The body freedom flutter phenomenon is one of the aeroelastic instabilities that occurs due to the coupling of the aeroelastic bending mode of the wing with the short-period mode in the flight dynamics of the aircraft. By using the aeroservoelastic model and applying closed loop control, this phenomenon can be suppressed in the operating conditions of the aircraft and the velocity of this event can be increased. The simplest model aircraft capable of displaying this instability includes the flexible wing and the planar flight dynamics model. For this purpose, the wing structure is modeled using the Euler-Bernoulli beam and, the theory of minimum variable state is used to model unstable aerodynamics to make the conditions suitable for modeling the system in state space. In the control section, the elevator is used as the control surface and LQR theory with Kalman filter is used to body freedom flutter suppression. Finally, the effect of adding a closed loop control to increase the body freedom flutter velocity and the limitations of this work are studied.