www ifr unistuttgart de Institute of Flight Mechanics

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control IFR – University of Stuttgart LISA Pathfinder Data Analysis Drift Mode Experiment A. Grynagier, W. Fichter C D K Barcelona, LISA 7 Symposium, June 17 th 2008 D KD C

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control Outline 1. 2. 3. 4. 5. Experiment description Control strategy and software implementation Simulation Analysis Conclusion Barcelona, LISA 7 Symposium, June 17 th 2008

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control Outline 1. 2. 3. 4. 5. Experiment description Control strategy and software implementation Simulation Analysis Conclusion Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de The LTP Science objective Dx x 1 Barcelona, LISA 7 Symposium, June 17 th 2008 x 2

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de The Drift Mode : 2 objectives §DC gravity term Dx x 1 Barcelona, LISA 7 Symposium, June 17 th 2008 x 2

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de The Drift Mode : 2 objectives §DC gravity term Dx x 1 Barcelona, LISA 7 Symposium, June 17 th 2008 x 2

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de The Drift Mode : 2 objectives §Force noise without actuation Dx x 1 Barcelona, LISA 7 Symposium, June 17 th 2008 x 2

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de The Drift Mode : 2 objectives §Force noise without actuation Dx x 1 Barcelona, LISA 7 Symposium, June 17 th 2008 x 2

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de The Drift Mode : 2 objectives §Force noise without actuation Dx x 1 Barcelona, LISA 7 Symposium, June 17 th 2008 x 2

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control The Drift Mode Functionning Ø Suspension control is switched off in sensitive axis Ø A Custom control mode is used Ø A control cycle is necessary Barcelona, LISA 7 Symposium, June 17 th 2008

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control The Drift Mode Specificities Ø Operational aspects § Not continuously controlled along sensitive axis § Unstable phase § Periodic control switches Ø Data Analysis aspects § There is no steady state § Science data is "sliced“ Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Modeling the dynamics §EOM for the experiment Ø Same type of equations in other DOFs Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Modeling the dynamics §EOM for the experiment Ø Same type of equations in other DOFs Ø Observation with cross talks (Perf budget - by M. Hirth) Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Modeling the dynamics §EOM for the experiment z y Barcelona, LISA 7 Symposium, June 17 th 2008 x Ø Same type of equations in other DOFs Ø For performance, the dynamics of x and φ must be coupled in the model Ø Assumption on electrodes 12 -3 -4 : voltage noise correlation between 1 -2, 3 -4 is close to +1

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Modeling the dynamics §EOM for the experiment Ø Same type of equations in other DOFs Ø For performance, the dynamics of x and φ must be coupled in the model Ø Assumption on electrodes 12 -3 -4 : voltage noise correlation between 1 -2, 3 -4 is close to +1 Ø DC voltage noise constant Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Constraints on the dynamics §External Forces and Torques Ø DC gravity is dominating Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Constraints on the dynamics §Actuation limitations Ø Choices § What are the DOFs? § Which actuators? § Which range? Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Constraints on the dynamics §Sensing limitations Ø IFO is best choice Barcelona, LISA 7 Symposium, June 17 th 2008

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control Outline 1. 2. 3. 4. 5. Experiment description Control strategy and software implementation Simulation Analysis Conclusion Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Control Strategy and Implementation § 3 Phases to build cycles Ø Drift phases § No control in sensitive axis § Duration 100 -500 s § Fall 4 -40 μm X 2 T 0 Barcelona, LISA 7 Symposium, June 17 th 2008 T 1 t

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Control Strategy and Implementation § 3 Phases to build cycles Ø Drift phases Ø Short impulses X 2 § A short impulse (~2 s) § at high force (~2. 6. 10 -7 N) § Open loop control T 0 T 1 Barcelona, LISA 7 Symposium, June 17 th 2008 t

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Control Strategy and Implementation § 3 Phases to build cycles Ø Drift phases Ø Short impulses Ø controlled maneuvers X 2 § Dampen the dynamics (loop closed) § Using sliding mode controller § Causes large gaps in data (~400 s) T 0 Barcelona, LISA 7 Symposium, June 17 th 2008 T 1 t

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Control Strategy and Implementation § 3 Phases to build cycles Ø Drift phases Ø controlled maneuvers Ø Short impulse Barcelona, LISA 7 Symposium, June 17 th 2008 3 Design Choices Ø Built a cycle out of the phases Ø Let Phi drift as well ? Ø WR/HR for the capacitive actuation ?

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control Strategy and Implementation : Some possible cycles Repeated Drifts/Controls Kicks : Fixed timeline but variable force D D K D C D Drifts/Controls with a kick Kicks : variable timeline but fixed force K D K D KD C TELECOMAND CONTROL Pre-defined sequence executed on a predefined timeline Barcelona, LISA 7 Symposium, June 17 th 2008 ON-BOARD CONTROL Sequence computed by On-Board. Computer

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Control Strategy and Implementation §A typical cycle Ø Telecomand based Ø Drift phases alternated with kicks Ø A controlled maneuver corrects for uncertainties C D K Barcelona, LISA 7 Symposium, June 17 th 2008 D KD C

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Control Strategy and Implementation §Cycle design Ø Telecomand based Ø Drift phases alternated with kicks Ø Stabilize with controlled maneuver Ø Force noise and Open loop mismatch limit number of kicks. Ø 1% FDC → 2000 s Barcelona, LISA 7 Symposium, June 17 th 2008 C D K D KD C

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Control Strategy and Implementation §Inplementation ØPhase Settings for a controlled manoeuver Custom Controller Mode phase Ø Settings for a drift Ø Settings for a kick Parameters Command Signal Electrodes 1 -4 Controlled Manoeuver 14 Sliding mode TBC No WR Drift 15 Nothing No WR Kick 15 Nothing Use command signal -2. 67. 10 -7 N for 0. 1<t<2. 1 s WR Barcelona, LISA 7 Symposium, June 17 th 2008

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control Outline 1. 2. 3. 4. 5. Experiment description Control strategy and software implementation Simulation Analysis Conclusion Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Simulation §Linear simulation Ø Using the toolbox /uc Ø Simple Ø Not accurate for large motions Ø Filters can be automatically derived from same model Barcelona, LISA 7 Symposium, June 17 th 2008 Ø Image of mario‘s work

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Simulation §Astrium‘s End-to-End simulator Ø Comprehensive element modelling Ø Real control algorithms and implementation constraints Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Simulation §Results Ø Simulation matching Barcelona, LISA 7 Symposium, June 17 th 2008 Ø Same kind of instabilities observed Ø But SC angular motion was perturbed by sliding mode controller Ø Strong coupling between θ and x !

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Simulation §Results Ø Simulation matching Ø Time response splitted between control phases Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Simulation §Results Ø Simulation matching Ø Time response splitted between control phases Ø Difference between PSDs is checked Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Simulation §Results Ø Simulation matching Ø Time response splitted between control phases Ø Difference between PSDs is checked Ø Model matching guarrantees goodness of filters for analysis : here calibration is needed Barcelona, LISA 7 Symposium, June 17 th 2008

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control Outline 1. 2. 3. 4. 5. Experiment description Control strategy and software implementation Simulation Analysis Conclusion Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving speed, position and acceleration estimates Ø Using a Kalman smoother Ø Also gives covariance N Linear sys U Kalman Smoother Barcelona, LISA 7 Symposium, June 17 th 2008 Y Xest ε, P

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving speed, position and acceleration estimates Ø Using a Kalman smoother Ø Also gives covariance N Linear sys U Kalman Smoother Barcelona, LISA 7 Symposium, June 17 th 2008 Y Xest ε, P

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Testing model matching Ø open loop parameteric estimation Ø Error sequence is: Ø Noise colors error, so criterion must be weighted N Linear sys U Kalman Smoother θ Barcelona, LISA 7 Symposium, June 17 th 2008 Y Xest ε, P Open loop Xerr dyn Λ

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Testing model matching Ø Log likelihood ratio is run on the time series Ø Ratio is optimized Ø DC forces and stiffnesses are evaluated N Y Linear sys U Kalman Smoother Xest ε, P Open loop Xerr dyn θ Ø Stiffness very observable Ø a 1 + a 2 + asc not observable Barcelona, LISA 7 Symposium, June 17 th 2008 Λ

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Actuation Noise must be taken out Ø Usefull data is isolated Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Problem : cutting frequency is of interest in the PSD Ø ~2 m. Hz and 0. 5 m. Hz Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Gap filling must be used at and below the cutting frequency It is combined with windowing of the whole signal Barcelona, LISA 7 Symposium, June 17 th 2008 Ø Show first example data filled and windowed

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Gap filling must be used at and below the cutting frequency Ø Obained by minimizing the criterion: Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Gap filling must be used at and below the cutting frequency Ø Obained by minimizing the criterion: Ø Works well at low freq. Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Gap filling must be used at and below the cutting frequency Ø Obained by minimizing the criterion: Ø Works well at low freq. Ø Works well at cutting freq. Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Gap filling must be used at and below the cutting frequency Ø Obained by minimizing the criterion: Ø Works well at low freq. Ø Works well at cutting freq. Ø Not so goot at high freq. Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Analysis §Retrieving Noise spectrum Ø Bounds on the estimate ? Barcelona, LISA 7 Symposium, June 17 th 2008

www. ifr. uni-stuttgart. de Institute of Flight Mechanics and Control Outline 1. 2. 3. 4. 5. 6. Introduction Experiment modeling Control strategy and software implementation Simulation Analysis Conclusion Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Conclusions Ø Drift mode is implementable, but data is interrupted Ø Implementation limitations have a cost Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Conclusions Ø Drift mode is implementable, but data is interrupted Ø Control stability limit is insufficiently known Ø Force noise in WR and φ cross talk TBC Barcelona, LISA 7 Symposium, June 17 th 2008

Institute of Flight Mechanics and Control www. ifr. uni-stuttgart. de Conclusions Ø DC Forces and torques can be estimated Ø PSD difficult to estimate at switching frequency Barcelona, LISA 7 Symposium, June 17 th 2008