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System Identification for X-dynamics

System Identification for X-dynamics. Data Analysis 4. LTP dynamics. 2 measured and controlled Degrees of Freedom within Measurement Bandwidth 3 Actuators (1 redundant) 4 Signals (2 redundant) A 2 Input-2 Output system with redundant sensing and actuation 4 Measurable transfer functions

jerry-mccormick
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System Identification for X-dynamics

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  1. System Identification for X-dynamics Data Analysis 4 S. Vitale

  2. LTP dynamics S. Vitale

  3. 2 measured and controlled Degrees of Freedom within Measurement Bandwidth 3 Actuators (1 redundant) 4 Signals (2 redundant) A 2 Input-2 Output system with redundant sensing and actuation 4 Measurable transfer functions If signals are used as stimuli, separates from rest of DOF (cross-talks shows as excess noise LTP dynamics within MBW S. Vitale

  4. Signals Dynamical variables The starting x-dynamics • In the absence of imperfections • o1 = x1 • o∆ = x2-x1 S. Vitale

  5. Force noise Read-out noise An example, the x-dynamics S. Vitale

  6. Control forces Force inputs An example, the x-dynamics S. Vitale

  7. 2 outputs 2 inputs An example, the x-dynamics The unmeasured variable A disappears, x1, x2,  x1o1, ∆x = x2-x1 o∆ S. Vitale

  8. An example, the x-dynamics (Frequency dependent) parameters to be measured S. Vitale

  9. Maximum likelihood estimator S. Vitale

  10. Maximum likelihood estimator S. Vitale

  11. Maximum likelihood estimator S. Vitale

  12. Signals only Maximum likelihood estimator S. Vitale

  13. The nominal response • - open loop force on S/C • open loop difference of force on test-masses S. Vitale

  14. The noise Channels are correlated • - open loop difference of force between test-mass 1 and S/C • open loop difference of force on test-masses S. Vitale

  15. The noise x1 x S. Vitale

  16. Pick matrices values that maximize Maximum likelihood estimator S. Vitale

  17. Requires Inversion of bigN x bigN matrix Requires non linear minimization tool Maximum Likelihood S. Vitale

  18. Good for studying the problem Allows simplified theory to be applied Allows quick estimation of Fisher Matrix and parameter resolution An alternative approach:linearisation S. Vitale

  19. Expand matrices as function of imperfections S. Vitale

  20. Linearization • To first order in: • # • noise S. Vitale

  21. Imperfections 1/4 S. Vitale

  22. Imperfections 2/4 S. Vitale

  23. Imperfections 3/4 An elementary model for delays and roll-off S. Vitale

  24. 20 Imperfection Parameters Each parameter generates a signal Imperfections 4/4 S. Vitale

  25. Example: Swept-sine input 0.03 mHz to 30 mHz in 104s S. Vitale

  26. S. Vitale

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  31. Extracting amplitudes Find h’s with no bias and minimal variance S. Vitale

  32. Playing with a very simplified model looking for G. Very large signal S. Vitale

  33. System identification requires Vector pre-processing (filter and linear combination) Multiple and correlated series Wiener filter/ Likelihood estimator Noise model parameterization from best measurement Dynamics pre-modeling Assessment of signals that can be uploaded ……. Conclusion S. Vitale

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