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

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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)

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23232323232323

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Maneuver duration = 12000 seconds.

Pitch angle Roll angleYaw angle

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Roll angle (deg)Yaw angle (deg)

Pitch angle (deg) Rate (deg/sec)

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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