On the Limitations of Linear Quadratic Regulation in Nonlinear 6-DOF Aircraft Dynamics Under Disturbances

This work investigates the limitations of Linear Quadratic Regulator (LQR) control when applied to nonlinear six-degrees-of-freedom (6-DOF) aircraft dynamics under disturbance conditions. While LQR provides optimal performance for linearized systems, its effectiveness degrades significantly in realistic nonlinear flight regimes. A nonlinear fixed-wing aircraft model is developed using rigid-body dynamics and aerodynamic force approximations. An LQR controller is designed around a trim condition and evaluated through high-fidelity MATLAB simulations with disturbance inputs. The results reveal critical instability phenomena, including persistent oscillations, trajectory divergence, altitude degradation, and actuator saturation. These behaviors are analyzed from both physical and control-theoretic perspectives, highlighting the impact of model mismatch, nonlinear coupling, and input constraints. The findings demonstrate that linear optimal control strategies may fail to ensure stability in nonlinear systems operating outside equilibrium conditions. This work emphasizes the need for more advanced control approaches such as model predictive control, adaptive control, and nonlinear control techniques in aerospace applications. This preprint is intended for submission to a peer-reviewed aerospace or control systems journal.