Closed-Form Solutions to the Constrained Control Allocation Problem

摘要

This paper describes the results of recent research into the problem of allocating several flight control effectors to generate moments acting on a flight vehicle. The results focus on the use of various generalized 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 constrained to certain limits. The control effectors are assumed to be individually linear in their effects throughout their ranges of motion, and independent of one another in their effects. It is shown that many current methods, including pseudo-inverses and other generalized inverses, allocate admissible controls for only a small portion of the moments that are attainable using other methods. Results are presented for a sample problem involving ten flight control effectors. The various allocation schemes are employed during an aggressive roll about the velocity vector at low dynamic pressure. The maneuver is designed such that all the required body-axis moments are attainable by some combination of the available control effectors. The performance of three specially derived generalized inverses, a daisy-chaining solution, and direct control allocation are compared.