A trim problem formulation for maximum control authority using the Attainable Moment Set geometry

This paper presents a generic trim problem formulation, in the form of a constrained optimization problem, which employs forces and moments due to the aircraft control surfaces as decision variables. The geometry of the Attainable Moment Set (AMS), i.e. the set of all control forces and moments attainable by the control surfaces, is used to define linear equality and inequality constraints for the control forces decision variables. Trim control forces and moments are mapped to control surface deflections at every solver iteration through a linear programming formulation of the direct Control Allocation algorithm. The methodology is applied to an innovative box-wing aircraft configuration with redundant control surfaces, which can partially decouple lift and pitch control, and allow direct lift control. Novel trim applications are presented to maximize control authority about the lift and pitch axes, and a “balanced” control authority. The latter can be intended as equivalent to the classic concept of minimum control effort. Control authority is defined on the basis of control forces and moments, and interpreted geometrically as a distance within the AMS. Results show that the method is able to capitalize on the angle of attack or the throttle setting to obtain the control surfaces deflections which maximize control authority in the assigned direction. More conventional trim applications for minimum total drag and for assigned angle of elevation are also explored.