CLOSED-FORM SOLUTIONS TO CONSTRAINED CONTROL ALLOCATION PROBLEM

This paper describes the results of recent research into the problem o f allocating several flight control effecters to generate moments acti ng on a flight vehicle. The results focus on the use of various genera lized inverse solutions and a hybrid solution utilizing daisy chaining . In this analysis, the number of controls is greater than the number of moments being controlled, and the ranges of the controls are constr ained to certain limits. The control effecters are assumed to be indiv idually linear in their effects throughout their ranges of motion and independent of one another in their effects. A standard of comparison is developed based on the volume of moments or moment coefficients a g iven method can yield using admissible control deflections. Details of the calculation of the various volumes are presented. Results are pre sented for a sample problem involving 10 flight control effecters. The effectivenesses of the various allocation schemes are contrasted duri ng an aggressive roll about the velocity vector at low dynamic pressur e. The performance of three specially derived generalized inverses, a daisy chaining solution, and direct control allocation are compared.