Drag-free control and drag force recovery of a small satellite

Small Satellite Technologies for Drag-free Control and Drag force

RecoveryAnh N. Nguyen ([email protected])

John W. Conklin ([email protected])

31ST ANNUAL AIAA/USU CONFERENCE ON SMALL SATELLITES

10-Aug-2017

Why do I care about drag-free spacecraft?

2

3

Navigation

4

GRACE Gravity Field Maps

Earth Science

5

May Jun Jul Aug

Sep Oct Nov Dec

Jan Feb Mar Apr

2004 Water height (from average) in cm

-20 -15 -10 -5 0 5 10 15 20

6

Fundamental Physics

GP-B: Geodetic & Frame dragging effects

7

Astrophysics

Gravitational Waves

What is a Drag-free Spacecraft?

.ext distF

scm

,

g

sc F

,

g

pm F

pmm

Newton’s Law of Gravitation

Proof mass (PM)

Earth

pmm

,

g

pmF

m

r

, /

g

pm pm pmm F r

,

g

pm F

,

g

i j F Force of gravity on from i j

10

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g

sc F

,

g

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pmm

Presence of Disturbance Forces

,

,

3

3

g pm pm

pm c a pm pm

g pm pmpm c a

pm

pm pm pm

pm pm

c apm pm

pm pm pm

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m m m

GM

r m m

F F F r

F F Fr

F Fr r

Proof-mass (PM) EOM

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3 2

g sc

sc c ext sc scg scsc c ext

sc

sc sc scsc

c extsc sc

sc sc sc

m

m m m

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F F Fr

F Fr r

Spacecraft (SC) EOM

/

/ /

/ / /

1

pm sc

pm sc

pm sc pm sc

z r

r r

z r r r

Measurement

11

, /3

/

g

i ii

i

GM mr

r

F

Gravitational Force

pm

residualF

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c cF F

Control Forces

Residual Forces

sc

controlF

pm

residualF

pm

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Governing Equation of Motion

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Measurement

Substitute (1) and (2) into (3)

./ 3 3

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3 3

4

pm pm sc

c a c extpm sc pm sc

pm pm pm sc sc sc

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GM GM

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F F F Fr r r

F F F Fr r

./ 5

pm sc pm

c c ext residualpm sc

pm sc sc pmm m m m

F F F Fr

When , pm scr r

12

Drag-free Design Concept

• Gravitational Reference Sensor (GRS)

• Inner free-floating proof mass (PM)

• Outer electrode housing

• Outer SC flies in formation with PM using propulsion system

• Performance measured by the amount of residual acceleration noise on PM, pm

residualF

./

/ . .

5

6

pm sc sc pm

c c ext residualpm sc

pm sc sc pm

pm pm sc sc

pm sc residual control control ext dist

m m m m

F F F Fr

r F F F F

13

Category ApplicationPerformance

(ms-2Hz-1/2), frequency (Hz)Metrology

(mHz-1/2)

Navigation

Autonomous, fuel-efficient orbit maintenance

≤10-10, near zero frequency

≤10 absolute

Precision real-time on-boardnavigation


≤10 absolute

Earth Science

Aeronomy ≤10-10, 10-2 to 1 Hz 1 absolute

Current Earth Geodesy[2] 10-10, 10-2 to 1 Hz 10-5 differential

Future Earth Geodesy[3] ≤10-10, 10-2 to 1 Hz ≤10-9 differential

Fundamental Physics

Equivalence Principle Tests[4] ≤10-10, 10-2 to 1 Hz ≤10-10 differential

Tests of General Relativity≤10-10, near zero

frequency≤1 absolute

Astrophysics Gravitational Waves[5] 3×10-15, 10-4 to 1 Hz ≤10-11 differential

Performance

14

[2] Tapley, B. D., Bettadpur, S., Watkins, M., & Reigber, C. (2004). Geophysical Research Letters, 31(9)., [3] Barney, R. D. (2010). DRAFT Science Instruments, Observatories, and Sensor Systems Roadmap, Technology Area 08., [4] Touboul, P., Rodrigues, M., Métris, G., & Tatry, B. (2001). Comptes Rendus de l'Académie des Sciences- Series IV- Physics, 2(9), 1271-1286., [5] Danzmann, K., & Rüdiger, A. (2003). LISA technology—concept, status, prospects. Classical and Quantum Gravity, 20(10), S1.

1. PM centered and shielded in housing.

Electrostatic Accelerometer

2. External disturbance

force acts on SC

3. Suspension compensates disturbance

4. PM remains in centered

Limited by suspension force noise and acceleration measurement noise

/pm scrsmall pm

residual Fsmall

pm sc

control control F F0

. .

. .

sc

ext dist

sc pm

ext dist control

F

F F

15

‘Accelerometer’ Drag-free control

3. Thruster minimizes suspension force

required to compensate disturbance.

2. Disturbance force acts on SC

4. PM remains in geodesic

1. PM centered and shielded in housing,

following pure geodesic 16

Propulsion minimizes suspension force, which is used as the error signal

/pm scrsmall pm

residual Fsmall

pm

control F . .

smallsc sc

control ext dist F F

small

No direct scientific data, need external measurements

‘True’ Drag-free control

3. Thruster system compensates disturbances


following pure geodesic



undisturbed17

18

Gravity Recovery and Climate Experiment (GRACE)487 kg (each), 2002

Gravity Probe-B (GP-B)3,100 kg, 2004

Gravity Field and Steady-State Ocean Circulation Explorer (GOCE)

1,077 kg, 2009

Disturbance Compensation System (DISCOS) [8]

3,100 kg, 1972

LISA Pathfinder (LPF)[9] 1,910 kg,

2014

LISA

Spacecraft 1

Spacecraft 2 Spacecraft 3

Laser Inteferometer Space Antenna (LISA) [10]

19

Category ApplicationPerformance

(ms-2Hz-1/2), frequency (Hz)

Metrology(mHz-1/2)

Navigation

Autonomous, fuel-efficient orbit maintenance


≤10 absolute

Precision real-time on-board navigation


≤10 absolute

Earth Science

Aeronomy ≤10-10, 10-2 to 1 Hz 1 absolute

Current Earth Geodesy[2] 10-10, 10-2 to 1 Hz 10-5 differential

Future Earth Geodesy[3] ≤10-10, 10-2 to 1 Hz ≤10-9 differential

Fundamental Physics

Equivalence PrincipleTests[4] ≤10-10, 10-2 to 1 Hz

≤10-10

differential

Tests of General Relativity≤10-10, near zero

frequency≤1 absolute

Astrophysics Gravitational Waves[5] 3×10-15, 10-4 to 1 Hz≤10-11

differential

20

Design 1: Single Thruster Drag-free

3. Control system fires thruster and orients SC

in direction of disturbance





21

I. Single Thruster Drag-free

3. Control system fires thruster and orients SC

in direction of disturbance





22

Single thruster and 3-DOF ADACS required to control position and orientation of the SC. Most fuel-efficient drag-free

/pm scrsmall pm

residual Fsmall

pm

control F0

. .

sc sc

control ext dist F F

small

No direct scientific data, need external measurements

Single Thruster Satellite Design

DRAG-FREE CUBESAT[10]

Orbit: Circular Polar

Altitude: 400 km

Period: 5554 s

SC Mass: 4 kg

SC Dimensions: 10 × 10 × 34 cm

Housing Dimensions:

50 mm cavity

TM Mass: 171 g

TM Radius: 12.5 mm

Min. Gap: 25 mm

ˆ x

ˆ y ˆ z

dF

23

Caging System[10]Test Mass with Differential Optical Sensor (DOSS)[10]

ion Electrospray Propulsion System (iEPS)[11]

Zero-G Test Flight

Instrumentation

COTS Attitude Determination and Control System (ADACS)[13]

VACCO Micro Propulsion System [12]

[10] Conklin, J., et. al. (2012). The Drag-free CubeSat., [11] Martel, F., Perna, L., & Lozano, P. (2012). Miniature Ion Electrospray Thrusters and Performance Test on CubeSats., [12] Vacco Space Products, [13] Blue Canyon Technologies, XACT

24

Performance ˆ x

ˆ y ˆ z

dF

RMS Errors (µN)

Fdx 0.73

Fdy 0.034

Fdz 0.0037

Acceleration measurement error(m/s2Hz-1/2) @10mHz

x ~10-11

y ~10-11

z ~10-1225

Residual Meas. Error (x)

m/s

2H

z-1/2

Fdx

(µN

)Fd

y(µ

N)

Fdz

(µN

)

Estimated and True Disturbance Forces

II. Drift-mode Accelerometer

1. PM centered and shielded in

housing

2. External disturbance force

acts on SC

4. Suspension OFF for 5 sec and meas. taken

before suspension turns ON

3. Suspension turned ON for 1 sec,

to compensate disturbances

Acceleration noise performance close to that of drag-free without the need for spacecraft propulsion

/

pm

pm sc residualr Fsmall

pm sc

control control F F0

. .

/ . .

/ . .

Actuation ON:

Actuation OFF:

sc

ext dist

pm sc

pm sc control ext dist

sc

pm sc ext dist

F

r F F

r F

26

27

Suspension ON

ImpulseSuspension OFF

Drift

Suspension ON

Impulse

12

14 2

5/25/2

1.0 10 m1 1.8 10 ms

5 s

pm

r ia

kickT

Expected Acceleration Measurement Noise[20]

Orbit Circular Polar

Altitude 400 km

Period 5554 s

SC Mass 250 kg

SC Radius 0.7 m

SC Length 1.4 m

28

SCPM

dF

cF

cT

xPM Mass 0.24 kg

PM/Housing Gap 1 mm

PM length 3 cm

Concept Spacecraft & PM Design

SmallSat GRACE II(GRACE shown)

Performance

29

10

12

12

1.1 10

5.6 10

4.3 10

ms-2Hz-1/2 at 10 HzMode

EA

DMA

c-DMA

DMA True and Estimated Acceleration ASDs

m-2

Hz-1

/2 Estimated Error

Bulk

In Summary

30

Technology Thruster?Suspension

System?Laser Inter-ferrometer?

Residual Acc. Noise(ms-2Hz-1/2)

Electrostatic Accelerometer

No Yes No 2×10-11GRACE[2],

2002

‘Accelerometer’ drag-free control

Yes (×6) No No4×10-11

~10-12

GP-B[6], 2004

GOCE[7], 2009

‘True’ drag-free control

Yes (×6) Yes

No

Yes

Yes

~10-10

~10-14

~10-15

DISCOS[8],

1972

LPF[9], 2014

LISA[5], 2034

Single-thruster drag-free control

Yes (×1) No No ~10-11

Drift-mode control

No Yes Yes ~10-12

31

32

Residual Acceleration

~10-12 ms-2Hz-1/2

GRS

What’s next?

34

Mars Gravity Field Maps

35

Europa

Near Earth Objects

??

References[1] Lambeck, K. (1988). Geophysical geodesy (p. 718). Oxford: Clarendon

[2] Tapley, B. D., Bettadpur, S., Watkins, M., & Reigber, C. (2004). The gravity recovery and climate experiment: Mission overview and early results.Geophysical Research Letters, 31(9).

[3] Barney, R. D. (2010). DRAFT Science Instruments, Observatories, and Sensor Systems Roadmap, Technology Area 08.

[4] Touboul, P., Rodrigues, M., Métris, G., & Tatry, B. (2001). MICROSCOPE, testing the equivalence principle in space. Comptes Rendus de l'Académie des Sciences-Series IV-Physics, 2(9), 1271-1286.

[5] Danzmann, K., & Rüdiger, A. (2003). LISA technology—concept, status, prospects. Classical and Quantum Gravity, 20(10), S1

[6] Everitt, C. W. F., DeBra, D. B., Parkinson, B. W., Turneaure, J. P., Conklin, J. W., Heifetz, M. I., ... & Wang, S. (2011). Gravity Probe B: Final results of a space experiment to test general relativity. Physical Review Letters, 106(22), 221101.

[7] Canuto, E. (2008). Drag-free and attitude control for the GOCE satellite.Automatica, 44(7), 1766-1780.

[8] Eisner, A., & Yuhasz, R. (1973). A Flight Evaluation of the DISCOS System on the TRIAD Satellite. JHU/APL TG-1216, April.

[9] Anza, S., Armano, M., Balaguer, E., Benedetti, M., Boatella, C., Bosetti, P., ... & Sandford, M. (2005). The LTP experiment on the LISA Pathfinder mission.Classical and Quantum Gravity, 22(10), S125.

[10] Conklin, J., Balakrishnan, K., Buchman, S., Byer, R., Cutler, G., DeBra, D., ... & Altwaijry, H. (2012). The Drag-free CubeSat.

[11] Martel, F., Perna, L., & Lozano, P. (2012). Miniature Ion Electrospray Thrusters and Performance Test on CubeSats.

[12] Vacco Space Products

[13] Blue Canyon Technologies, XACT

[14] Picone, J. M., Hedin, A. E., Drob, D. P., & Aikin, A. C. (2002). NRLMSISE‐00 empirical model of the atmosphere: Statistical comparisons and scientific issues. Journal of Geophysical Research: Space Physics (1978–2012),107(A12), SIA-15.

[15] Wang, D. Y., McLandress, C., Fleming, E. L., Ward, W. E., Solheim, B., & Shepherd, G. G. (1997). Empirical model of 90–120 km horizontal winds from wind‐imaging interferometer green line measurements in 1992–1993. Journal of Geophysical Research: Atmospheres (1984–2012), 102(D6), 6729-6745.

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[16] Musen, P. (1960). The influence of the solar radiation pressure on the motion of an artificial satellite. Journal of Geophysical Research, 65(5), 1391-1396.[17] Bhanderi, D. D. (2005). Spacecraft Attitude Determination with Earth Albedo Corrected Sun Sensor Measurements. Department of Control Engineering, Aalborg university.[18] Texas Instruments TMS320C6748 Fixed/Floating-point Digital Signal Processor[19] . A. N. Nguyen, J. W. Conklin, “Three-axis drag-free control and drag force recovery of a single thruster small satellite”. AIAA Journal and Spacecraft and Rockets, submitter, (2014). [20] Conklin, J. W. (2014). Drift mode accelerometry for spaceborne gravity measurements. arXiv preprint arXiv:1402.6772.[21] Ball press release http://www.ballaerospace.com/page.jsp?page=30&id=297[22] Neeck, S. P., & Volz, S. M. (2013, October). NASA Earth science missions. InSPIE Remote Sensing (pp. 88890C-88890C). International Society for Optics and Photonics.[23] R. Shelley, A. Chilton, T. Olatunde, G. Ciani, G. Mueller, J. W. Conklin, “The UF Torsion Pendulum, a LISA Technology Testbed: Design and Initial Results”, Proceedings of the 10th International LISA Symposium, Journal of Physics: Conference Series, submitted, (2015).[24] Gerardi, D., Allen, G., Conklin, J. W., Sun, K. X., DeBra, D., Buchman, S., ... & Johann, U. (2009). Advanced drag-free concepts for future space-based interferometers: acceleration noise performance. arXiv preprint arXiv:0910.0758.[25] Schumaker, B. L. (2003). Disturbance reduction requirements for LISA.Classical and Quantum Gravity, 20(10), S239.[26] Chilton, A., Shelley, R., Olatunde, T., Ciani, G., Conklin, J. W., & Mueller, G. (2015). The UF Torsion Pendulum, a LISA Technology Testbed: Sensing System and Initial Results. In Journal of Physics: Conference Series (Vol. 610, No. 1, p. 012038). IOP Publishing.[27] Wang, Q. L., Yeh, H. C., Zhou, Z. B., & Luo, J. (2009). Improving the sensitivity of a torsion pendulum by using an optical spring method. Physical Review A, 80(4), 043811.

References

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Drag-free control and drag force recovery of a small satellite

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