Analysis and Control of Aircraft Longitudinal Dynamics with Large Flight Envelopes

TL;DR

This paper develops a unified control approach for aircraft longitudinal dynamics over large flight envelopes, analyzing equilibrium orientations and introducing a transformation to extend vectored-thrust control to generic aircraft shapes.

Contribution

It analyzes equilibrium orientation existence and uniqueness, and introduces a spherical equivalency transformation to enable advanced control laws for diverse aircraft shapes.

Findings

Equilibrium orientation exists regardless of reference velocity due to shape symmetries.

Uniqueness of equilibrium orientation is linked to spherical equivalency.

Control laws are extended to generic shapes using the transformation.

Abstract

The paper contributes towards the development of a unified control approach for longitudinal aircraft dynamics with large flight envelopes. Prior to the control design, we analyze the existence and the uniqueness of the equilibrium orientation along a 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 so-called spherical equivalency, i.e. the existence of 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. These laws extend the so-called vectored--thrust control paradigm %developed for systems subject to orientation-independent external forces, e.g. spherical shapes, to the case of generic body shapes subject to steady aerodynamics.