Micro-newton Thruster Modulation and Analysisfor the LISA Pathfinder

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe

24 July 2014

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Background

I eLISA – space-based gravitational wave observatory

I Free falling bodies and gravitational waves

I Inertial sensor and relative motion

I LISA Pathfinder (LPF) – technology demonstration package

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Propulsion system

I Colloid micro-newton thrusters (CMNTs)

I Translation and attitude controlI Test mass reference

I Configuration and control loop

I Consistency check and error tracking

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Thrust modulation

I Thruster modulation frequency assignment

I Frequency-domain signal analysis

I Response amplitudes and directions

I Measurables: thruster calibrations, orientations, time delaysI Location of space craft’s center of mass?

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

“Raw” dataLTPDA 2.9.dev (R2012b)2014−07−24 14:18:28.877 UTCltpda: 8ddf0bbiplot

100 110 120 130 140 150 160 170 180 190 200−6

−4

−2

0

2

4

6x 10

−7

Acc

eler

atio

n [m

s−2

]

Origin: 2014−07−09 08:00:00.000 − Time [s]

xyz

Figure 1: Linear accelerations of test mass 1 relative to space craft

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

“Raw” data (frequency domain)LTPDA 2.9.dev (R2012b)2014−07−29 19:30:57.283 UTCltpda: 919ccc6iplot

10−5

10−4

10−3

10−2

10−1

100

101

10−18

10−16

10−14

10−12

10−10

10−8

Acc

eler

atio

n [m

s−2

]

Frequency [Hz]

xyz

Figure 2: Frequency-domain linear accelerations of test mass 1 relativeto space craft

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

“Raw” data (frequency domain)LTPDA 2.9.dev (R2012b)2014−07−29 19:31:00.576 UTCltpda: 919ccc6iplot

6.5 7 7.5 8

x 10−3

10−13

10−12

10−11

10−10

10−9

Acc

eler

atio

n [m

s−2

]

Frequency [Hz]

xyz

Figure 3: Frequency-domain linear accelerations of test mass 1 relativeto space craft (zoomed in)

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Signal filteringLTPDA 2.9.dev (R2012b)2014−07−28 18:51:00.306 UTCltpda: 919ccc6LTPDAPipeline.runStep

6.5 7 7.5 8

x 10−3

10−12

10−10

10−8

10−6

10−4

10−2

100

102

Nor

mal

ized

sig

nal a

mpl

itude

[]

Frequency [Hz]

Figure 4: Data streams filtered at modulation frequency of thruster 1

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Signal filteringLTPDA 2.9.dev (R2012b)2014−07−28 18:51:56.257 UTCltpda: 919ccc6LTPDAPipeline.runStep

6.5 7 7.5 8

x 10−3

10−12

10−10

10−8

10−6

10−4

10−2

100

102

Nor

mal

ized

sig

nal a

mpl

itude

[]

Frequency [Hz]

Figure 5: Data streams filtered at modulation frequency of thruster 4

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Signal filteringLTPDA 2.9.dev (R2012b)2014−07−28 18:52:50.793 UTCltpda: 919ccc6LTPDAPipeline.runStep

6.5 7 7.5 8

x 10−3

10−12

10−10

10−8

10−6

10−4

10−2

100

102

Nor

mal

ized

sig

nal a

mpl

itude

[]

Frequency [Hz]

Figure 6: Data streams filtered at modulation frequency of thruster 7

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Data analysis

I Principal component analysis(PCA)

I Time-independent linear andangular acceleration vectors

I Covariance matrixI Eigenvectors and eigenvalues

Cij = 〈(xi − 〈xi 〉) (xj − 〈xj〉)〉

I Model (in)dependenceFigure 7: PCA sketch

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Data analysisLTPDA 2.9.dev (R2012b)2014−07−24 18:05:57.238 UTCltpda: 8ddf0bbiplot

3 3.005 3.01 3.015 3.02 3.025 3.03 3.035 3.04 3.045 3.05

x 104

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Nor

mal

ized

sig

nal a

mpl

itude

Time [s]

commandresponse

Figure 8: Normalized modulation commanded to thruster 1 and angularacceleration of test mass 1 about x-axis.

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Confidence intervals

I Spacecraftsub-system model

I “Residual” signals

I Variation of thrusterparameters

I Noise-weighted innerproduct

LTPDA 2.9.dev (R2012b)2014−08−18 15:16:26.366 UTCltpda: 919ccc6iplot

4 5 6 7 8 9 10 11

x 10−3

10−24

10−22

10−20

10−18

10−16

10−14

10−12

[m

2 s−4

Hz−1

]

Frequency [Hz]

estimatedresidual

Figure 9: Linear acceleration accelerations oftest mass 1

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Future efforts

I Testing various space craft models

I Porting code to LTPDA infrastructure

I Alternate characterization methods

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder

Thank you

Michael A. Perlin, Jacob P. Slutsky, J. Ira Thorpe:

Micro-newton Thruster Modulation and Analysis for the LISA Pathfinder