2009 IEEE Aerospace Conference

“Spacecraft Jitter Prediction using 6-DOF Disturbance Measurements”

Bryce CarpenterOliver MartinJason Hinkle

Sierra Nevada CorporationSpace Systems Group

IEEE Aerospace ConferenceMarch 2009

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Problem Statement

Beijing-1

Launch Oct. 2005

4-meter resolution, 24-kilometer swath

agriculture, city planning, hydrology, 2008 Olympics, …

Challenges

• Flexibility• Lower Cost• Rapid Development• Increased Agility• …

• Power availability• Smaller aperture• Decreased pointing stability• …

Demand for Small Satellites

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Paper Contribution

• Presentation Overview

4. System-Level Jitter Prediction

An analytical technique for system-level jitter

characterization prior to system integration

3. Structural Response Analysis

2. Frequency Domain Analysis

1. Hexapod Reaction Balance

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Historical Background

2005 – 2007

Distributed Sensing Experiment (DSE)

Missile Defense Agency (MDA)

February 2008

Trailblazer

Operationally Responsive Space

(ORS)

August 2, 2008

Falcon 1, Flight 3 launches from Omelek Island in Kwajalein Atoll

SpaceX

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Hexapod Reaction Balance

• Measurement device for accurately recording a wide range of dynamic force and torque responses

Property Value

Torque resolution 0.2 mN-m

Force resolution 2 mN

Maximum static torque 100 Nm

Maximum static force 1300 N

Transducer bandwidth 0.01 - 36 kHz

Stiffness normal to interface plate 200 N/μm

Unloaded first resonance 800 Hz

6

5

4

3

2

1

F

F

F

F

F

F

A

M

M

M

F

F

F

z

y

x

z

y

xSteel Flexures

Force Transducers

Kinematic Transformation

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Previous Hexapod Uses

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Frequency Domain Analysis

• Convert time-series to frequency domain using

Discrete Fourier Transform:

0 200 400 600 800 1000 1200 1400 1600-4.5

-4

-3.5

-3

-2.5

-2

-1.5

-1

log 10

(Nm

)

Frequency (Hz)

FFT, Torque about Hexapod +Y Axis, 100 rps

1,,0,1 1

0

2

Nkex

NX

N

n

N

knj

nk

0 0.02 0.04 0.06 0.08 0.1-0.1

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

0.1

time (s)

torq

ue

(N

m)

Torque about Hexapod +Y Axis, 100rps

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+Y Torque Waterfall Plot

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10-1

100

101

102

103

104

10-15

10-10

10-5

100

Force Disturbance PSD

Freq (Hz)

N2 /H

z

X

YZ

10-1

100

101

102

103

104

10-15

10-10

10-5

100

Torque Disturbance PSD

Freq (Hz)

(Nm

)2 /Hz

X

YZ

Power Spectral Density

• Convert DFT to PSD: 1,,0,*

Nkf

XXS kkX k

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10-1

100

101

102

103

104

10-10

10-5

Structure Transfer Function About BF+Z due to Force

Freq (Hz)

rad

/N

X

YZ

10-1

100

101

102

103

104

10-12

10-10

10-8

10-6

Structure Transfer Function About BF+Z due to Torque

Freq (Hz)

rad

/(N

m)

X

YZ

Structural Frequency Response Analysis

• Conduct frequency response analysis in NASTRAN to determine camera motion due to RW disturbance

CommDeck

AvionicsDeck

PayloadBay

28,339 Nodes

33,895 Elements

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System Jitter Prediction

Disturbance Data

(Time Domain)

DFT(Freq Domain)

PSD(Freq Domain)

N

Nm

N

Nm

Structure Resonance

(Freq Domain)u^2

Rad/N

Rad/Nm

*N^2/Hz

Rad^2/N^2

*

(Nm)^2/Hz

Rad^2/(Nm)^2

+

Rad^2/Hz

Rad^2/Hz

CombinedLOS Motion

Reaction Wheel Disturbance

Flexible Body Response

PredictedPayload Jitter

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Payload Jitter Results

10-1

100

101

102

103

104

10-35

10-30

10-25

10-20

10-15

10-10

LOS Motion in Frequency Domain

Frequency (Hz)

rad2 /H

z

Y

Z

10-1

100

101

102

103

104

0

0.5

1

1.5

2

2.5

3

3.5x 10

-8 Cumulative Motion vs. Frequency

Frequency (Hz)

rad

Y

Z

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Conclusion

• SNC has developed the Hexapod to accurately measure high frequency forces and torques

• Analysis of Hexapod data can be combined with a FEM frequency response analysis to determine system pointing stability

-2 0 2

x 10-5

-2

0

2

x 10-5 Jitter Blob

Y-Axis (rad)

Z-A

xis

(ra

d)

0 0.2 0.4 0.6 0.8-2

-1

0

1x 10

-6 Z-Axis Motion

Time (sec)

rad

0 0.2 0.4 0.6 0.8-1

0

1

2x 10

-5 Y-Axis Motion

Time (sec)

rad

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Acknowledgments

This material is based upon work supported by the U.S. Army Space and Missile Defense

Command under Contract No. HQ0006-04-D-0002.”