Presently, advanced control theory plays a major role in the aircraft system for the control of Yaw, Roll and Pitch angles, which was very much necessary for the stabilization of aircraft system. Following the works of the control system community for aircraft applications, this paper concentrates on the control of Yaw angle by designing various optimal Linear Quadratic Regulator (LQR) controllers using standard existing tools. The optimal controllers are designed for the aircraft, tested and validated using MATLAB/SIMULINK environment, and the results are compared with different system conditions to select the best optimal LQR feedback controllers in future aircraft control systems.