# A Supervised Neural Network Control for Magnetorheological Damper in an Aircraft Landing Gear
## 1 Introduction  
Aircraft landing gears are critical elements that effectively mitigate and absorb vibrations and shocks during the takeoff and landing process to support the safe operation of the aircraft. Therefore, the landing gears must maintain their performance in various landing situations. The damper is the heart of the landing gear, which is the central part responsible for absorbing and dissipating kinetic energy during the touchdown and taxing phases. However, oleo-pneumatic dampers, the most commonly used passive devices, are designed only at a critical case following FAR Part 25 [1]. Thus, the passive dampers are limited in improving the landing performance in different landing cases. Magnetorheological (MR) dampers have received significant attention to replace these passive dampers. The MR damper has many applications, such as suppressing chatter conditions during the milling operations of thin-floor components [2], changing the structural behavior of buildings during earthquakes [3], and reducing vibrations in gun recoil control [4]. An MR damper is a semi-active device that adjusts the damping force due to the fluid inside the damper by changing the magnetic field formed in the coil around the orifice. Thus, for the effectiveuse of the MR damper, a controller is designed to produce an appropriate electrical current, which generates the desired damping force [5]. Thus far, many control algorithms for MR damper landing gears have been developed and applied through drop test simulations or experiments. For example, [PERSON] and [PERSON] developed an adaptive control to mitigate the peak force transferred to the aircraft structure during touchdown [6]. [PERSON] and et al. designed and analyzed an MR landing gear system for a helicopter and then developed feedback control algorithms to apply a constant damping force over the desired sink speed range [7]. [PERSON] and [PERSON] invested in an intelligent control algorithm based on a human-simulated control to reduce the peak impact load of sprung mass within the stroke of a damper [8]. [PERSON] and [PERSON] applied a sliding mode control to reduce the vibration during touchdown [9]. The controllers in the previous studies require measurements or estimates of the strut force of a damper, i.e., the internal reaction between the cylinder and piston of the damper. It is not possible in operating aircraft landing gears to measure the strut force directly due to its nature. The strut force can be indirectly measured and estimated with multiple sensors and mathematical models, increasing the system complexity and cost. Moreover, in the estimation models and controllers, the aircraft mass is assumed to be known, of which the accuracy is, however, limited. Thus, the controllers underdeliver due to the inaccurate information on the aircraft mass and strut force in certain practical operations of the dampers. This problem also occurs in force control [10] and hybrid control [11] developed in previous studies by the authors. Machine learning is a subset of artificial intelligence [12] that has proven its ability to improve the adaptiveness of autonomous systems, such as self-driving cars [13] and robotics [14], without exact prior knowledge of the systems and operating environment. [PERSON] and et al. [15] developed a back-propagation artificial neural network, which is optimized by an artificial bee colony algorithm based on the control force calculated by a linear quadratic regulator. [PERSON] and et al. [16] applied an intelligent controller based on a neural network to improve the landing performance in different landing cases. The neural network is trained by using a genetic algorithm and policy gradient estimation. If a neural net with system state variables as its inputs is used to generate a control command, a controller could be designed to adaptively operate in differing landing situations without parameter estimates or models.