Multiple Control Effector Rate Limiting

The effect of the choice of control allocation scheme upon individual control effector rate demands is examined. Three previously reported and one new variation of control allocation schemes are described and compared. The new allocation scheme exploits the maximum attainable moment-rates of a given control effector configuration and is called moment rate allocation. The bases of comparison are single-axis sinusoidal and triangular sawtooth, and multi-axis helical time-varying moment demands placed upon the allocation schemes. It is shown that (1) the choice of allocation scheme greatly affects the onset of effective rate-limiting for a particular time-varying input, but not consistently for all inputs; (2) widely varying results are obtained depending on whether the input is singleor multiaxis, and on the amplitude and shape of the input; (3) none of the observed behavior (except as regards generalized inverses) was easily predictable for arbitrary time-varying inputs; and (4) from the point of view of moment and moment-rate generating capabilities, moment rate allocation yielded clearly best results. NOMENCLATURE u .........................Vector of controls m.........................Vector of moments m .........................Number of controls B .........................Matrix of control effectiveness P .........................Generalized Inverse Matrix AMS ....................Attainable Moment Subset AMRS .................Attainable Moment Rate Subset GI .......................Generalized Inverse DC ......................Daisy-Chaining DA.......................Direct Allocation MRA ...................Moment-Rate Allocation Rest .....................Restoring d ..........................Desired * Asst. Prof, Aerospace & Ocean Engineering Dept. Senior Member, AIAA. ** Graduate Student, Aerospace & Ocean Engineering Dept.