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Institute ofFlight Mechanics and Control

Barcelona, LISA7 Symposium, June 17th 2008

IFR – University of Stuttgart

LISA Pathfinder Data AnalysisDrift Mode Experiment

A. Grynagier, W. Fichter

C D K D K D K D C

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Outline

1. Experiment description2. Control strategy and software

implementation3. Simulation4. Analysis5. Conclusion

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Outline




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The LTP Science objective


x1 x2

xnoise

noiseFsusg

oxo

FFFx

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noiseFsusg FFFx

The Drift Mode : 2 objectives

DC gravity term


x1 x2

x

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noiseFsusgDCg FFxKFx .


DC gravity term


x1 x2

x

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Force noise without actuation


noiseFsusg FFFx

x1 x2

x

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x1 x2

xnoiseFsussusg FnFFx 0

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x1 x2

xnoise

noiseFsussusg

oxo

FnFFx

0

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The Drift Mode Functionning

Suspension control is switched off in sensitive axis

A Custom control mode is usedA control cycle is necessary


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The Drift Mode Specificities

Operational aspects Not continuously controlled along sensitive axis Unstable phase Periodic control switches

Data Analysis aspects There is no steady state Science data is "sliced“


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Modeling the dynamics

EOM for the experiment Same type of equations

in other DOFs


m

fffxxax

m

ffxaxx

susgDC

susDCgsc

121

222

11

2111

..

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EOM for the experiment Same type of equations

in other DOFs Observation with cross

talks(Perf budget - by M. Hirth)


m

fffxxax

m

ffxaxx

susgDC

susDCgsc

121

222

11

2111

..

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EOM for the experiment Same type of equations in

other DOFs For performance, the

dynamics of x and φ must be coupled in the model

Assumption on electrodes 1-2-3-4 : voltage noise correlation between 1-2, 3-4 is close to +1


xy

z

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EOM for the experiment Same type of equations in

other DOFs For performance, the

dynamics of x and φ must be coupled in the model

Assumption on electrodes 1-2-3-4 : voltage noise correlation between 1-2, 3-4 is close to +1

DC voltage noise constant


ybm

fffxxax

bym

ffxaxx

susgDC

susDCgsc

121

222

111

12111

..

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Constraints on the dynamics

External Forces and Torques DC gravity is dominating


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Actuation limitations Choices

What are the DOFs? Which actuators? Which range?


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Sensing limitations Sensing limitations IFO is best choice


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Outline




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Control Strategy and Implementation

3 Phases to build cycles Drift phases

No control in sensitive axis Duration 100-500 s Fall 4-40 μm


t

X2

T0 T1

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3 Phases to build cycles Drift phases Short impulses

A short impulse (~2s) at high force (~2.6.10-7N) Open loop control


t

X2

T0 T1

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3 Phases to build cycles Drift phases Short impulses controlled maneuvers

Dampen the dynamics (loop closed)

Using sliding mode controller

Causes large gaps in data (~400s)


t

X2

T0 T1

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3 Phases to build cycles Drift phases controlled maneuvers Short impulse

3 Design Choices Built a cycle out of the

phases Let Phi drift as well ? WR/HR for the capacitive

actuation ?


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Control Strategy and Implementation : Some possible cycles


Repeated Drifts/Controls Kicks : Fixed timeline but variable force

Drifts/Controls with a kick Kicks : variable timeline but fixed force

TELECOMAND CONTROLPre-defined sequence executed on a

pre-defined timeline

ON-BOARD CONTROLSequence computed by On-Board-

Computer

D C D C D

D K D C D K D C

D K D K D

K D K D K D K

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A typical cycle Telecomand based Drift phases alternated

with kicks A controlled maneuver

corrects for uncertainties


C D K D K D K D C

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Cycle design


C D K D K D K D C

Telecomand based Drift phases alternated

with kicks Stabilize with controlled

maneuver Force noise and Open

loop mismatch limit number of kicks.

1% FDC → 2000s

3...1kN

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Inplementation Settings for a controlled

manoeuver Settings for a drift phase Settings for a kick


Phase Parameters

Custom Mode

Controller Command Signal Electrodes 1-4

Controlled Manoeuver

14 Sliding modeTBC

No WR

Drift 15 Nothing No WR

Kick 15 Nothing Use command signal-2.67.10-7N

for 0.1<t<2.1s

WR

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Outline




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Simulation

Linear simulation Using the toolbox /uc Simple Not accurate for large

motions Filters can be

automatically derived from same model

Image of mario‘s work


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Simulation

Astrium‘s End-to-End simulator Comprehensive element

modelling Real control algorithms

and implementation constraints


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Simulation

Results Simulation matching Same kind of instabilities

observed But SC angular motion

was perturbed by sliding mode controller

Strong coupling between θ and x !


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Simulation

Results Simulation matching Time response splitted

between control phases


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Simulation


between control phases Difference between

PSDs is checked


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Simulation


between control phases Difference between

PSDs is checked Model matching

guarrantees goodness of filters for analysis : here calibration is needed


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Outline




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Analysis

Retrieving speed, position and acceleration estimates

Using a Kalman smoother

Also gives covariance


Linear sysU

Kalman Smoother

Y

ε, P

Xest

N

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U

Analysis

Testing model matching open loop parameteric

estimation Error sequence is:

Noise colors error, so

criterion must be weighted


Linear sys

Kalman Smoother

Y

ε, P

Xest

N

Open loop dyn

θ

Xerr Λ

1,1 tXtXtXX estestesterr

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Analysis

Testing model matching Log likelihood ratio is

run on the time series Ratio is optimized DC forces and

stiffnesses are evaluated

Stiffness very observable a1 + a2 + asc not observable


ULinear sys

Kalman Smoother

Y

ε, P

Xest

N

Open loop dyn

θ

Xerr Λ

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Analysis

Retrieving Noise spectrum Actuation Noise must be

taken out Usefull data is isolated


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Analysis

Retrieving Noise spectrum Problem : cutting

frequency is of interest in the PSD

~2 mHz and 0.5 mHz


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Analysis

Retrieving Noise spectrum Gap filling must be

used at and below the cutting frequencyIt is combined with windowing of the whole signal

Show first example data filled and windowed


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Analysis

Retrieving Noise spectrum Gap filling must be used

at and below the cutting frequency

Obained by minimizing the criterion:


dyyyJ penaltyguessfilled

22

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Analysis




Works well at low freq.


dyyyJ penaltyguessfilled

22

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Analysis




Works well at low freq. Works well at cutting

freq.


dyyyJ filledguessfilled

222

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Analysis




Works well at low freq. Works well at cutting freq. Not so goot at high freq.


dyyyJ filledguessfilled

222

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Analysis

Retrieving Noise spectrum


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Analysis

Retrieving Noise spectrum Bounds on the

estimate ?


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Outline

1. Introduction2. Experiment modeling3. Control strategy and software



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Conclusions

Drift mode is implementable, but data is interrupted

Implementation limitations have a cost


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Conclusions

Drift mode is implementable, but data is interrupted

Control stability limit is insufficiently known

Force noise in WR and φ cross talk TBC


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Conclusions

DC Forces and torques can be estimated

PSD difficult to estimate at switching frequency


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