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## C D K D K D K D C

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**IFR – University of StuttgartLISA Pathfinder Data**AnalysisDrift Mode ExperimentA. Grynagier, W. Fichter C D K D K D K D C Barcelona, LISA7 Symposium, June 17th 2008**Outline**• Experiment description • Control strategy and software implementation • Simulation • Analysis • Conclusion Barcelona, LISA7 Symposium, June 17th 2008**Outline**• Experiment description • Control strategy and software implementation • Simulation • Analysis • Conclusion Barcelona, LISA7 Symposium, June 17th 2008**The LTP Science objective**Dx x1 x2 Barcelona, LISA7 Symposium, June 17th 2008**The Drift Mode : 2 objectives**DC gravity term Dx x1 x2 Barcelona, LISA7 Symposium, June 17th 2008**The Drift Mode : 2 objectives**DC gravity term Dx x1 x2 Barcelona, LISA7 Symposium, June 17th 2008**The Drift Mode : 2 objectives**Force noise without actuation Dx x1 x2 Barcelona, LISA7 Symposium, June 17th 2008**The Drift Mode : 2 objectives**Force noise without actuation Dx x1 x2 Barcelona, LISA7 Symposium, June 17th 2008**The Drift Mode : 2 objectives**Force noise without actuation Dx x1 x2 Barcelona, LISA7 Symposium, June 17th 2008**The Drift Mode Functionning**Suspension control is switched off in sensitive axis A Custom control mode is used A control cycle is necessary Barcelona, LISA7 Symposium, June 17th 2008**The Drift Mode Specificities**Barcelona, LISA7 Symposium, June 17th 2008 • 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“**Modeling the dynamics**EOM for the experiment Same type of equations in other DOFs Barcelona, LISA7 Symposium, June 17th 2008**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**Modeling the dynamics**EOM for the experiment Same type of equations in other DOFs For performance, the dynamics of x and φmust be coupled in the model Assumption on electrodes 1-2-3-4 : voltage noise correlation between 1-2, 3-4 is close to +1 z x y Barcelona, LISA7 Symposium, June 17th 2008**Modeling the dynamics**EOM for the experiment Same type of equations in other DOFs For performance, the dynamics of x and φmust 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**Constraints on the dynamics**External Forces and Torques Barcelona, LISA7 Symposium, June 17th 2008 DC gravity is dominating**Constraints on the dynamics**Actuation limitations • Choices • What are the DOFs? • Which actuators? • Which range? Barcelona, LISA7 Symposium, June 17th 2008**Constraints on the dynamics**Sensing limitations • Sensing limitations • IFO is best choice Barcelona, LISA7 Symposium, June 17th 2008**Outline**• Experiment description • Control strategy and software implementation • Simulation • Analysis • Conclusion Barcelona, LISA7 Symposium, June 17th 2008**Control Strategy and Implementation**3 Phases to build cycles • Drift phases • No control in sensitive axis • Duration 100-500 s • Fall 4-40 μm X2 T0 T1 t Barcelona, LISA7 Symposium, June 17th 2008**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 X2 T0 T1 t Barcelona, LISA7 Symposium, June 17th 2008**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) X2 T0 T1 t Barcelona, LISA7 Symposium, June 17th 2008**Control Strategy and Implementation**3 Phases to build cycles 3 Design Choices Built a cycle out of the phases Let Phi drift as well ? WR/HR for the capacitive actuation ? • Drift phases • controlled maneuvers • Short impulse Barcelona, LISA7 Symposium, June 17th 2008**Control Strategy and Implementation : Some possible cycles**D K D K D D C D C D K D K D K D K D K D C D K D C Barcelona, LISA7 Symposium, June 17th 2008**Control Strategy and Implementation**A typical cycle C D K D K D K D C Barcelona, LISA7 Symposium, June 17th 2008 Telecomand based Drift phases alternated with kicks A controlled maneuver corrects for uncertainties**Control Strategy and Implementation**Cycle design • Telecomand based • Drift phases alternated with kicks • Stabilize with controlled maneuver • Force noise and Open loop mismatch limit number of kicks. • 1% FDC → 2000s C D K D K D K D C Barcelona, LISA7 Symposium, June 17th 2008**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**Outline**• Experiment description • Control strategy and software implementation • Simulation • Analysis • Conclusion Barcelona, LISA7 Symposium, June 17th 2008**Simulation**Linear simulation Image of mario‘s work • Using the toolbox /uc • Simple • Not accurate for large motions • Filters can be automatically derived from same model Barcelona, LISA7 Symposium, June 17th 2008**Simulation**Astrium‘s End-to-End simulator • Comprehensive element modelling • Real control algorithms and implementation constraints Barcelona, LISA7 Symposium, June 17th 2008**Simulation**Results Same kind of instabilities observed But SC angular motion was perturbed by sliding mode controller Strong coupling between θ and x ! • Simulation matching Barcelona, LISA7 Symposium, June 17th 2008**Simulation**Results Barcelona, LISA7 Symposium, June 17th 2008 Simulation matching Time response splitted between control phases**Simulation**Results Barcelona, LISA7 Symposium, June 17th 2008 Simulation matching Time response splitted between control phases Difference between PSDs is checked**Simulation**Results Barcelona, LISA7 Symposium, June 17th 2008 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**Outline**• Experiment description • Control strategy and software implementation • Simulation • Analysis • Conclusion Barcelona, LISA7 Symposium, June 17th 2008**Analysis**Retrieving speed, position and acceleration estimates • Using a Kalman smoother • Also gives covariance N Y Linear sys U Kalman Smoother Xest ε, P Barcelona, LISA7 Symposium, June 17th 2008**Analysis**Retrieving speed, position and acceleration estimates N Y Linear sys U Kalman Smoother Xest ε, P Barcelona, LISA7 Symposium, June 17th 2008 Using a Kalman smoother Also gives covariance**Analysis**Testing model matching • open loop parameteric estimation • Error sequence is: • Noise colors error, so criterion must be weighted N Y Linear sys U Kalman Smoother Xest Open loop dyn ε, P Λ Xerr θ Barcelona, LISA7 Symposium, June 17th 2008 Open loop dyn**Analysis**N Y Linear sys Testing model matching Stiffness very observable a1 + a2 + asc not observable U • Log likelihood ratio is run on the time series • Ratio is optimized • DC forces and stiffnesses are evaluated Kalman Smoother Xest Open loop dyn ε, P Λ Xerr θ Barcelona, LISA7 Symposium, June 17th 2008**Analysis**Retrieving Noise spectrum • Actuation Noise must be taken out • Usefull data is isolated Barcelona, LISA7 Symposium, June 17th 2008**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**Analysis**Retrieving Noise spectrum Show first example data filled and windowed Barcelona, LISA7 Symposium, June 17th 2008 Gap filling must be used at and below the cutting frequencyIt is combined with windowing of the whole signal**Analysis**Retrieving Noise spectrum Barcelona, LISA7 Symposium, June 17th 2008 Gap filling must be used at and below the cutting frequency Obained by minimizing the criterion:**Analysis**Retrieving Noise spectrum Barcelona, LISA7 Symposium, June 17th 2008 Gap filling must be used at and below the cutting frequency Obained by minimizing the criterion: Works well at low freq.**Analysis**Retrieving Noise spectrum Barcelona, LISA7 Symposium, June 17th 2008 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.**Analysis**Retrieving Noise spectrum Barcelona, LISA7 Symposium, June 17th 2008 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.**Analysis**Retrieving Noise spectrum Barcelona, LISA7 Symposium, June 17th 2008**Analysis**Retrieving Noise spectrum Barcelona, LISA7 Symposium, June 17th 2008 Bounds on the estimate ?**Outline**• Introduction • Experiment modeling • Control strategy and software implementation • Simulation • Analysis • Conclusion Barcelona, LISA7 Symposium, June 17th 2008**Conclusions**• Drift mode is implementable, but data is interrupted • Implementation limitations have a cost Barcelona, LISA7 Symposium, June 17th 2008