Design of a Nonlinear Roll Mechanism for Airplanes Using Lie Brackets for High Alpha Operation

Abstract

A nonlinear controllability analysis for fixed-wing aircraft has been performed in an earlier effort by the authors, which revealed a novel roll mechanism due to a nonlinear interaction between elevator and aileron control inputs. In this effort, we perform a detailed investigation of this novel roll mechanism, called Lie Bracket Roll Augmentation (LIBRA). First, we show the nonlinear flight physics associated with the LIBRA mechanism. Second, using the Fliess functional expansion, we perform a theoretical study of the effectiveness (degree of controllability) of the LIBRA mechanism in comparison to the conventional mechanism (using ailerons only). Third, to simulate the airplane response to a LIBRA input, we cast the problem of executing the LIBRA mechanism as a nonholonomic motion planning problem. In such a problem, a Lie bracket input is applied to generate motion along an unactuated direction. A Lie bracket input represents a nonlinear interaction between two (or more) control inputs to steer the system along a direction that is not directly actuated by any of these inputs (or their linear combinations). In this language, the LIBRA mechanism is simply a Lie bracket interaction between the elevator and aileron control inputs. We modify existing nonholonomic motion planning algorithms for systems with drift to be more feasible for flight control applications with bounded controls. We show that the LIBRA novel roll mechanism is superior compared to the conventional one during stall, where the aileron sensitivity degrades. In particular, the novel roll mechanism can provide an order of magnitude enhancement in the rolling capability over the conventional roll mechanism near stall.