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In this paper, in order to reduce a landing gear vibration two adaptive control systems are designed considering the landing and taxi phases. For this purpose, 6 degree of freedom equations of motion of the landing gear and the related transfer functions are extracted. A reduced order model of the overall transfer functions are given as a result of complicated dynamic model. A Lyapunov based model reference adaptive control is designed to absorb the vibration of front wheel of the landing gear at touchdown. In addition, a minimum variance adaptive controller is designed and implemented on the system to reject the band level disturbances during the taxi phase. The band disturbances are modeled as a colored Gaussian noise and the system parameters as well as noise characteristics are estimated using extended least square approach. Both control systems are investigated to assess the best performance. Numerical simulations of the system in Matlab/Simulink environment show the preferences and satisfactory performances of the proposed vibration control systems. These results are calculated against various inputs including model reference adaptive control and minimum variance approaches