# A Supervised Neural Network Control for Magnetorheological Damper in an Aircraft Landing Gear
## 5 Supervised Learning of Neural Network Controller
### Comparison between the Hybrid Controller with Estimates and Intelligent Controller  
Thus far, the hybrid controller is assumed to obtain the load cell data for the ground reaction force and exact aircraft mass. However, in the practical operation environment of aircraft landing gear, only the estimates of the force and mass are available. For selecting the skyhook gain and computing the desired damping force, the strut force \(F_{\mathrm{s}}\) in the damper needs is estimated instead of \(F_{T}\)[17]. \[F_{\mathrm{s}}=A_{a}\bigg{(}P_{0}\bigg{(}\frac{V_{0}}{V_{0}-A_{a}\;s}\bigg{)}^{ n}-ATM\bigg{)}+C_{1}\dot{\mathrm{s}}+C_{2}\big{(}s\big{)}^{2} \tag{12}\]  
where \(A_{a}\) is the cross-area of the head piston, \(P_{0}\) is the initial air chamber charging pressure, \(n\) is the polytropic process index, \(ATM\) is the atmospheric pressure, \(V_{0}\) is the initial air chamber volume, \(C_{1}\) and \(C_{2}\) are nonlinear viscous force constants. All parameters in Equation (12) are defined from previous studies [11; 17]. The aircraft mass is assumed to be estimated in flight with approximately 5% error. In order to compare the controllers in practical assumptions, drop tests are executed by applying the proposed controller and the hybrid controller without load cell data, and thus the damping force is estimated by using Equation (12) and the aircraft mass is given with a 5% random error. The drop test experimental results with the hybrid controller and the intelligent control are shown in Figures 15 and 16 and Table 5. The neural network produced lower damping forces and higher efficiency than the hybrid controller for all cases. Because the aircraft mass estimate has some error, the skyhook gain cannot be well tuned so that the flatness of \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Landing Conditions**} & \multicolumn{3}{c}{**Hybrid Control**} & \multicolumn{3}{c}{**Intelligent Control**} \\ \cline{2-7}  & \(F_{T}^{max}\) **(kN)** & \(s^{max}\) **(m)** & \(\eta\) **(\%)** & \(F_{T}^{max}\) **(kN)** & \(s^{max}\) **(m)** & \(\eta\) **(\%)** \\ \hline Case 1: \(m_{1}\) = 220 kg, \(v\) = 1.83 m/s & 4.97 & 0.175 & 88.5 & 5.16 & 0.165 & **91.5** \\ \hline Case 2: \(m_{1}\) = 220 kg, \(v\) = 2.32 m/s & 6.48 & 0.177 & 87.0 & 6.50 & 0.173 & **88.6** \\ \hline Case 3: \(m_{1}\) = 220 kg, \(v\) = 2.85 m/s & 8.31 & 0.181 & 86.0 & 8.36 & 0.180 & **86.7** \\ \hline Case 4: \(m_{1}\) = 200 kg, \(v\) = 1.88 m/s & 4.97 & 0.162 & **88.7** & 5.07 & 0.157 & 88.0 \\ \hline Case 5: \(m_{1}\) = 200 kg, \(v\) = 2.31 m/s & 6.38 & 0.166 & **86.4** & 6.43 & 0.165 & 85.8 \\ \hline Case 6: \(m_{1}\) = 200 kg, \(v\) = 2.81 m/s & 8.13 & 0.172 & **85.2** & 8.20 & 0.173 & 84.4 \\ \hline Case 7: \(m_{1}\) = 180 kg, \(v\) = 1.83 m/s & 4.81 & 0.151 & **85.4** & 5.00 & 0.152 & 83.1 \\ \hline Case 8: \(m_{1}\) = 180 kg, \(v\) = 2.35 m/s & 6.27 & 0.153 & **85.4** & 6.36 & 0.155 & 84.0 \\ \hline Case 9: \(m_{1}\) = 180 kg, \(v\) = 2.80 m/s & 7.94 & 0.160 & **84.5** & 7.89 & 0.163 & 83.0 \\ \hline Case 10: \(m_{1}\) = 160 kg, \(v\) = 1.84 m/s & 4.73 & 0.148 & **79.6** & 4.92 & 0.145 & 78.4 \\ \hline Case 11: \(m_{1}\) = 160 kg, \(v\) = 2.32 m/s & 6.24 & 0.147 & 80.9 & 6.25 & 0.147 & **81.1** \\ \hline Case 12: \(m_{1}\) = 160 kg, \(v\) = 2.80 m/s & 7.75 & 0.149 & **82.9** & 7.82 & 0.152 & 81.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Damper performance using the hybrid controller with exact information and intelligent controller in other cases, which are different to training and testing cases. The best efficiency for each case is marked in bold. the efficiency curves of the hybrid controller is degraded. Moreover, in the hybrid controller, because the struct force is estimated instead of using the measured ground reaction force, the control input of the force control rule in Equation (6) cannot be accurate during the first compression phase, where the upper envelope of the efficiency curve forms.