# A Supervised Neural Network Control for Magnetorheological Damper in an Aircraft Landing Gear
## 3 Performance Measure of Aircraft Landing Gear in Drop Tests  
As mentioned in the previous section, the damper of an aircraft landing gear must effectively absorb the kinetic energy of the aircraft in order to minimize the impact and  
Figure 4: Components of the MR damper (landing gear without tire).  
Figure 3: Structure of landing gear equipped with MR damper.  
vibration caused at the moment of landing. Accordingly, it is necessary to reduce the stroke of the damper and the strut force transmitted to the aircraft fuselage through the damper. The strut force is composed of the damping force, the spring force from the air chamber, and the friction at the bearings. It is important to measure the elements of the strut force without a significant increase in cost and complexity. Therefore, the ground reaction force is generally utilized in performance measures for aircraft landing gear tests. The most commonly used performance measure to quantify the effectiveness of energy absorption of the damper is shock absorber efficiency [11,19]. The shock absorber efficiency \(\eta\) is defined by the ratio between the energy absorbed by the damper during the first stroke and the product of maximum ground reaction force \(F_{T}^{max}\) and maximum stroke \(s^{max}\)[11].  
\[\eta=\frac{\int_{0}^{s^{max}}F_{T}ds}{s^{max}\frac{F_{T}^{max}}{T}} \tag{1}\]  
Figure 5 shows a force-stroke curve, called the efficiency curve, of a typical single landing gear. The efficiency curve is the trajectory of the force-stroke pair of the damper's behavior during landing, and visualizes the implication of the energy absorption efficiency: the ratio between the area below the curve in \(s=[0,s^{max}]\) and the square area of \(F_{T}^{max}\times s^{max}\). Therefore, the closer to the square the curve is, the higher the efficiency is. Observe that the typical efficiency curve has two peaks at the first compression phase, where the stroke translates from 0 to \(s^{max}\). The first peak occurs when the stroke velocity reaches its maximum value because the nonlinear spring force from the air chamber is relatively small compared to the damping force proportional to the velocity. The second peak appears when the stroke reaches \(s^{max}\), where the spring force dominates the strut force. Since \(F_{T}^{max}\) and \(s^{max}\) are reached in the first compression phase, the shock absorber efficiency is determined by the shape of the efficiency curve in this phase. Therefore, if the heights of the two peaks are adjusted to be the same, and the dent between them is filled with a controllable MR damping force, the efficiency could be significantly improved. During touchdown, two main parameters, which are aircraft mass (\(m_{1}\)) and sink speed (\(v\)), have a huge impact on the potential and kinetic energy of the aircraft [19]. Thus, only aircraft mass and sink speed are considered in this research. According to the conditions of our experiment, the ranges of aircraft mass and sink speeds are given by:  
\[\begin{array}{l}150\;\mathrm{kg}\leq m_{1}\leq 230\;\mathrm{kg}\\ 1\;\mathrm{m}/\mathrm{s}\leq v\leq 3\;\mathrm{m}\;/\mathrm{s}\end{array} \tag{2}\]  
Figure 5: Efficiency curve of a typical landing gear.