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Master Plan Analyses

Master Plan Analyses. DA#6. X-dynamics update. The changes. 2-inputs/2-outputs system (IFO signals x 1 , x  ) Multi parameter dynamical model. o i, 1. o 1. o i, . o . The effective dynamics. Basic dynamics. 2-body difference of force drives the two differential coordinates.

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Master Plan Analyses

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  1. Master Plan Analyses DA#6 S. Vitale

  2. X-dynamics update S. Vitale

  3. The changes S. Vitale

  4. 2-inputs/2-outputs system (IFO signals x1, x) Multi parameter dynamical model oi,1 o1 oi, o The effective dynamics S. Vitale

  5. Basic dynamics • 2-body difference of force drives the two differential coordinates. • Only two inputs are needed • Force on x1 can be applied either via oi1 (Thrusters) or via gx1 (Electrostatic) • If gx1=-Hdfoi1 formulas stay the same but cross-talk coefficient changes meaning. • Careful: to apply gx1 must increase stiffness. S. Vitale

  6. Signal amplitude adjusted to compensate for gain and to avoid force saturation S. Vitale

  7. Blue: x. Red: x1 S. Vitale

  8. Real displacement S. Vitale

  9. Results S. Vitale

  10. Same approach: response linear in imperfections Imperfections unknown amplitudes to be extracted by Wiener-Kolmogorov (vectorial) theory Stimuli also applied as forces to distinguish actuation cross-talk y-x Cross-Talk S. Vitale

  11. Starting point S. Vitale

  12. Force input “Displacement” input Linearisation S. Vitale

  13. S. Vitale

  14. Dynamics 2: y- nominal Acting on TM for S/C attitude TM attitude irrelevant to first order S. Vitale

  15. Dynamics 2: Solving for S/C acceleration S. Vitale

  16. Dynamics 3: x and imperfections • No inputs on x • No imperfections on x • Nominal response = 0 S. Vitale

  17. S. Vitale

  18. Various Matrices S. Vitale

  19. Dynamics and control imperfections S. Vitale

  20. Signal and actuation imperfections S. Vitale

  21. Two cases: Displacement command within drag-free loop Excites thrusters Probes thrusters cross-talk Electrostatic TM cross-talk only excited through very low frequency attitude control Force command on TM1 and TM2 Probes electrostatics Numerical Calculation S. Vitale

  22. Acceleration noise on x axis. Noise cross-talk neglected Channel 1 (S/C-TM1) Channel  (TM2-TM1) |Cross-spectrum| S. Vitale

  23. Case 1: displacement excitation y1 y2 Force limited < 10 µN S. Vitale

  24. Excitation S. Vitale

  25. Response S. Vitale

  26. Response, absolute attitude S. Vitale

  27. Results (Preliminary): statistically independent combinations Signal cross-talk y-to- measured with high resolution If ifo sensitivity calibrated on ground, thruster cross-talk and cross-stiffness can be disentangled S. Vitale

  28. Case 2: force excitation (<1µm displacement) y1 y2 S. Vitale

  29. Force excitation S. Vitale

  30. Displacement response S. Vitale

  31. Results (preliminary): statistically independent imperfections Actuation cross-talk measured with high resolution Signal cross-talk y-to- also measured scaled for smaller excitation S. Vitale

  32. Actuation cross-talk channel 1 S. Vitale

  33. Actuation cross-talk channel  S. Vitale

  34. Signal cross-talk channel  S. Vitale

  35. Key element: converting data from displacement to acceleration Acceleration PSD S. Vitale

  36. Time domain operation more transparent Double derivative required Non-casual filter preferred Currently in torsion pendulum: 2nd order fit to 5 points Getting the filter S. Vitale

  37. S. Vitale

  38. Next steps Complete technical note Complete analysis for acceleration PSD Get the number for z -x cross-talk -x cross-talk More difficult -x cross-talk Planning S. Vitale

  39. S. Vitale

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