**) 20 Hz, (**c**) 30 Hz, (**d**) 50 Hz.  
Consequently, suppressing the disturbance caused by hysteresis can improve the error suppression ability of the fine tracking system.