## 4 Results & Discussion  
The scanning trajectory and scanning error curve are as shown in Figures 12 and 13. \begin{table}
\begin{tabular}{c c} \hline
**Name** & **PTN-1 Metal Grating Angle Encoder** \\ \hline
**Communication protocol** & BiSS-C \\ \hline
**Absolute bit count** & 21 bit-28 bit \\ \hline
**Supply voltage** & 5 \(\pm\) 0.5 V \\ \hline
**Electrical rated speed** & 300–2100 r/min \\ \hline
**Working current** & \(\leq\)350 mA \\ \hline
**Working temperature** & \(-\)40–75 \({}^{\circ}\)C \\ \hline
**Storage temperature** & \(-\)55–+80 \({}^{\circ}\)C \\ \hline
**IP rating** & IP64 \\ \hline
**Impact** & Under working conditions, \(\leq\)1000 m/s\({}^{2}\), three-axis, 6 ms \\ \hline
**Vibration** & Under working conditions, 55–2000 HZ, \(\leq\)300 m/s\({}^{2}\), three-axis \\ \hline
**Relative humidity** & \(\leq\)90\%RH, non-condensing \\ \hline
**Maximum outer diameter** & 412 mm \\ \hline
**Accuracy** & 3\({}^{\prime\prime}\) \\ \hline
**Angular resolution** & 0.02\({}^{\prime\prime}\) \\ \hline \end{tabular}
\end{table} 
Table 6: Encoder parameters. \begin{table}
\begin{tabular}{c c c} \hline
**Motor Position** & **Shaft System 1** & **Shaft System 2** \\ \hline
**Model** & YT450-10-A & YT434-10-A \\ \hline
**Installation form** & Segmented packaging & Segmented packaging \\ \hline
**Motor type** & Permanent Magnet DC Torque Motor & Permanent Magnet DC Torque Motor \\ \hline
**Maximum no-load speed** & 100 r/min & 110 r/min \\ \hline
**Peak stall torque** & 80 N\(\cdot\)m & 70 N\(\cdot\)m \\ \hline
**Peak stall voltage** & 27 V & 27 V \\ \hline
**Peak stall current** & 32 A & 30 A \\ \hline
**Continuous stall torque** & 40 N\(\cdot\)m & 35 N\(\cdot\)m \\ \hline
**Continuous stall current** & 16 A & 15 A \\ \hline
**Continuous stall voltage** & 13.5 V & 13.5 V \\ \hline
**Weight** & 0.12 kg & 0.51 kg \\ \hline \end{tabular}
\end{table} 
Table 5: Main parameters of motors. The scanning range was a circular area with a half angle of 15\({}^{\circ}\). The experimental results show that under the disturbance of a maximum ship attitude angle of 10\({}^{\circ}\) and a frequency of 0.1 Hz, the maximum scanning error of the traditional control system was approximately 0.8 mrad. During the entire scanning process, the scanning error was controlled within 0.462 mrad (RMS) and the full circular field of view was scanned within 34 s. In contrast, the maximum scanning error of the designed control system was 0.5 mrad and the scanning error was controlled within 0.328 mrad (RMS) throughout the scanning process, with the full circular field of view being scanned within 28 s. It can be concluded that the Fuzzy PID control system for the rotating dual-grating two-dimensional scanning model based on inertial navigation feedforward technology has greater scanning accuracy and faster scanning speed compared to the traditional dual-loop control system, validating the effectiveness of the designed system. In this experiment, the combined application of inertial navigation feedforward technique and Fuzzy PID control algorithm significantly mitigated servo control errors induced by hull disturbances. However, residual error sources persisted in the results, with these errors including but not limited to the following: CCD sensor detection inaccuracies, bore-sight alignment deviations, mean square errors caused by mechanical backlash-induced  
Figure 12: Scanning trajectory of the old control system’s experimental platform: **(a)** scanning trajectory; **(b)** scanning error in the \(X\) and \(Y\) directions (approximately 0.8 mrad). Figure 13: Scanning trajectory of the new control system’s experimental platform: **(a)** scanning trajectory; **(b)** scanning error in the \(X\) and \(Y\) directions (approximately 0.5 mrad). random oscillations, signal-processing latency errors, stiction-induced hysteresis, and temporal-synchronization discrepancies--all potentially contributing to increased final scanning errors.