Gearing Matrix Definition via Control Allocation Optimization Applied to an Over Actuated Aircraft

In over actuated aircrafts a simple relationship between control inputs and forces/moments generated does not exist, however they have become very attractive for their wide range of applications. Control allocation aims at finding a unique surface control distribution as function of flight condition to perform the desired maneuver. The goal of this paper is to present a control allocation methodology applied on a generic over actuated aircraft aimed to determine the surface gearing matrix weights in different operative conditions to minimize the total power consumption. First, the non-linear model of the control forces and moments is derived for an over actuated aircraft. Then, two different optimization problems are introduced: the first to compute the trim equilibrium for any flight condition to minimize power consumption by the aircraft; the second to minimize the surface deflections required to produce desired control forces/moments starting from the trim point previously found. Finally, the optimized solution is subjected to engineering judgement to neglect the ineffective surfaces that do not provide a significant contribution to the required maneuver.