Analysis and Control of Aircraft Longitudinal Dynamics subject to Steady Aerodynamic Forces

The paper contributes towards the development of a unified control approach for longitudinal aircraft dynamics. Prior to the control design, we analyze the existence and the uniqueness of the equilibrium orientation along a desired reference velocity. We show that shape symmetries and aerodynamic stall phenomena imply the existence of the equilibrium orientation irrespective of the reference velocity. The equilibrium orientation, however, is not in general unique, and this may trigger an aircraft loss-of-control for specific reference velocities. Conditions that ensure the local and the global uniqueness of the equilibrium orientation are stated. We show that the uniqueness of the equilibrium orientation is intimately related to the possibility of applying the spherical equivalency, i.e. a thrust change of variable rendering the direction of the transformed external force independent of the vehicle's orientation, as in the case of spherical shapes. Once this transformation is applied, control laws for reference velocities can be designed. We show that these laws extend the thrust direction control paradigm developed for systems with orientation-independent external forces, e.g. spherical shapes, to orientation-dependent external forces, e.g. generic shapes.