# Disturbance Observer-Based Anti-Shock Controller for Laser Beam Steering Systems
## 4 Performance of Anti-Shock Controller for FSM System  
The simulated performance results of the DOB-based anti-shock controller for FSM control systems revealed that the target rotational position was maintained successfully at 0 \(\upmu\)rad (i.e., neutral rotational position). When the 15 Hz bandwidth \(Q_{20}\) and \(Q_{31}\) filters were used in the DOB-based FSM control system, the RMS CES values were 100.1 and 88.8 \(\upmu\)rad, respectively. Furthermore, when the 30 Hz bandwidth \(Q_{20}\) and \(Q_{31}\) filters were used in the DOB-based FSM control system, the RMS CES values were 74.9 and 63.9 \(\upmu\)rad, respectively, as illustrated in Figure 10a,b. The overall simulated performance results of the DOB-based anti-shock controller for FSM control systems are summarized in Table 2.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specification**} & \multirow{2}{*}{**PI Controller**} & \multicolumn{2}{c}{\(\mathbf{Q_{20}}\) **Filter**} & \multicolumn{2}{c}{\(\mathbf{Q_{31}}\) **Filter**} \\ \cline{3-6}  & & **15 Hz** & **30 Hz** & **15 Hz** & **30 Hz** \\ \hline Minimum rotational position error (rms) & 119.9 \(\upmu\)rad & 100.1 \(\upmu\)rad & 74.9 \(\upmu\)rad & 88.8 \(\upmu\)rad & 63.9 \(\upmu\)rad \\ \hline Reduced rate & - & 16.5\% & 37.6\% & 25.9\% & 46.7\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Simulated performance results obtained using DOB-based anti-shock controller for FSM control systems.  
Figure 9: Disturbance-rejection performance of DOB-based anti-shock controller for FSM control systems: (**a**) \(Q_{20}\) and (**b**) \(Q_{31}\) filters.  
The experimental performance results are presented in Figure 11. The experimental performance results of the DOB-based anti-shock controller for FSM control systems revealed that the target rotational position was maintained successfully at 0 \(\upmu\)rad (i.e., neutral rotational position). According to Figure 11a, the root mean square (RMS) residual CES of the PI controller was 9.9 \(\upmu\)rad. When the 15 Hz bandwidth \(Q_{20}\) and \(Q_{31}\) filters were used in the DOB-based FSM control system, the RMS CES values were 100.1 and 88.8 \(\upmu\)rad, respectively, as illustrated in Figure 11b,c. Furthermore, when the 30 Hz bandwidth \(Q_{20}\) and \(Q_{31}\) filters were used in the DOB-based FSM control system, the RMS CES values were 74.9 and 63.9 \(\upmu\)rad, respectively, as illustrated in Figure 11d,e.  
Eventually, the disturbance-rejection performance in the DOB-based anti-shock controller for FSM systems improved as the order of the denominator and numerator increased, and as the bandwidth of the \(Q\) filter increased. The overall performance results of the DOB-based anti-shock controller for FSM control systems are summarized in Table 3. These results indicate that the performance of the proposed anti-shock controller was superior to that of the controller reported in previous studies [37; 38].  
Figure 10: Simulated performance results obtained using DOB-based anti-shock controller for FSM control systems: (**a**) \(Q_{20}\) filter (15/30 Hz), and (**b**) \(Q_{31}\) filter (15/30 Hz).  
Figure 11: _Cont._  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Specification**} & \multirow{2}{*}{**PI Controller**} & \multicolumn{2}{c}{**Q20 Filter**} & \multicolumn{2}{c}{**Q31 Filter**} \\ \cline{3-6}  & & **15 Hz** & **30 Hz** & **15 Hz** & **30 Hz** \\ \hline Minimum rotational & \multirow{2}{*}{106.0 μrad} & \multirow{2}{*}{79.1 μrad} & \multirow{2}{*}{54.7 μrad} & \multirow{2}{*}{72.2 μrad} & \multirow{2}{*}{43.4 μrad} \\ position error (rms) & & & & & \\ \hline Reduced rate & - & 25.3\% & 48.4\% & 31.9\% & 59.1\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental performance results obtained using DOB-based anti-shock controller for FSM control systems.