# Robust Adaptive Control for an Aircraft Landing
## 4 Algorithm Control Designation
### Adaptive Hybrid Controller  
In this work, a self-tuning control (STC) [25] concept is applied to deal with the different landing scenarios. Figure 3 describes the flow of an adaptive hybrid controller. With the measurements from at least two types of sensors (e.g., a position sensor which measures the stroke, and an accelerometer, which measures the acceleration of the aircraft), the adaptive controller requires the estimates of aircraft mass and sink speed for calculating an appropriate skyhook gain and target damping force for a hybrid control block. The hybrid control [18] is a combination of the force control [26] and the skyhook control [27] methods. The force control is a method of maximizing the impact energy absorption efficiency of a damper by filling up the gap between \(F_{\text{max}}\) and damper force curve over stroke. Figure 4a depicts a typical force-stroke curve of passive damping. Since the damper force is not always maximized to \(F_{\text{max}}\), one may expect it will be more efficient if the damper force is kept constant for as long as possible during the first contraction of the damper. In the force control, a simple base controller or non-controlled passive damping is used until the stroke velocity reaches the first local maximum after touchdown, and then the damping force is controlled to be a constant value, called the target damping force \(F_{\text{target}}\). The base controller is designed to produce \(F_{\text{target}}\) at \(s_{1}\), where its velocity is maximized \(\dot{s}_{1}=\dot{s}^{*}{}_{1}\), and lower magnitude thereafter. As in [4], the target damping force is defined as the damper work from 0 to \(s_{\text{max}}\) divided by 90% of the maximal stroke in passive damping:  
\[F_{\text{target}}= \begin{array}{c}\int\limits_{0}^{s_{\text{max}}}F_{d,passive }ds\\ \frac{0}{0.9s_{\text{max},passive}}\end{array}  \tag{20}\]  
Then, the control input force is given by:  
\[u=\left\{ \begin{array}{cc}0,&F_{\text{target}}<F_{d}\\ F_{\text{target}}-F_{d},&F_{\text{target}}\geq F_{d}\end{array} \right. \tag{21}\]  
This target damping force depends on the dynamic energy at touchdown, which is characterized by the aircraft mass \(m_{1}\) and initial sink speed \(v\). Thus, the target value should be defined for each unique landing condition. To build a table of target damping force over various aircraft mass and  
Figure 3: Adaptive hybrid control algorithm. sink speed values, multiple numerical simulations of the damper without any control were executed covering a wide variety of the parameters. The results are plotted in Figure 4b: the target damping force increases with larger aircraft mass and faster sink speed. The base controller used in this paper is the skyhook controller, and it runs before the force control becomes active. The skyhook control produces additional damping input against the velocity of the sprung mass \(\dot{z}_{1}\). It is a widely used method in suspension systems because it is simple to implement and requires a minimal number of system states, i.e., \(\dot{z}_{1}\) and \(\dot{s}_{1}\). By tuning its damping gain, the impact energy absorption efficiency of a semi-active damper can be significantly increased over passive damping. The rule of the skyhook control in a semi-active damper is expressed as:  
\[u= \begin{cases}C_{sky}\dot{z}_{1},&\dot{z}_{1}\dot{s}\geq 0\\ 0,&\dot{z}_{1}\dot{s}<0\end{cases}  \tag{22}\]  
where \(C_{sky}\) is the skyhook gain. Unlike general types of differential control, the control input should be 0 when \(\dot{z}_{1}\) and \(\dot{s}\) are opposite in sign because the damping force of an MR damper is only applied in the opposite direction of the relative movement of the piston and cylinder. Since a base controller for the force control should create damping force \(F_{d}=F_{\text{target}}\) at \(s_{1}\), the skyhook gain is determined by:  
\[C_{sky}=\left\{