Research on attainable moment subset of singular over-actuated system

Attainable moment subset (AMS) is an important concept in control allocation problem of aircrafts with multiple control surfaces. It is produced by effectors and can be expressed as a mapping of the subset of constrained controls into the moment space. Determination of AMS is useful to calculate the aerodynamic efficiency of combined surfaces and evaluate the performance of the allocation system. But existing AMS calculation methods can only solve the cases that every 3 by 3 matrix formed of the columns of control effectiveness matrix be of full rank. And there is no method for the cases that not satisfy the condition. Focusing on this problem, the geometry structure characteristics of AMS is deeply studied. With the relationships among vertexes, edges and faces of AMS determined, a method is proposed to solve the problem. Simulation results show that the method can solve the AMS of singular over actuated system well.