1. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Barcelona, LISA7 Symposium, June 17th 2008 IFR – University of Stuttgart LISA Pathfinder Data Analysis Drift Mode Experiment A. Grynagier, W. Fichter C D K D K D K D C

2. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Barcelona, LISA7 Symposium, June 17th 2008 Outline 1.Experiment description 2.Control strategy and software implementation 3.Simulation 4.Analysis 5.Conclusion

3. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Outline 1.Experiment description 2.Control strategy and software implementation 3.Simulation 4.Analysis 5.Conclusion Barcelona, LISA7 Symposium, June 17th 2008

4. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control The LTP Science objective Barcelona, LISA7 Symposium, June 17th 2008 x1x1 x2x2 xx

5. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control The Drift Mode : 2 objectives  DC gravity term Barcelona, LISA7 Symposium, June 17th 2008 x1x1 x2x2 xx

6. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control The Drift Mode : 2 objectives  DC gravity term Barcelona, LISA7 Symposium, June 17th 2008 x1x1 x2x2 xx

7. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control The Drift Mode : 2 objectives  Force noise without actuation Barcelona, LISA7 Symposium, June 17th 2008 x1x1 x2x2 xx

8. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control The Drift Mode : 2 objectives  Force noise without actuation Barcelona, LISA7 Symposium, June 17th 2008 x1x1 x2x2 xx

9. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control The Drift Mode : 2 objectives  Force noise without actuation Barcelona, LISA7 Symposium, June 17th 2008 x1x1 x2x2 xx

10. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control 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

11. www.ifr.uni-stuttgart.de Institute of Flight 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

12. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Modeling the dynamics  EOM for the experiment  Same type of equations in other DOFs Barcelona, LISA7 Symposium, June 17th 2008

13. www.ifr.uni-stuttgart.de Institute of Flight 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

14. www.ifr.uni-stuttgart.de Institute of Flight 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 x y z

15. www.ifr.uni-stuttgart.de Institute of Flight 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

16. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Constraints on the dynamics  External Forces and Torques  DC gravity is dominating Barcelona, LISA7 Symposium, June 17th 2008

17. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Constraints on the dynamics  Actuation limitations  Choices  What are the DOFs?  Which actuators?  Which range? Barcelona, LISA7 Symposium, June 17th 2008

18. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Constraints on the dynamics  Sensing limitations  Sensing limitations  IFO is best choice Barcelona, LISA7 Symposium, June 17th 2008

19. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Outline 1.Experiment description 2.Control strategy and software implementation 3.Simulation 4.Analysis 5. Conclusion Barcelona, LISA7 Symposium, June 17th 2008

20. www.ifr.uni-stuttgart.de Institute of Flight 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 X2X2 T0T0 T1T1

21. www.ifr.uni-stuttgart.de Institute of Flight 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 -7 N)  Open loop control Barcelona, LISA7 Symposium, June 17th 2008 t X2X2 T0T0 T1T1

22. www.ifr.uni-stuttgart.de Institute of Flight 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 X2X2 T0T0 T1T1

23. www.ifr.uni-stuttgart.de Institute of Flight 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

24. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control 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 kickKicks : variable timeline but fixed force TELECOMAND CONTROL Pre-defined sequence executed on a pre-defined timeline ON-BOARD CONTROL Sequence computed by On-Board- Computer D C D C D D K D C D K D K D K D K D K D K

25. www.ifr.uni-stuttgart.de Institute of Flight 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 C D K D K D K D C

26. www.ifr.uni-stuttgart.de Institute of Flight 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% F DC → 2000s

27. www.ifr.uni-stuttgart.de Institute of Flight 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 PhaseParameters Custom Mode ControllerCommand SignalElectrodes 1-4 Controlled Manoeuver 14Sliding mode TBC NoWR Drift15NothingNoWR Kick15NothingUse command signal -2.67.10 -7 N for 0.1<t<2.1s WR

28. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Outline 1.Experiment description 2.Control strategy and software implementation 3.Simulation 4.Analysis 5.Conclusion Barcelona, LISA7 Symposium, June 17th 2008

29. www.ifr.uni-stuttgart.de Institute of Flight 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

30. www.ifr.uni-stuttgart.de Institute of Flight 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

31. www.ifr.uni-stuttgart.de Institute of Flight 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

32. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Simulation  Results  Simulation matching  Time response splitted between control phases Barcelona, LISA7 Symposium, June 17th 2008

33. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Simulation  Results  Simulation matching  Time response splitted between control phases  Difference between PSDs is checked Barcelona, LISA7 Symposium, June 17th 2008

34. www.ifr.uni-stuttgart.de Institute of Flight 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

35. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Outline 1.Experiment description 2.Control strategy and software implementation 3.Simulation 4.Analysis 5.Conclusion Barcelona, LISA7 Symposium, June 17th 2008

36. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Analysis  Retrieving speed, position and acceleration estimates  Using a Kalman smoother  Also gives covariance Barcelona, LISA7 Symposium, June 17th 2008 Linear sys U Kalman Smoother Y ε, P Xest N

37. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Analysis  Retrieving speed, position and acceleration estimates  Using a Kalman smoother  Also gives covariance Barcelona, LISA7 Symposium, June 17th 2008 Linear sys U Kalman Smoother Y ε, P Xest N

38. www.ifr.uni-stuttgart.de Institute of Flight 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 Ope n loop dyn θ Xerr Λ

39. www.ifr.uni-stuttgart.de Institute of Flight 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  a 1 + a 2 + a sc not observable Barcelona, LISA7 Symposium, June 17th 2008 U Linear sys Kalman Smoother Y ε, P Xest N Open loop dyn θ Xerr Λ

40. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Analysis  Retrieving Noise spectrum  Actuation Noise must be taken out  Usefull data is isolated Barcelona, LISA7 Symposium, June 17th 2008

41. www.ifr.uni-stuttgart.de Institute of Flight 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

42. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Analysis  Retrieving Noise spectrum  Gap filling must be used at and below the cutting frequency It is combined with windowing of the whole signal  Show first example data filled and windowed Barcelona, LISA7 Symposium, June 17th 2008

43. www.ifr.uni-stuttgart.de Institute of Flight 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

44. www.ifr.uni-stuttgart.de Institute of Flight 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

45. www.ifr.uni-stuttgart.de Institute of Flight 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

46. www.ifr.uni-stuttgart.de Institute of Flight 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

47. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Analysis  Retrieving Noise spectrum Barcelona, LISA7 Symposium, June 17th 2008

48. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Analysis  Retrieving Noise spectrum  Bounds on the estimate ? Barcelona, LISA7 Symposium, June 17th 2008

49. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Outline 1.Introduction 2.Experiment modeling 3.Control strategy and software implementation 4.Simulation 5.Analysis 6.Conclusion Barcelona, LISA7 Symposium, June 17th 2008

50. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Conclusions  Drift mode is implementable, but data is interrupted  Implementation limitations have a cost Barcelona, LISA7 Symposium, June 17th 2008

51. www.ifr.uni-stuttgart.de Institute of Flight 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

52. www.ifr.uni-stuttgart.de Institute of Flight Mechanics and Control Conclusions  DC Forces and torques can be estimated  PSD difficult to estimate at switching frequency Barcelona, LISA7 Symposium, June 17th 2008