# A Supervised Neural Network Control for Magnetorheological Damper in an Aircraft Landing Gear
## 4 Hybrid Controller with Load Cell Data and Known Aircraft Mass
### Control Scheme in Practical Operation Environment  
In practical operating environments of landing gears equipped with MR dampers, the mass information of the aircraft supported by each landing gear may not be accurate, and the ground reaction force or strut force cannot be measured, so MR damper controllers must be driven with estimates based on mathematical models. It is assumed that the sensors that the controllers can use are limited to an accelerometer generally installed in the aircraft and a position sensor that measures the stroke of the landing gear to avoid an unnecessary increase in weight and cost. The control structure of the MR damper in this context is depicted in Figure 9. Among the two main factors that determine the landing conditions of the aircraft, mass and descent speed, the descent speed is obtained with high precision by integrating the output of the accelerometer. Thus, the skyhook and hybrid controller can adjust the control parameters for corresponding landing conditions if updated mass information is also given before touchdown. One method of estimating the aircraft mass is using the least mean square method as below [11; 23]:  
\[\hat{m}_{1}=\frac{\int F_{T}(g-\ddot{z}_{1})dt}{\int\left(g-\ddot{z}_{1}\right)^ {2}dt} \tag{6}\]  
\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}{**Hybrid Control**} \\ \cline{3-11}  & & \(F_{T}^{max}\) & \(s^{max}\) & \(\eta\) & \(F_{T}^{max}\) & \(s^{max}\) & \(\eta\) & \(F_{T}^{max}\) & \(s^{max}\) & \(\eta\) \\ \cline{3-11}  & & (kN) & (m) & (\%) & (kN) & (m) & (\%) & (kN) & (m) & (\%) \\ \hline \multirow{3}{*}{\(m_{1}=150\) kg} & \(v=1\) m/s & **3.09** & 0.160 & 81.4 & **3.09** & 0.16 & 81.4 & 3.85 & **0.148** & **84.9** \\ \cline{2-11}  & \(v=2\) m/s & 5.55 & 0.168 & 72.4 & 5.55 & 0.168 & 72.4 & **5.36** & **0.150** & **79.4** \\ \cline{2-11}  & \(v=3\) m/s & **8.59** & 0.176 & 72.5 & **8.59** & 0.176 & 72.5 & 8.60 & **0.157** & **81.0** \\ \hline \multirow{3}{*}{\(m_{1}=190\) kg} & \(v=1\) m/s & 3.90 & 0.174 & 72.8 & 3.51 & 0.169 & 84.2 & **3.34** & **0.166** & **89.6** \\ \cline{2-11}  & \(v=2\) m/s & **5.83** & 0.182 & 78.2 & **5.83** & 0.182 & 78.2 & 5.90 & **0.167** & **85.3** \\ \cline{2-11}  & \(v=3\) m/s & 9.21 & 0.188 & 77.5 & 9.21 & 0.188 & 77.5 & **9.17** & **0.176** & **83.0** \\ \hline \multirow{3}{*}{\(m_{1}=230\) kg} & \(v=1\) m/s & 5.20 & 0.180 & 65.3 & 4.17 & 0.172 & 85.5 & **3.93** & **0.172** & **90.5** \\ \cline{2-11}  & \(v=2\) m/s & 6.84 & 0.186 & 75.6 & 6.81 & **0.183** & 77.9 & **6.16** & 0.184 & **85.8** \\ \cline{1-1} \cline{2-11}  & \(v=3\) m/s & 9.93 & 0.194 & 80.6 & 9.93 & 0.194 & 80.6 & **9.78** & **0.191** & **85.1** \\ \hline \hline \end{tabular}
\end{table}
Table 1: Damper performance using passive damping, skyhook controller, and hybrid controller in differing landing cases. The best result for each criterion is marked in bold.  
Figure 8: (**a**) Voltage applied to MR core, (**b**) efficiency curve. The drop test results of the landing gear using the passive damper, skyhook controller, and hybrid controller in the case of \(m_{1}=190\) kg, \(v=1\) m/s.  
This method requires the ground reaction force or an estimate of it. Therefore, it takes at least tens of milliseconds to obtain an accurate mass estimate, resulting in degradation in the control performance. Another possible method is Bayesian inference to estimate the value in a fuel-flow model, and the aircraft mass is then calculated by:  
\[\hat{m}_{1}=m_{T}-m_{fuel} \tag{7}\]  
where \(m_{T}\) is the total take-off weight, and \(m_{fuel}\) is the consumed fuel mass in flight. This method can estimate the aircraft mass before touchdown and the typical error is less than 5% [24]. This error causes the controller to be imperfect in adaptability to different landing conditions.