Aerospace and Electronic Systems Magazine July 2017 - 30

Reaction Control Thruster Configurations for a Three-Axis Attitude Control System

Figure 3.

The uniform angular momentum distribution on a sphere's surface.

The simulation is divided in two parts: static behavior simulation and dynamic behavior simulation.

STATIC BEHAVIOR ANALYSIS
The aim of static analysis is to achieve a configuration with minimum fuel consumption in any direction by assessing the overall
angular momentum space. In [18], for a given configuration, a
specific direction is determined so that it produces the minimum
angular momentum in the presence of a time constraint. However,
this definition is not appropriate for selecting the optimal configuration, because we assume that there is no time constraint to
provide angular momentum. Therefore, it can be seen that other
configurations have the same level of angular momentum with less
fuel consumption.
In this paper, it is proposed to compare different configurations
in terms of control capabilities and fuel consumption statically.
The fuel consumption-assessing criterion should be revised in the
following form: Total fuel consumption is equal to the summation
of each thruster's fuel consumption for a given configuration in
different directions. In such a case, the time constant is omitted.
To realize the following definition, it is assumed that a number of
sample points are uniformly distributed on a unit sphere's surface
according to Figure 3. The more points on the sphere's surface, the
more accurate the comparison among configurations. If the points
are linked to the sphere's center, it will be seen that the resulting
unit vectors cover the whole three-axis space. In other words, every vector can be constructed by multiplying the mentioned vector

by a scalar. Afterward, for each point on the sphere's surface, the
LP in (10) is carried out.
The numerical simulations are assessed in the terms of minimum C.C., the direction of minimum C.C., maximum C.C., the
direction of maximum C.C., and fuel consumption according to
Table 6. The C.C. in each direction is calculated by dividing angular momentum by fuel consumption in that direction. It was considered that angular momentum points are located on the sphere
surface; therefore, the C.C. is obtained by reversing fuel consumption in each direction. The C.C. distribution corresponding to the
first configuration is demonstrated in Figure 4 as an example.

Figure 4.

A sample of the C.C. distribution of the first configuration.

30

IEEE A&E SYSTEMS MAGAZINE

JULY 2017



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