# A Comparative Study of Control Methods for X3D Quadrotor Feedback Trajectory Control
## 5 Conclusions  
The system proposed in this manuscript is a quadrotor. Controlling and stabilizing the quadrotor is a substantial issue due to nonlinearity and under-actuated configurations, such as a lower number of control inputs than degrees of freedom (DOF). A comparison of four alternative control methods, such as the LQR controller, PID controller, fuzzy controller, and model reference adaptive PID controller using the MIT rule, has been provided in this article for an X3D quadrotor. These controllers demonstrate the stability, robustness, and control of a quadrotor during maneuvers and trajectory tracking in the presence of nonlinear dynamics. The results of simulations demonstrate that given the identical translation position, altitude, and attitude inputs, each control system responds differently. However, based on the features that are required for the quadrotor application, it is possible to select the most suited system. When compared to other controllers at almost the same operating conditions, the LQR controller yields the highest accuracy in x, y, and z-step performance. The LQR controller has a 0.0% overshoot and a 4.1% shorter settling time than other controllers, particularly nonlinear controllers. In terms of the highest settling time and overshoot, the model reference adaptive PID controller using the MIT rule performs the worst. It is worth mentioning that the linear controller methods are quite ubiquitous and easy to implement, and they may be used for a wide range of real-world control systems. For potential research directions, all the controllers will be deployed on the X3D quadrotor board, and the X3D quadrotor's real-time performance, validation, and authentication of all control systems will be monitored; in addition, other machine learning and deep learning algorithms will be implemented for autonomous operation. Conceptualization, T.S., J.A., M.H.J., A.U.R., E.T.E., N.A.G. and M.S. ; methodology, T.S., J.A., M.H.J., A.U.R., E.T.E., N.A.G. and M.S. ; software, T.S. and J.A. ; validation, M.H.J. and A.U.R. ; formal analysis, T.S., E.T.E., N.A.G. and M.S. ; investigation, M.H.J. and M.S. ; resources, E.T.E. and N.A.G. ; data curation, T.S. and J.A. ; writing--original draft preparation, T.S., J.A., M.H.J., A.U.R., E.T.E., N.A.G., M.S. ; T.S., J.A., M.H.J., A.U.R., E.T.E., N.A.G. and M.S. ; visualization, M.H.J. ; supervision, M.H.J. and M.S. ; project administration, E.T.E. and N.A.G. ; funding acquisition, E.T.E. and N.A.G. All authors have read and agreed to the published version of the manuscript. This research was supported by Future University Researchers Supporting Project Number FUESP-2020/48 at Future University in Egypt, New Cairo 11845, Egypt. **Institutional Review Board Statement:** Not applicable. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Controllers**} & \multicolumn{6}{c}{**Performance Index (\(y\)-axis)**} \\ \cline{2-7}  & **Setting Time \(T_{S}\)** & **Rise Time \(T_{r}\)** & **Overshoot (\%)** & **Peak Time \(T_{p}\)** & **RMS Error** & **NRMS Error** \\ \hline PID & 19.08 & 1.1 & 43.2 & 4 & 0.17 & 0.12 \\ \hline LQR & 4.18 & 2.5 & 0.0 & 30 & 0.21 & 0.21 \\ \hline Fuzzy Logic & 37.54 & 3.35 & 39.162 & 8.8 & 0.24 & 0.18 \\ \hline MRAPC with MIT & 170.74 & 104.7 & 8.8 & 213.1 & 0.425 & 0.426 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance comparison of all controllers for the lateral position (\(Y\)-axis). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Controllers**} & \multicolumn{6}{c}{**Performance Index (z-axis)**} \\ \cline{2-7}  & **Setting Time \(T_{S}\)** & **Rise Time \(T_{r}\)** & **Overshoot (\%)** & **Peak Time \(T_{p}\)** & **RMS Error** & **NRMS Error** \\ \hline PID & 7.06 & 0.6 & 4.7 & 2.2 & 0.08 & 0.08 \\ \hline LQR & 4.16 & 2.25 & 0.0 & 30 & 0.18 & 0.18 \\ \hline Fuzzy Logic & 14.21 & 32.75 & 2.67 & 50 & 0.814 & 0.815 \\ \hline MRAPC with MIT & 21.86 & 3.3 & 0.77 & 26.85 & 0.056 & 0.056 \\ \hline \hline \end{tabular}
\end{table}