In-orbit experiments and characterisation of LISA Pathﬁndermoriond.in2p3.fr/J11/transparents/hewitson.pdf · 2011-03-22 · M Hewitson, LPF Data Analysis, Moriond, 21st March 2011

In-orbit experiments and characterisation of LISA Pathfinder

M Hewitson for the LPF teamMoriond, 21st March 2011

Monday, March 21, 2011

M Hewitson, LPF Data Analysis, Moriond, 21st March 2011

You have 90 days to optimise and fully characterise a complex instrument in

space, which has never before operated as a complete system.

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Your mission, should you choose to accept it...



LPF Mission-time Aims

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• Noise hunting and system optimisation to reach free-fall level of 3×10-14 ms-2 / √Hz• iterative process through experiments, system

identification, loop optimisation• reduce noise sources• reduce noise couplings

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• Noise hunting and system optimisation to reach free-fall level of 3×10-14 ms-2 / √Hz• iterative process through experiments, system

identification, loop optimisation• reduce noise sources• reduce noise couplings

• Develop detailed system and noise model for LPF• goes hand in hand with system optimisation and

identification• will enable us to fully explain the observed residual

force noise• model can then be used to project the performance

towards LISA

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Controlling LPF (simplified)

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• TM1 is drag-free along x• no actuation

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• IFO measures the position of SC (optical bench) relative to TM1 with pm precision

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• SC is made to follow TM1 using the μN thrusters

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• SC is made to follow TM1 using the μN thrusters• Position of TM2 relative to TM1 is measured interferometrically

(sensitive differential measurement)• TM2 serves as a quite reference for the motion of TM1

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• Differential position of two TMs is maintained with low bandwidth (1mHz) by electrostatic actuation of TM2

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• At lowest frequencies SC orientation is sensed with a star tracker and (ultimately) controlled using μN thrusters

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• Other degrees-of-freedom are sensed by either IFO or capacitive sensing (GRS) and controlled via μN thrusters or electrostatic actuation

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• Other degrees-of-freedom are sensed by either IFO or capacitive sensing (GRS) and controlled via μN thrusters or electrostatic actuation

• We control 15/18 degrees of freedom using 3 sensors and 4 actuators

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Example optimisation: stiffness matching

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• Each test mass has a ‘stiffness’ coupling to the SC due to the electrostatic actuation voltages and gravitational attraction (50/50)

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• This is different for each test mass• position of TMs relative to SC c.o.m.• different actuation voltages (one test-mass is drag-free so no

actuation along x)

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actuation along x)• Shaking of the SC couples differently to each TM

• this leaks in to the sensitive differential test-mass measurement

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actuation along x)• Shaking of the SC couples differently to each TM

• this leaks in to the sensitive differential test-mass measurement• Matching the stiffness reduces the coupling of SC jitter

into the sensitive dx measurement• actual stiffness can be determined through targeted experiments• stiffness can be matched by adjusting the actuation voltage

levels

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The plan of attack: Experiment Master Plan

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• A battery of experiments has been designed and is undergoing optimisation and testing

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• These experiments will be packed together in an optimal way to form the mission time-line• various constraints are in place here:

• some experiments are prerequisites of others• some experiments disturb the system and need to be placed

carefully (thermal experiments)

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• Some of the experiments will be repeated under different conditions and as the instrument performance improves

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• Some of the experiments will be repeated under different conditions and as the instrument performance improves

• Naturally, the results of each experiment will, to some extent, determine the following experiments and their precise configuration• we need to analyse the experiments in (almost) real-time

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Mission time outline

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Data Flow

DataConverter

LTPDARepository

LTPDAClient

LTPDAClient

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Data Analysis Infrastructure

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•Some of the requirements on data analysis tools:• robust and flexible to support real-time analysis• outputs/results should be accountable/traceable• toolset should contain a wide variety of typical

characterisation and lab analysis tools

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characterisation and lab analysis tools•This led us to design and build LTPDA

• toolbox for MATLAB• provides a general object-oriented data analysis

framework• useful in many contexts, not just LPF

• all results are encapsulated as objects• these objects contain a full history of the actions

performed on them

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characterisation and lab analysis tools•This led us to design and build LTPDA

• toolbox for MATLAB• provides a general object-oriented data analysis

framework• useful in many contexts, not just LPF

• all results are encapsulated as objects• these objects contain a full history of the actions

performed on them

9http://www.lisa.aei-hannover.de/ltpda/Monday, March 21, 2011

http://www.lisa.aei-hannover.de/ltpda/

http://www.lisa.aei-hannover.de/ltpda/


Experiment validation

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1.Each proposed experiment needs to be designed to fit in to the operational context• identify the required initial state of the LPF• determine the duration of the experiment• determine the required telemetry needed to interpret the results• identify the end state of the LPF and the constraints placed on subsequent

experiments

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experiments2.The feasibility of the experiment needs to be assessed and the

experiment adjusted until it can be carried out• map experiment description to real system parameters• assess the impact of the experiment on the time-line

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3.Any associated data analysis needs to be designed and analysed for sensitivity• what results should the analysis produce, and with what accuracy?• how should the data be analysed?

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4.The data analysis tools need to be identified, written and tested• which tools within the LTPDA framework are needed?

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4.The data analysis tools need to be identified, written and tested• which tools within the LTPDA framework are needed?

5.A full end-to-end simulation of the experiment needs to be performed

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Experiment simulation

•We have a mission simulator• LSS: LISA Pathfinder STOC Simulator

• STOC: Science and Technology Operations Centre

•Full 3D non-linear, closed-loop dynamical simulator developed by industry

•For validation purposes, it produces the closest approximation we have to real LPF data

End-to-end modelling for drag-free missions with application to LISA Pathfinder, N Brandt et al, Automation and Remote Control, 66/6, 2004

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Characterising the Simulator

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• Why?• It is the basis on which we validate our experiments• It gives us realistic data with which to develop and validate

our analyses• It is the most complete system model available

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• Why?• It is the basis on which we validate our experiments• It gives us realistic data with which to develop and validate

our analyses• It is the most complete system model available

• Strategy:• get data out of the simulator at all possible points in the loop• measure the (open-loop) transfer functions of individual

elements in the loop, wherever possible• non-linear blocks can’t be done this way• blocks which mix many inputs to one output need special

treatment• inspect the simulator code to validate the measurements and

expectation

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System model

Controllers

Sensing• IFO• GRS• ST

Dynamics

Actuators• μN thrusters• Cap. Act.

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System model

Controllers

Sensing• IFO• GRS• ST

Dynamics

Actuators• μN thrusters• Cap. Act.

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Closed-loop measurement

• Inject guidance signals (set-point)•Measure open-loop TF

• guidance to error signal

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Closed-loop measurement

• Inject guidance signals (set-point)•Measure open-loop TF

• guidance to error signal

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Drag-free loop along x

simulator datalinear ss model



Suspension loop

•Reminder: Position of TM2 relative to TM1 is controlled via the differential TM position IFO output (o12)

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Suspension loop


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Suspension loop


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System Parameters

•LPF has thousands of tunable parameters• In flight we can only change system parameters•Physical characteristics of the system need to

be identified (measured/estimated)

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System Parameters

•LPF has thousands of tunable parameters• In flight we can only change system parameters•Physical characteristics of the system need to

be identified (measured/estimated)

Name Value Description

A1 1.0 μN thrusters overall gainA2 1.0 Cap. Act. overall gain

S21 0.0 Imperfection of IFO common-mode rejection

D1 0.0 Delay on drag-free loop guidance input

D2 0.0 Delay on suspension loop guidance input

ω12 -1×10-6 s-2 TM1-SC total stiffness

ω122 -7×10-7 s-2 Differential test-mass stiffness (ω22 - ω12)16



Parameter estimation

•One of the key activities will be the characterisation of the (sensitive) x-axis controls

•A series of experiments has been designed for just this purpose

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Bayesian parameter estimation in the second LISA Pathfinder Mock Data ChallengeNofrarias et al, Phys. Rev. D 82, 122002 (2010)

Non-linear parameter estimation for the LTP experimentGiuseppe Congedo et al, Proceedings of the 8th International LISA Symposium



Experiments 1 and 2

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Experiments 1 and 2

•Experiment 1:• inject a sequence of sinusoidal signals into the drag-

free loop guidance input• shake SC along x

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Experiments 1 and 2

•Experiment 1:• inject a sequence of sinusoidal signals into the drag-

free loop guidance input• shake SC along x

•Experiment 2:• inject a sequence of sinusoidal signals into the

suspension loop guidance input• shake TM2 along x

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x1

x12o12

o1


Model

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IFO[m]

[m]

[m]

[m]


x1

x12o12

o1


Model

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IFO[m]

[m]

[m]

[m]

S21


x1

x12o12

o1


Model

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IFO[m]

[m]

[m]

[m]

i1

CdfA1

D1

S21


x1

x12o12

o1


Model

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IFO[m]

[m]

[m]

[m]

i1

CdfA1

D1

[N]μN

ThrustersSC/TM1

Dynamicsω21

[N]

S21


x1

x12o12

o1


Model

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IFO[m]

[m]

[m]

[m]

i1

CdfA1

D1

[N]μN

ThrustersSC/TM1

Dynamicsω21

[N]

i12D2

CsusA2

S21


x1

x12o12

o1


Model

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IFO[m]

[m]

[m]

[m]

i1

CdfA1

D1

[N]μN

ThrustersSC/TM1

Dynamicsω21

[N]

i12D2

CsusA2TM2

DynamicsTM2

Cap. Act. [N]ω22

[N]

S21


x1

x12o12

o1


Model

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IFO[m]

[m]

[m]

[m]

i1

CdfA1

D1

[N]μN

ThrustersSC/TM1

Dynamicsω21

[N]

i12D2

CsusA2TM2

DynamicsTM2

Cap. Act. [N]ω22

[N]

S21

ω2∆



Modelling the system

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Modeling LISA Pathfinder for Data AnalysisMarc Diaz Aguilo et al, Proceedings of the 8th International LISA Symposium




•We have different modelling schemes implemented in LTPDA• symbolic equation models, various transfer function

representations, state-space models

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•We have different modelling schemes implemented in LTPDA• symbolic equation models, various transfer function

representations, state-space models

•Models can be used for:• template generation• noise simulations• fast, easier to develop

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Fitting the data

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Fitting the data

•We have three different methods for parameter estimation:• linear least-squares fit• non-linear least-squares fit• MCMC

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Fitting the data

•We have three different methods for parameter estimation:• linear least-squares fit• non-linear least-squares fit• MCMC

•All analyse multiple experiments• multiple input signals• multiple system models• multiple output signals

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Example: MCMC

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Results on simulator data

•We simulated exp. 1 and 2 using mission simulator

•We estimate parameters of our simple 1D models using the three methods

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Quality of fit

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Drag-free loop closed-loop TF

Drag-free to S

uspension loop coupling



Residuals

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Drag-free loop Suspension loop



Using the parameter estimates

•The parameter estimates can feed the model•We then use the model to explain the observed

noise from the simulator• noise projections

•Use the 3D linear state-space models to run noise simulations

• Input noise models are the same as those in the simulator• follow mission requirements

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Projection Strategy

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Projection Strategy

1. We use our linear state-space model of LPF

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Projection Strategy

1. We use our linear state-space model of LPF2. Inject a single noise source, e.g., capacitive actuation

noise for TM1

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Projection Strategy


noise for TM13. Run simulation (72H)

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Projection Strategy


noise for TM13. Run simulation (72H)4. Save time series

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Projection Strategy


noise for TM13. Run simulation (72H)4. Save time series5. Make spectral density estimates of two longitudinal

IFO outputs (o1,o12)

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Projection Strategy



IFO outputs (o1,o12)6. Convert these to acceleration (a1, aΔ) and make

spectral density estimates

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Projection Strategy




spectral density estimates7. Repeat for other noise sources

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Projection Strategy




spectral density estimates7. Repeat for other noise sources8. Make correlated sum of all time-series and convert this

to acceleration and make spectral density estimates

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Projection Strategy




spectral density estimates7. Repeat for other noise sources8. Make correlated sum of all time-series and convert this

to acceleration and make spectral density estimates9. Make projection plots

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TM differential position noise

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Converting to acceleration

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•We want to know the residual acceleration on the SC and the differential acceleration between the two TMs

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•Need to take out the effect of the dynamics • compute the in-loop acceleration needed to produce

the position observations

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•Need to take out the effect of the dynamics • compute the in-loop acceleration needed to produce

the position observations•Account for the control loops

• the in-loop accelerations can be corrected for the commanded accelerations coming from the controllers

• this gives us the out-of-loop (or residual) accelerations of the bodies

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Differential test-mass acceleration

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Differential test-mass acceleration

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Free-flight

• One of the leading noise sources will be capacitive actuation on TM2• Switch off TM2 actuation

• Can only be done for a short time (~100s)

• Get more free-flight by kicking TM2 away and let it drift back• tossing a coin

• Analyse the data between the kicks• low-noise since cap. act. noise

is not present

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Free-flight

• One of the leading noise sources will be capacitive actuation on TM2• Switch off TM2 actuation

• Can only be done for a short time (~100s)

• Get more free-flight by kicking TM2 away and let it drift back• tossing a coin

• Analyse the data between the kicks• low-noise since cap. act. noise

is not present

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Summary

•Always expect the unexpected!• analysis tools need to be flexible and robust• modelling system needs to be highly configurable• operations science team needs to be well trained and

familiar with all aspects of the system•We will be ready through:

• on-ground unit- and system-level hardware testing• mock data challenges• operational exercises• training sessions• rigorous testing

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Documents

In-orbit experiments and characterisation of LISA Pathﬁndermoriond.in2p3.fr/J11/transparents/hewitson.pdf · 2011-03-22 · M Hewitson, LPF Data Analysis, Moriond, 21st March 2011