Analysis Of Aircraft Pitch Axis Stability Augmentation System Using

Analysis of stability of the pitch axis of an aircraft has been a well studied problem. Historically, researchers have analyzed the stability and robustness of a family of linearized closed loop A/C models. An inherent limitation of such an approach is that the parametrization of a family of closed loop A/C models could be conservative leading to a) conservative control designs or b) pose difficulty in control design itself. With the development of Sum-Of-Squares (SOS) optimization techniques, researchers have shown that it is possible to analyze the stability properties of nonlinear systems. In this paper, we use SOS programming approaches to analyze the stability and robustness properties of the controlled pitch axis (6 state system) of a nonlinear model of an A/C. The controller is a LTI Dynamic Inversion based control law designed for the short period dynamics of the A/C. The closed loop system is tested for its robustness to uncertainty in the location of center of gravity along the body x-axis. Results in the form of stability regions about a trim point are computed and verified using simulations.