Aerospace and Electronic Systems Magazine July 2017 - 33

Pasand, Hassani, and Ghorbani
Table 7. Extended

No. Pulses
Linear Displacement (m)
Average
No.
Pulses per
Thruster

Mean
PW
(ms)

Conf. 1

333

137

Conf. 2

193

Conf. 3

Conf. No.

Standard Deviation (ms)
1*

Three
Axis

Fuel
Cons.
(kg)

2**

3***

x

y

z

110

20

10

665

665

−739

140

99

29

10

−15.9

6.1

3.1

17.3

1.27

195

138

100

30

10

10

−2

−3.4

10.8

1.25

Conf. 4

236

157

110

30

10

−16.1

9.7

7.2

20.1

1.50

Conf. 5

177

156

109

40

10

0.74

−1.6

1.5

2.3

1.23

Conf. 6

289

112

100

20

10

−2

−0.9

1.8

2.8

1.27

Conf. 7

178

109

100

30

10

12.9

13.2

−12.7

22.4

1.05

Conf. 8

199

113

100

50

10

−8.9

−9.5

8.6

15.6

1.23

Conf. 9

309

116

99

19

10

263

246

−248

Conf. 10

158

115

99

39

10

−1.8

0.1

0.2

1.8

0.90

Conf. 11

221

133

100

50

10

−2

−0.9

1.8

2.8

1.41

Conf. 12

224

130

100

50

10

6.5

7.6

−6.9

12.2

1.37

Conf. 13

174

116

110

30

10

−0.46

−0.20

0.37

0.62

1.04

Conf. 14

188

113

100

30

10

−0.73

−0.21

0.61

0.98

1.14

1,196

437

20.8

6.82

Conf., configuration; Cons., consumption.
* 68% of total data.
** 95% of total data.
*** 99.7% of total data.

of 0.047° and 0.046° on average, respectively. Afterward, configuration 10, with an accuracy of 0.051°, has the best performance. From Table 7, it is clear that there is no meaningful link
between the number of thrusters and the average of the three-axis
accuracy.
Thruster valves are exposed to erosion and corrosion when
they are opened and closed. To minimize thruster valve wear, it is
desirable to minimize the number of thruster firings by the PWPF
modulator. According to the table, the average number of pulses
per thruster is approximately proportional to the fuel consumption.
For example, while the fuel consumption of configuration 10 is
0.90 kg and its average number of pulses per thruster is 158, the
fuel consumption of configuration 4 is 1.5 and its average number
of pulses per thruster is 236. Consequently, selecting a configuration with less fuel consumption leads to a configuration with fewer
pulses, less wear, and a longer life cycle.
According to Table 7, configurations with four and six thrusters have wider pulses compared to configurations with more
thrusters. This makes sense, because fewer thrusters are employed to realize the required torques; therefore, the configuration needs to have wider working pulses. Based on the informaJULY 2017

tion, the minimum pulse width of the PWPF modulators is equal
to 10 ms, the same as the closed-loop sampling rate. In addition,
68% of pulse-width data, which lie within [−1σ, 1σ], are between
0 and 99 or 110 ms for all configurations. In Figure 5, the distribution of PWPF modulator pulse width is showed. Considering that the acceptable PWPF pulse width is 50 ms-because of
some cold-gas thruster design considerations-the percentage of
pulses in the acceptable range is shown above each figure. According to Figure 5, configurations 1 and 9 have fewer pulses
in the acceptable range. This percentage for other configurations
ranges from 85% to 95%.
With regard to the point that thrusters do not produce meaningful thrust in the coast phase, in general, linear displacement
is negligible in the coast phase compared to the firing phase,
which is supposed to apply more powerful thrusters. Regardless
of the mission, it can be claimed that increasing the number of
thrusters to 16 decreases the linear displacement considerably.
In addition, configurations 5, 6, 10, and 11 benefit from a low
value of linear displacement. It can be seen that configuration
1 and 9 have the worst performance from the aspect of linear
displacement.

IEEE A&E SYSTEMS MAGAZINE

33



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