Constrained control allocation

This paper addresses the problem of the allocation of several flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being controlled, and the ranges of the controls are constrained to certain limits. The controls are assumed to be individually linear in their effect throughout their ranges of motion, and independent of one another in their effects. The geometries of the subset of the constrained controls and of its image in moment space are examined. A direct method of allocating these several controls is presented, that guarantees the maximum possible moment is generated within the constraints of the controls. The results are illustrated by an example problem involving three controls and two moments.