Trim for Maximum Control Authority using the Attainable Moment Set

Abstract

This paper presents a method to find trimmed flight conditions while maximizing the available control authority about one or more motion axes. Maximum pitch-up, or lift-up, control authority could find interesting application in aborted landing situations, while maximum balanced control authority about all motion axes is a reformulation of the classic concept of minimum control effort. The trim problem is formulated in the form of a constrained optimization problem. The constraints and the objective function are obtained by exploiting the geometric properties of the Attainable Moment Set, a convex polytope containing the forces and moments attainable by the aircraft control effectors. The method is applied to an innovative box-wing aircraft configuration called PrandtlPlane, whose double wing system can accommodate a large number of control surfaces, and hence allow Pure Torque and Direct Lift Control possibilities. Control surface deflections are compared for trim conditions with maximum control authority in the pitch axis, in the lift axis, and maximum balanced control authority, for symmetric and asymmetric flight. 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.

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

“…The paper formalizes, streamlines and expands the previous research effort, reported in [4]. With respect to the previous work, several new applications are presented for a box-wing aircraft configuration.…”

Required Moment Sets: Enhanced Controllability Analysis for Nonlinear Aircraft Models

“…In order to finally perform a control set-based controllability analysis, the attainable control set needs to be calculated and transformed to the query direction-based control set interface. There are methods for evaluating the attainable moments for nonlinear control effector models [5]. For the exemplary multirotor electric vertical take off vehicle (eVTOL) configurations that are the focus of this paper, simplified propellers with thrust and propeller torque that is linear in the squares of the angular propeller rates are used.…”

“…A method which enables the applicability to nonlinear systems was investigated in [4]. A more novel trim and optimization-based method for calculating a nonlinear AMS was developed in [5]. After the AMS is calculated, a very important question is also how to judge the controllability of the given AMS.…”

Attainable Moment Set Optimization to Support Configuration Design: A Required Moment Set Based Approach

“…where m ∈ R k is the moment vector; u ∈ R m is the input vector (k and m are the number of moments and inputs, respectively); B ∈ R k×m is the so-called effectiveness matrix representing each input's moment generation capability; u and u are respectively the lower and upper limits of the inputs. This concept can be extended to other quantities, such as generalized forces or pseudo controls, e.g., direct forces or angular accelerations, as long as the quantity is algebraically related to the system inputs [3]. The AMS has a big impact on the performance of a system from a control perspective.…”

“…As for AMS optimization, a generic AMS framework is proposed in [7] to aid visualize AMSs of complex systems during design phase, which is then conceptually applied to the Max Launch Abort System escape vehicle to help decide the optimal orientation of the thrust nozzles. In [3], a trim routine is developed for an unconventional box-wing configuration to maximize local AMS at operation point. Although it does not directly relate to effector configuration of the system, it implements an optimization framework to exploit best control capability given the system redundancy.…”