# Robust Adaptive Control for an Aircraft Landing
## 1 Introduction  
When an aircraft makes contact with the ground, the impact energy should be effectively dissipated and absorbed by its landing gears for safety concerns, as well as for the comfort of pilots and passengers [1]. However, a conventional passive oleo-pneumatic landing gear with a fixed size orifice may not respond as expected in all circumstances. To solve this problem, there have been many studies for active [2; 3] or semi-active landing gears [4; 5; 6] in recent years through numerical simulations or simple experimental studies. Among those studies, the landing gear using a magnetorheological (MR) damper is the most promising candidate to replace the conventional passive landing gear because it can be implemented with compact size, cheap production cost, and enhanced reliability, and it also does not require a high-power actuator nor a large power supply [7]. An MR damper is a semi-active system containing MR fluid of which hydraulic damping force can be adjusted by applying electric current to coils around the orifice of the damper. Thus, a semi-active controller is designed to improve the damping performance by determining the optimal amount of applied electric current. However, an MR damper usually exhibits nonlinear characteristics, including the hysteresis of the output force over relative velocity and the nonlinear stiffness owing to the state transition of the MR fluid from liquid to semi-solid [8; 9]. Thus, there are challenging problems for researchers in the development of MR damper controllers. Previous studies in MR damper control can be categorized into two approaches. The first one is to improve the adaptability of the damper under the different scenarios. For example, [PERSON] and [PERSON] [10] applied an optimal feedback control algorithm to reduce the impact forces with different sink speeds at landing and aircraft weights. [PERSON] and [PERSON] [11] developed an algorithm based on human simulated intelligent control. The performance of the controller was verified by numerical simulations with varying aircraft mass and sink speed. [PERSON] et al. [12] proposed a bang-bang type and a continuous type current controller to achieve a desired constant damper force over a range of sink speeds. The other approach is to deal with uncertainties and disturbances in the MR damper. [PERSON] et al. [13] applied a semi-active sliding mode control for vehicle suspension to improve the ride comfort and handling safety under the random road excitations. [PERSON] et al. [14] proposed a decentralized sliding mode control for building structures. In the applications to aircraft landing gear, [PERSON] et al. [15] developed an adaptive backstepping control with H\({}_{\infty}\) performance to cope with vibration during the taxing phase. [PERSON] et al. [16] investigated the robust model predictive control in aircraft landing gear to deal with shimmy vibration. [PERSON] et al. [17] applied a sky-ground hook controller to improve the efficiency in certain landing conditions. However, the application of a robust controller for an MR damper of an aircraft landing gear in the touchdown phase to deal with uncertainties in different landing scenarios has not yet been investigated. The main contribution of this study is to develop a robust control algorithm for an MR damper in an aircraft landing gear, in order to improve a shock absorption efficiency metric, named total energy absorber efficiency, under differing landing scenarios and uncertainties. In the previous work [18; 19], in which some of the authors of this paper were involved, it was shown that at certain conditions, a hybrid controller exhibits a better shock absorption performance than a skyhook controller. As a continuation of the previous work, as the first step, an indirect adaptive control scheme is designed and applied to the hybrid controller to improve the adaptability against variable aircraft mass and sink speed.