# Robust Adaptive Control for an Aircraft Landing
## 6 Conclusions  
This research investigated the robust adaptive control for a single landing gear system equipped with an MR damper. With a mathematical model of the landing gear, a robust controller based on the adaptive hybrid control and sliding mode control algorithm was proposed. Comparative numerical simulations under the various landing conditions (i.e., aircraft weights and sink speeds) and parametric uncertainties (i.e., ambient temperature, viscous damping coefficient, damping force estimate error) were conducted to analyze the effectiveness of the proposed control algorithm. From the simulations, it was verified that the damper using the proposed controller has acceptable and stable performance with high total energy absorber efficiency and an improved adaptability and robustness in differing landing scenarios and uncertainties.  
Both the adaptive hybrid control and sliding mode control are built on a mathematical model. Thus, the difficulty of this approach is to develop an accurate mathematical model. Therefore, as future work, drop-test experiments of a landing gear system can be set up to verify the damper model and the performance of the control. On the other hand, because the damping process of a landing gear occurs in very short time, the time delay of an MR damper can be a crucial factor in determining the effectiveness of control. Thus, to deal with the time delay, control methods based on artificial intelligent techniques, such as a reinforcement neural network or genetic algorithm neural network, can be applied to the MR damper.  
This work was initiated and designed by [PERSON]. The numerical simulations were completed by [PERSON]. The data analysis, and writing the paper were completed by [PERSON] and [PERSON]. The suggestions for the simulation design and paper writing were done by [PERSON] and [PERSON]. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea).  
**Acknowledgments:** This work was supported by the Technology Innovation Program (intelligent landing gear with variable damping force for 1500 lb class) (10073291).  
**Conflicts of Interest:** The authors declare no conflict of interest.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Adaptive Hybrid Control**} & \multicolumn{3}{c}{**SMC-Adaptive Hybrid Control**} \\ \hline
**Parameters** & \(\mathbf{F_{\text{max}}}\) **(kN)** & \(\mathbf{s_{\text{max}}}\) **(m)** & \(\mathbf{\eta}\) **(\%)** & \(\mathbf{F_{\text{max}}}\) **(kN)** & \(\mathbf{s_{\text{max}}}\) **(m)** & \(\mathbf{\eta}\) **(\%)** \\ \hline p\({}_{0}\) (bar)/T (\({}^{\circ}\)C) & & & & & & \\
6.36/\(-\)40 & 21.4 & 0.223 & 92.5 & 21.8 & 0.213 & 94.0 \\
7.45/0 & 21.6 & 0.216 & 92.4 & 21.8 & 0.211 & 94.3 \\
8.00/20 & 21.8 & 0.209 & 93.9 & 21.8 & 0.210 & 93.8 \\
8.55/40 & 22.7 & 0.204 & 92.3 & 21.8 & 0.209 & 93.3 \\ \hline C (kNs/m) & & & & & & \\
7.23 (+10\%) & 22.8 & 0.202 & 92.8 & 22.1 & 0.208 & 93.0 \\
6.91 (+5\%) & 22.4 & 0.206 & 93.4 & 21.9 & 0.210 & 93.0 \\
6.58 (base value) & 21.8 & 0.209 & 93.9 & 21.8 & 0.210 & 93.8 \\
6.25 (\(-\)5\%) & 22.0 & 0.214 & 91.0 & 21.8 & 0.210 & 93.9 \\
5.92 (\(-\)10\%) & 23.8 & 0.216 & 83.7 & 21.9 & 0.209 & 93.6 \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c c c} \hline \hline \(Error(F)=100\%\frac{\widehat{F}_{d}-F_{d}}{\widehat{F}_{d}}\) & & & & & & \\ \(-10\%\) & 23.9 & 0.195 & 91.9 & 21.9 & 0.209 & 93.8 \\ \(-5\%\) & 22.8 & 0.201 & 93.0 & 21.8 & 0.209 & 93.7 \\
0\% & 21.8 & 0.209 & 93.9 & 21.8 & 0.210 & 93.8 \\
5\% & 21.8 & 0.215 & 91.3 & 21.8 & 0.210 & 93.7 \\
10\% & 21.8 & 0.217 & 90.8 & 21.8 & 0.210 & 93.5 \\ \hline \hline \end{tabular}
\end{table}
Table 4: The performance of the damper using the adaptive hybrid control and SMC adaptive hybrid control under parametric uncertainties.