Abstract: In this paper the mathematical model representing the dynamic of a Unmanned Aerial Vehicle (UAV) is studied in order to analyse its behaviour. In order to stabilize the entire system, linear Quadratic Regulator (LQR) control is used in such a way to set both PD and PID controls in position variables. A set simulation is performed to carry out the results for linear and non linear models. The LQR-PD and LQR-PID allow to move the plant's poles of UAV in the left half plane since without controller the systems is unstable. Simulations, LQR-PD and LQR-PID controllers are designed by using Matlab/Simulink. The simulations are performed to show how LQR tuned PD and PID controllers lead to zero the error of the position along Z earth direction, stop the rotation of Unmanned Aerial Vehicle (UAV) around body axes and stabilize the hexarotor.