CONSTRAINED CONTROL ALLOCATION

This paper addresses the problem of the allocation of several airplane flight controls to the generation of specified body-axis moments. The number of controls is greater than the number of moments being contro lled, and the ranges of the controls are constrained to certain limits . They are assumed to be individually linear in their effect throughou t their ranges of motion and independent of one another in their effec ts. The geometries of the subset of the constrained controls and of it s image in moment space are examined. A direct method of allocating th ese several controls is presented that guarantees the maximum possible moment can be generated within the constraints of the controls. It is shown that no single generalized inverse can yield these maximum mome nts everywhere without violating some control constraint. A method is presented for the determination of a generalized inverse that satisfie s given specifications which are arbitrary but restricted in number. W e then pose and solve a minimization problem that yields the generaliz ed inverse that best approximates the exact solutions. The results are illustrated at each step by an example problem involving three contro ls and two moments.