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https://ntrs.nasa.gov/search.jsp?R=20160011230 2020-04-28T14:29:06+00:00Z
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• Pure yaw maneuver : roll and pitch angles remain zero.
• Consider a 180 deg. pure yaw maneuver. This maneuver is performed using thrusters.
• For such a maneuver the torques in roll ( 𝑇𝑥) and pitch ( 𝑇𝑦) can be written as:
𝑇𝑥 = − 𝐶 − 𝐵 + 𝐴 𝑛 𝛼𝑐𝑜𝑠𝛼𝑇𝑦 = 𝐶 + 𝐵 − 𝐴 𝑛 𝛼𝑠𝑖𝑛𝛼
where:A, B, C - are the ISS principal moments of inertia, 𝑛 - orbital rate, 𝛼 − yaw angle.
• For the ISS mass properties and common maneuver durations (about 5400 sec.) these torques are large with respect to the CMG capabilities.
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0 1000 2000 3000 4000 5000
-200
-100
0
100
200
Time (sec)
Ro
ll t
orq
ue (
Nm
)
Roll torque during a 180 deg. pure
yaw maneuver.
• Torque is rather large - much more than the ISSCMGs can handle without desaturation.
• Goal of a maneuver optimization is to reducethese torques.
• Gravity torques can be used to solve the problem by compensating for these torques.
• This compensation is the essence of the suggested method.
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Torque telemetry
Calculated torque
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𝛾 = 𝜆 𝛼 𝑐𝑜𝑠𝛼 + 𝜆1 𝛼 𝛼 𝑠𝑖𝑛𝛼 + 𝜆2 𝛼 𝑐𝑜𝑠𝛼𝛽 = 𝜇 𝛼 𝑠𝑖𝑛𝛼 + 𝜇1 𝛼 𝛼 𝑐𝑜𝑠𝛼 + 𝜇2 𝛼 𝑠𝑖𝑛𝛼, where:
𝜆 = −(𝐶−𝐵+𝐴)
4𝑛(𝐶−𝐵), 𝜇 =
(𝐶−𝐴+𝐵)
4𝑛(𝐶−𝐴)
𝜆1 =−3𝐴 𝜆−𝐴𝜇 + 𝐶−𝐵−𝐴 𝜇
4𝑛2 (𝐶−𝐵), 𝜇1 =
−3𝐴 𝜆−𝐴𝜇 + 𝐶−𝐵−𝐴 𝜇
4𝑛2 (𝐶−𝐴)
𝜆2 = 𝜀1𝐴 𝜆
4𝑛2 (𝐶−𝐵), 𝜇2 = 𝜀2
𝐵 𝜇
4𝑛2 (𝐶−𝐴)(𝜀1 = 0.1 , 𝜀2 = 0.6, for example, for OPM).
• 𝜀1 and 𝜀2 values are obtained based on the selected optimization criteria.• Equations for a more accurate solution can be found in [3].
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Roll torque reduction.Pitch torque reduction. Yaw torque reduction.
Simulations showed that the proposed solution provides the maneuverperformance similar to the existing computational solution.
Time (sec) Time (sec)Time (sec)
Roll
torq
ue
(Nm
)
Yaw
torq
ue
(Nm
)
Pit
chto
rque
(Nm
)
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Roll torque reduction.Pitch torque reduction. Yaw torque reduction.
More significant torque reduction forlonger maneuver.
Time (sec) Time (sec)Time (sec)
Roll
torq
ue
(Nm
)
Pit
chto
rque
(Nm
)
Yaw
torq
ue
(Nm
)
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Maneuver duration = 5400 seconds.Legend:
Blue line – analytical solution
Brown line – Draper Laboratory computational solution
Pitch torque comparison. Roll torque comparison.
0 1000 2000 3000 4000 5000-50
-40
-30
-20
-10
0
10
20
30
40
Time (sec)
Pit
ch t
orq
ue
(Nm
)
0 1000 2000 3000 4000 5000
-100
-80
-60
-40
-20
0
20
40
60
Time (sec)
Roll
torq
ue
(Nm
)
0 1000 2000 3000 4000 5000 6000-60
-40
-20
0
20
40
60
Time (sec)
Yaw
torw
ue
(Nm
)
Yaw torque comparison.
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Maneuver duration 5400 seconds.Legend:
Blue line – analytical solution
Brown line – Draper Laboratory computational solution
0 1000 2000 3000 4000 5000 6000-5
0
5
10
15
20
25
30
35
Time (sec)
Pit
ch
an
gle
(d
eg
.)
0 1000 2000 3000 4000 5000 6000
-15
-10
-5
0
5
10
15
Time (sec)
Roll
angle
(deg.)
Pitch profile. Roll profile. Yaw profile.
2020
OPM to -XVV. Torques: Red – yaw, Yellow– roll, Green – pitch
Flight dataCalculated OPM
212121212121
Time(sec)
Pro
pel
lan
t (k
g)
Current OPM duration =5400s
duration =7000s
duration =9000s
22222222
Torques: Red – yaw, Blue– roll, Green – pitch
Roll torque increased,
pitch torque decreased
Roll torque decreased,
pitch torque increased
Total prop consumption
the same
Prop (kg)Torque (Nm) Torque (Nm)
22
23232323232323
24242424242424
2525252525
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Maneuver duration = 12000 seconds.
Pitch angle Roll angleYaw angle
272727
Roll angle (deg)Yaw angle (deg)
Pitch angle (deg) Rate (deg/sec)
282828282828
ISS mass properties - year 2016 CMG saturation level : H ~ 19500 Nms
Version 2. (final momentum is less)
Max H = 12070 Nms (~ 61% ).Version 1.
Max H = 11610 Nms (~ 60% ).
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Maneuver duration = 9000 sec.
CMG Momentum (H)
Maneuver duration = 8000 sec.
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X
𝛼
Z
x1
y1
, z1
x2
z2
, y2
, x3
z3 y3
O Y
𝛽
𝛾
Euler angles: 𝛼 − yaw angle, 𝛽 − pitch angle, 𝛾 − roll angle.Define position of a body coordinate system with respect to LVLH.
X Y
Z Orbit of the
station
ISS velocity
vector
LVLH coordinate system
Center of Earth
O
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Time(sec)
Integrals of the absolute torque values per axis
Current OPM duration =5400s
duration =7000s
duration =9000s