Aircraft and Differential Flatness

We investigate apparent and intrinsic singularities of a flat model of aircrafts, illustrated with numerical simulations using Python and Maple. We consider failure situations and maneuvers for which apparent singularities of the previously known flat outputs may appear, making necessary to use some of the new flat outputs we consider. Basically, the aircraft flat outputs are $x$, $y$, $z$, the coordinates of the gravity center, completed with any function of the sideslip angle $\beta$, the angle of attack $\alpha$, the bank angle $\mu$ and the thrust $F$. The choice of $\beta$ was previously used, but does not allow gravity-free flight, for which $\mu$ is the best choice, as well as for decrabe maneuver. The choice of $F$ is adapted for dead-stick landing conditions with $\beta\neq0$, such as forward slip maneuver. This approach also allows to replace usual control with new controls in case of failures, e.g. differential thrust can be used in case of rudder failure. Our results are illustrated by numerical simulations, using realistic non linear aerodynamics models. In a first stage, we investigate the ability of the flatness based control to reject perturbations. Since flatness in that case requires some model simplification, in a second stage, we focus on model errors and show that a suitable feed-back allows to keep trajectories with the complete real model close to the trajectories planned with the simplified one.