The purpose of control allocation is to choose a configuration of the control effectors to meet a specified objective. Mathematically, the attainable moment subset (AMS) produced by control surfaces can be expressed as a mapping of the subset of constrained controls into the moment space. The determination of the AMS is very important to the solving of the allocation problem. For the two-dimensional allocation problem, a numerical algorithm is proposed to solve the AMS on-line. For the complex three-dimensional allocation problem, by analyzing its allocation characteristic, some comprehensive mathematic analyses are given to solve the three-dimension AMS. After that, an improved direct allocation algorithm based on the determination of AMS is proposed. Compared to the common direct allocation algorithm at fast speed, the improved algorithm can find the right facet which intersects with the desired moment and improves the real time performance of the allocation system well.
With the improvement of the aircraft performance in reliability, maneuverability and survivability, the number of the control effectors increases a lot. How to distribute the three-axis moments into the control surfaces reasonably becomes an important problem. Daisy chain method is simple and easy to be carried out in the design of the allocation system. But it can not solve the allocation problem for entire attainable moment subset. For the lateral-directional allocation problem, the allocation efficiency of the daisy chain can be directly measured by the area of its subset of attainable moments. Because of the non-linear allocation characteristic, the subset of attainable moments of daisy-chain method is a complex non-convex polygon, and it is difficult to solve directly. By analyzing the two-dimensional allocation problems with a “micro-element” idea, a numerical calculation algorithm is proposed to compute the area of the non-convex polygon. In order to improve the allocation efficiency of the algorithm, a genetic algorithm with the allocation efficiency chosen as the fitness function is proposed to find the best pseudo-inverse matrix.