C D K D K D K D C
description
Transcript of C D K D K D K D C
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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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Institute ofFlight Mechanics and Control
Barcelona, LISA7 Symposium, June 17th 2008
Outline
1. Experiment description2. Control strategy and software
implementation3. Simulation4. Analysis5. Conclusion
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Institute ofFlight Mechanics and Control
Outline
1. Experiment description2. Control strategy and software
implementation3. Simulation4. Analysis5. Conclusion
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
The LTP Science objective
Barcelona, LISA7 Symposium, June 17th 2008
x1 x2
xnoise
noiseFsusg
oxo
FFFx
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noiseFsusg FFFx
The Drift Mode : 2 objectives
DC gravity term
Barcelona, LISA7 Symposium, June 17th 2008
x1 x2
x
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Institute ofFlight Mechanics and Control
noiseFsusgDCg FFxKFx .
The Drift Mode : 2 objectives
DC gravity term
Barcelona, LISA7 Symposium, June 17th 2008
x1 x2
x
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Institute ofFlight Mechanics and Control
The Drift Mode : 2 objectives
Force noise without actuation
Barcelona, LISA7 Symposium, June 17th 2008
noiseFsusg FFFx
x1 x2
x
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Institute ofFlight Mechanics and Control
The Drift Mode : 2 objectives
Force noise without actuation
Barcelona, LISA7 Symposium, June 17th 2008
x1 x2
xnoiseFsussusg FnFFx 0
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Institute ofFlight Mechanics and Control
The Drift Mode : 2 objectives
Force noise without actuation
Barcelona, LISA7 Symposium, June 17th 2008
x1 x2
xnoise
noiseFsussusg
oxo
FnFFx
0
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Institute ofFlight Mechanics and Control
The Drift Mode Functionning
Suspension control is switched off in sensitive axis
A Custom control mode is usedA control cycle is necessary
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
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“
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Modeling the dynamics
EOM for the experiment Same type of equations
in other DOFs
Barcelona, LISA7 Symposium, June 17th 2008
m
fffxxax
m
ffxaxx
susgDC
susDCgsc
121
222
11
2111
..
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Institute ofFlight Mechanics and Control
Modeling the dynamics
EOM for the experiment Same type of equations
in other DOFs Observation with cross
talks(Perf budget - by M. Hirth)
Barcelona, LISA7 Symposium, June 17th 2008
m
fffxxax
m
ffxaxx
susgDC
susDCgsc
121
222
11
2111
..
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Institute ofFlight Mechanics and Control
Modeling the dynamics
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
Barcelona, LISA7 Symposium, June 17th 2008
xy
z
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Institute ofFlight Mechanics and Control
Modeling the dynamics
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
Barcelona, LISA7 Symposium, June 17th 2008
ybm
fffxxax
bym
ffxaxx
susgDC
susDCgsc
121
222
111
12111
..
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Institute ofFlight Mechanics and Control
Constraints on the dynamics
External Forces and Torques DC gravity is dominating
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Constraints on the dynamics
Actuation limitations Choices
What are the DOFs? Which actuators? Which range?
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Constraints on the dynamics
Sensing limitations Sensing limitations IFO is best choice
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Outline
1. Experiment description2. Control strategy and software
implementation3. Simulation4. Analysis5. Conclusion
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Control Strategy and Implementation
3 Phases to build cycles Drift phases
No control in sensitive axis Duration 100-500 s Fall 4-40 μm
Barcelona, LISA7 Symposium, June 17th 2008
t
X2
T0 T1
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Institute ofFlight Mechanics and Control
Control Strategy and Implementation
3 Phases to build cycles Drift phases Short impulses
A short impulse (~2s) at high force (~2.6.10-7N) Open loop control
Barcelona, LISA7 Symposium, June 17th 2008
t
X2
T0 T1
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Institute ofFlight Mechanics and Control
Control Strategy and Implementation
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)
Barcelona, LISA7 Symposium, June 17th 2008
t
X2
T0 T1
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Institute ofFlight Mechanics and Control
Control Strategy and Implementation
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 ?
Barcelona, LISA7 Symposium, June 17th 2008
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Control Strategy and Implementation : Some possible cycles
Barcelona, LISA7 Symposium, June 17th 2008
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
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Institute ofFlight Mechanics and Control
Control Strategy and Implementation
A typical cycle Telecomand based Drift phases alternated
with kicks A controlled maneuver
corrects for uncertainties
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Control Strategy and Implementation
Cycle design
Barcelona, LISA7 Symposium, June 17th 2008
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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Institute ofFlight Mechanics and Control
Control Strategy and Implementation
Inplementation Settings for a controlled
manoeuver Settings for a drift phase Settings for a kick
Barcelona, LISA7 Symposium, June 17th 2008
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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Institute ofFlight Mechanics and Control
Outline
1. Experiment description2. Control strategy and software
implementation3. Simulation4. Analysis5. Conclusion
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
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
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Simulation
Astrium‘s End-to-End simulator Comprehensive element
modelling Real control algorithms
and implementation constraints
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
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 !
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Simulation
Results Simulation matching Time response splitted
between control phases
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Simulation
Results Simulation matching Time response splitted
between control phases Difference between
PSDs is checked
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Simulation
Results Simulation matching Time response splitted
between control phases Difference between
PSDs is checked Model matching
guarrantees goodness of filters for analysis : here calibration is needed
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Outline
1. Experiment description2. Control strategy and software
implementation3. Simulation4. Analysis5. Conclusion
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Analysis
Retrieving speed, position and acceleration estimates
Using a Kalman smoother
Also gives covariance
Barcelona, LISA7 Symposium, June 17th 2008
Linear sysU
Kalman Smoother
Y
ε, P
Xest
N
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Institute ofFlight Mechanics and Control
Analysis
Retrieving speed, position and acceleration estimates
Using a Kalman smoother
Also gives covariance
Barcelona, LISA7 Symposium, June 17th 2008
Linear sysU
Kalman Smoother
Y
ε, P
Xest
N
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Institute ofFlight Mechanics and Control
U
Analysis
Testing model matching open loop parameteric
estimation Error sequence is:
Noise colors error, so
criterion must be weighted
Barcelona, LISA7 Symposium, June 17th 2008
Linear sys
Kalman Smoother
Y
ε, P
Xest
N
Open loop dyn
θ
Xerr Λ
1,1 tXtXtXX estestesterr
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Institute ofFlight Mechanics and Control
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
Barcelona, LISA7 Symposium, June 17th 2008
ULinear sys
Kalman Smoother
Y
ε, P
Xest
N
Open loop dyn
θ
Xerr Λ
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum Actuation Noise must be
taken out Usefull data is isolated
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum Problem : cutting
frequency is of interest in the PSD
~2 mHz and 0.5 mHz
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
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
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum Gap filling must be used
at and below the cutting frequency
Obained by minimizing the criterion:
Barcelona, LISA7 Symposium, June 17th 2008
dyyyJ penaltyguessfilled
22
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum Gap filling must be used
at and below the cutting frequency
Obained by minimizing the criterion:
Works well at low freq.
Barcelona, LISA7 Symposium, June 17th 2008
dyyyJ penaltyguessfilled
22
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum Gap filling must be used
at and below the cutting frequency
Obained by minimizing the criterion:
Works well at low freq. Works well at cutting
freq.
Barcelona, LISA7 Symposium, June 17th 2008
dyyyJ filledguessfilled
222
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum Gap filling must be used
at and below the cutting frequency
Obained by minimizing the criterion:
Works well at low freq. Works well at cutting freq. Not so goot at high freq.
Barcelona, LISA7 Symposium, June 17th 2008
dyyyJ filledguessfilled
222
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Analysis
Retrieving Noise spectrum Bounds on the
estimate ?
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Outline
1. Introduction2. Experiment modeling3. Control strategy and software
implementation4. Simulation5. Analysis6. Conclusion
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Conclusions
Drift mode is implementable, but data is interrupted
Implementation limitations have a cost
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Conclusions
Drift mode is implementable, but data is interrupted
Control stability limit is insufficiently known
Force noise in WR and φ cross talk TBC
Barcelona, LISA7 Symposium, June 17th 2008
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Institute ofFlight Mechanics and Control
Conclusions
DC Forces and torques can be estimated
PSD difficult to estimate at switching frequency
Barcelona, LISA7 Symposium, June 17th 2008