## 1 Introduction  
The landing gear system of an aircraft consists of the main landing gear and the nose gear. The nose gear is mainly located under the nose of the aircraft. The role of the nose gear is steering the aircraft during takeoff, landing, and taxiing and is not used for direct impact energy dissipation during landing. The main landing gear braces the aircraft's fuselage by dissipating most of the impact energy generated by the weight and sink speed of the aircraft during landing. For a stable landing, the shock absorbers of the main landing gear must be designed to dissipate sufficient shock energy. An oleo-pneumatic shock absorber (abbreviated as oleo-strut) is the most popular one used in modern aircraft landing gear systems. A structure called a metering pin is used inside the oleo-strut to vary the orifice area, and hence the damping force, in response to the piston displacement. Because the oleo-strut is the passive damper, its performance is limited. Therefore, the research on active and semi-active shock absorbers for the aircraft landing gear systems is being undertaken through several different approaches. A magnetorheological (MR) fluid shock absorber is an attractive candidate to achieve optimal landing performance in almost all landing conditions. In general, a valve mechanism for the fluid flow is used for the MR shock absorber [1]. It is well known that MR fluid reacts to the magnetic field as a mixture of carbonyl-iron powder (CIP) and silicone oil. In the presence of the magnetic field, the in-fluid CIP particles are aligned in the direction of the magnetic field to form chain structures. The structure creates yield stress, resisting the flow of the MR fluid, which is a characteristic of the Bingham-plastic flow [2; 3]. Thanks to the Bingham-plastic characteristics in response to the magnetic field, it is possible to achieve the desired damping force, resisting the fluid flow by controlling the magnetic field. Therefore, MR fluid is being actively used for several dynamic devices or systems that require a controllable damping force under different operating conditions. These systems include seismic dampers in civil structures, vehicle suspension systems, seat dampers, and lateral dampers for trains. In order to accurately predict the pressure drop (or damping force) of an MR shock absorber, several design models have been proposed so far [4; 5; 6; 7; 8]. One of the critical design parameters of MR shock absorbers is to determine the gap (or flow path) in which the flow resistance of the MR fluid is controlled by the magnetic core. In the flow path, two occur: the major pressure loss and the minor pressure loss. The major loss is caused by the fluid's dynamic viscosity generating a hydraulic resistance force in the gap. On the other hand, the minor loss is caused by inertia due to the density of the fluid generated in the inlet and outlet of the gap, which sharply bents the flow path and the developing region. The faster the operating speed of the MR shock absorber, the greater the effect of the minor loss because it is sensitive to the fluid velocity. In previous works on the design of MR shock absorbers, only the major pressure loss has been considered because the application systems are operated in the low operating speed range (or low stroke velocity), which is less than 0.5 m/s. Recently, several works on MR shock absorbers applicable to aircraft landing gear systems have been proposed. In some works [9; 10], MR shock absorbers for aircraft landing gear systems were designed, analyzed, and experimentally validated under low-frequency conditions, and showed suitable damping force. An aircraft landing gear system with an MR shock absorber was designed, and the landing performance via the skyhook controller was evaluated in [11]. Robust adaptive control was proposed for the aircraft landing gear system equipped with an MR damper based on the adaptive hybrid control and sliding mode control algorithm to take account of the parameter uncertainties [12].