# Robust Adaptive Control for an Aircraft Landing
## 5 Simulation Results and Discussion  
To verify the effectiveness of the controller, numerical simulations with different control methods were performed. Passive damping, skyhook control, and adaptive hybrid control were applied and compared with the SMC-adaptive hybrid control. All simulations and computations were carried out using MATLAB with SIMSCAPE-SIMULINK. The outputs of controllers were investigated in terms of the maximum damper force, the maximum stroke, and the maximal total energy absorber efficiency under various aircraft weights and sink speeds. Both Figure 8 and Table 2 show the simulation results in the case of a heavy load and high speed (\(m_{1}=680\) kg and \(v=3\) m/s). The SMC-adaptive hybrid control shows the best performance compared with the passive damper and skyhook control. The damper using the proposed controller produces the lowest absolute displacement and aircraft acceleration in magnitude. This means that the proposed controller is able to reduce more vibration in the landing gear system, which may increase passenger comfort. In addition, the proposed controller improves the total energy absorber efficiency of the damper to nearly 94%, which is 5% and 15% higher than the skyhook control and passive damping, respectively. Moreover, the comparison results of different sink speeds and masses are shown in Table 3. The results show that the proposed controller has the smallest value of both maximum stroke and damper force, and the total energy absorber efficiency is up to about 10% more than that of the skyhook controller. Figure 8: The simulation results of the MR damper using the passive damping, skyhook control, and sliding mode control (SMC)-adaptive hybrid control in the case of \(m_{1}=680\) kg and \(v=3\) m/s: (**a**) displacement of the aircraft; (**b**) acceleration of the aircraft; (**c**) load-stroke curve; (**d**) electric current. Figure 9 and Table 4 show the comparative damping performances of the adaptive hybrid control and SMC-adaptive hybrid control under parameter uncertainties. The controllers are compared with three varying parameters picked as the uncertainties in landing: the change of air pressure with ambient temperature, inaccuracy of viscous damping coefficient, and the error of damping force estimate. Under the parameter variation, the performance of the adaptive hybrid control is degraded. In particular, the shock absorber efficiency reduces by about 10% when the viscous damping coefficient decreases by 10%. The maximum damping force increases by 10% when the damper force is underestimated by 10%. On the other hand, the SMC-adaptive hybrid controller maintains the performances under the parameter variation, and thus, its robustness under parametric uncertainties in landing is verified. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \begin{tabular}{c} **Maximum of** \\ **Stroke \(s_{max}\) (m)** \\ \end{tabular} & \
\begin{tabular}{c} **Maximum of Damping** \\ **Force \(F_{max}\) (kN)** \\ \end{tabular} &
\begin{tabular}{c} **Total Energy Absorber** \\ **Efficiency \(\eta\) (\%)** \\ \end{tabular} \\ \hline Passive damper & 0.221 & 24.2 & 80.4 \\ Skyhook control & 0.217 & 21.8 & 90.6 \\ SMC-adaptive hybrid control & 0.210 & 21.8 & 93.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The efficiency of the damper using the passive damper, skyhook control, and SMC-adaptive hybrid control in the case of \(m_{1}=680\) kg and \(v=3\) m/s. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Passive Damper**} & \multicolumn{3}{c}{**Skyhook Control**} & \multicolumn{3}{c}{ \begin{tabular}{c} **SMC-Adaptive** \\ **Hybrid Control** \\ \end{tabular}  } \\ \hline  & \begin{tabular}{c} \(F_{\max}\) \\ **(kN)** \\ \end{tabular}  & \begin{tabular}{c} \(s_{\max}\) \\ **(m)** \\ \end{tabular}  & \begin{tabular}{c} \(\eta\) (\%)** \\ \end{tabular}  & \begin{tabular}{c} \(F_{\max}\) \\ **(kN)** \\ \end{tabular}  & \begin{tabular}{c} \(s_{\max}\) \\ **(m)** \\ \end{tabular}  & \begin{tabular}{c} \(\eta\) (\%)** \\ \end{tabular}  &