## 5 Result and Discussion
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Motion** & **Controller** & **Rise Time, s** & **Settling Time, s** & **Overshoot, \%** & **Steady-State Error** & **RMSE** \\ \hline \multirow{6}{*}{Roll} & PD & 0.8081 & 1.4739 & 0.0003 & 0.0000 & 0.3983 \\ \cline{2-7}  & PID & 0.4097 & 0.7524 & 1.1111 & 0.0043 & 0.3770 \\ \cline{2-7}  & LQR & 2.1045 & 3.4910 & 0.5358 & 0.0054 & 0.4562 \\ \cline{2-7}  & P-LQR & 0.7936 & 1.4624 & 0.9776 & 0.0041 & 0.3884 \\ \cline{2-7}  & PD-LQR & 0.7497 & 1.2859 & 0.4363 & 0.0041 & 0.3768 \\ \cline{2-7}  & PD2-LQR & 0.7653 & 1.3093 & 0.5610 & 0.0042 & 0.3748 \\ \cline{2-7}  & GWO PD2 LQR & 0.0461 & 0.0839 & 0.0029 & 0.0028 & 0.2174 \\ \cline{2-7}  & IGWO PD2 LQR & 0.0317 & 0.0526 & 0.0077 & 0.0013 & 0.2207 \\ \hline \multirow{6}{*}{Pitch} & PD & 0.8073 & 1.4726 & 0.0003 & 0.0000 & 0.3975 \\ \cline{2-7}  & PID & 0.4120 & 0.7779 & 1.1391 & 0.0044 & 0.3780 \\ \cline{2-7}  & LQR & 2.1047 & 3.4923 & 0.5360 & 0.0054 & 0.4567 \\ \cline{2-7}  & P-LQR & 0.8024 & 1.4708 & 1.0229 & 0.0041 & 0.3898 \\ \cline{2-7}  & PD-LQR & 0.7438 & 1.2702 & 0.4502 & 0.0041 & 0.3782 \\ \cline{2-7}  & PD2-LQR & 0.7608 & 1.2951 & 0.6169 & 0.0043 & 0.3764 \\ \cline{2-7}  & GWO PD2 LQR & 0.0466 & 0.0847 & 0.0025 & 0.0029 & 0.2190 \\ \cline{2-7}  & IGWO PD2 LQR & 0.0322 & 0.0533 & 0.0081 & 0.0013 & 0.2224 \\ \hline \multirow{6}{*}{Yaw} & PD & 0.8167 & 1.4605 & 0.0511 & 0.0000 & 0.3683 \\ \cline{2-7}  & PID & 0.4096 & 0.7259 & 0.5967 & 0.0043 & 0.3416 \\ \cline{2-7}  & LQR & 2.0923 & 3.4511 & 0.5720 & 0.0057 & 0.3983 \\ \cline{2-7}  & P-LQR & 0.8162 & 1.4219 & 0.3872 & 0.0045 & 0.3225 \\ \cline{2-7}  & PD-LQR & 0.8020 & 1.4009 & 0.3650 & 0.0036 & 0.3220 \\ \cline{2-7}  & PD2-LQR & 0.7675 & 1.3394 & 0.3798 & 0.0037 & 0.3216 \\ \cline{2-7}  & GWO PD2 LQR & 0.0261 & 0.0468 & 0.0185 & 0.0024 & 0.1722 \\ \cline{2-7}  & IGWO PD2 LQR & 0.0182 & 0.0308 & 0.0018 & 0.0012 & 0.1751 \\ \hline \multirow{6}{*}{Altitude} & PD & 0.7904 & 1.4203 & 0.0279 & 0.0000 & 0.3234 \\ \cline{2-7}  & PID & 0.7621 & 1.2380 & 0.6035 & 0.0038 & 0.3256 \\ \cline{2-7}  & LQR & 2.7063 & 4.4146 & 0.3441 & 0.0021 & 0.3702 \\ \cline{2-7}  & P-LQR & 1.2440 & 3.9587 & 8.0415 & 0.0035 & 0.3246 \\ \cline{2-7}  & PD-LQR & 0.7405 & 1.3420 & 1.0609 & 0.0036 & 0.3259 \\ \cline{2-7}  & PD2-LQR & 0.7935 & 1.2534 & 0.6056 & 0.0039 & 0.3223 \\ \hline GWO PD2 LQR & 0.1342 & 0.2203 & 0.0000 & 0.0034 & 0.3760 \\ \hline IGWO PD2 LQR & 0.1365 & 0.2245 & 0.0000 & 0.0014 & 0.3754 \\ \hline \end{tabular}
\end{table} 
Table 3: Performance comparison of the controller (in value). For steady-state error, the PD controller shows better precision in tracking the desired reference in all four motions. IGWO PD2-LQR controller produces lower RMSE in roll, pitch, and yaw motions, while the PD2-LQR controller is better in altitude motion. The overall worst performance is exhibited by the LQR controller that gave the slowest rise time and settling time and the highest steady-state error and RMSE in roll, pitch, and yaw motions. However, the altitude motion LQR controller only performed worse in terms of rise time and settling time, while the worst steady-state error is produced by the PD2-LQR controller and the worst RMSE produced by the IGWO PD2-LQR controller. PID controller is the worst in roll, pitch, and yaw motions for percentage overshoot, while the P-LQR controller is the worst in altitude motion. In terms of the rise time, IGWO PD2-LQR exhibit the fastest response with 0.0317 s, 0.0322 s, 0.0182 s, and 0.1365 s, while the LQR controller had the slowest response with 2.1045 s, 2.1047 s, 2.0923 s, and 2.7063 s in roll, pitch, yaw, and altitude motions respectively. We can see that up to 90% improvement can be made if the IGWO PD2-LQR controller is