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Adaptive FIRs taking place at Lasti

Adaptive FIRs taking place at Lasti. Richard Mittleman Laurent Ruet Brett Shapiro April 2006. The Problem. FIR Implementation. The basic block diagram for an FIR filter of length N . The delays result in operating on prior input samples. The hk values are the coefficients used

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Adaptive FIRs taking place at Lasti

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  1. Adaptive FIRstaking place at Lasti Richard Mittleman Laurent Ruet Brett Shapiro April 2006 LIGO-G060161-00-Z

  2. The Problem LIGO-G060161-00-Z

  3. FIR Implementation The basic block diagram for an FIR filter of length N. The delays result in operating on prior input samples. The hk values are the coefficients used for multiplication, so that the output at time n is the summation of all the delayed samples multiplied by the appropriate coefficients. Or H = Filter Coefficients X = Input Values Y = Output Value LIGO-G060161-00-Z

  4. IIR Implementation Or LIGO-G060161-00-Z

  5. IIR Implementation LIGO-G060161-00-Z

  6. Adaptive Algorithm d x Plant + - e FIR-Filter y Gradient = FIR filter, of length N, has coefficients h LIGO-G060161-00-Z

  7. Control Strategy K1 A B + + + + + + + + + STS () Fsts () Ground Output () FPS ()=0 PS + Input Geo FGeo () () () Wit + Output Plant K2 FSup Feedback LIGO-G060161-00-Z

  8. FIR Implementation G + Plant Plant-B B - Actuators Shaping Filter Output Filter H(FIR) S = Shaping Filter O = Output Filter P = Plant(Actuator to Witness Sensor) G = Ground input LIGO-G060161-00-Z

  9. No Compensation Path LIGO-G060161-00-Z

  10. Simple Implementation LIGO-G060161-00-Z

  11. Feed Forward Sensor On The BSC Wilcoxon Accelerometer Feed Forward Sensor LIGO-G060161-00-Z

  12. SISO BSC Model STS + STS_f G + To Pier top + + + + PS PS_f To payload + Plant + A GEO Geo_f WIL FIR WIT + Sup_f + = Sensors = Filters LIGO-G060161-00-Z

  13. Closed Loop Response Closed Loop Equation Simplifying XXXf = A filter XXXg = Ground to sensor TF XXXd = Actuator to sensor TF And the Witness response is A = Actuator Drive Signal G = Ground Signal Where Y has ground to sensor Transfer Functions and Z has drive to sensor Transfer Functions LIGO-G060161-00-Z

  14. Extra Feed Back Path G + Plant Plant-B B - K Actuators + H(FIR) - Filter Update Coefficients = feed forward sensor K = feed back to feed forward senor LIGO-G060161-00-Z

  15. Make an approximation Initially H = 0 After it has converged H ~= B So use LIGO-G060161-00-Z

  16. LIGO-G060161-00-Z

  17. ***SENSOR CORRECTION IS OFF*** LIGO-G060161-00-Z

  18. What needs to get Done • Work more with the Model • Redo HEPI with 6 DOF and optimized sensor correction • (hopefully after the installation of the control Quad pendulum prototype in April) • Port to LIGO controls • Other Ideas and wonderful suggestions? LIGO-G060161-00-Z

  19. Adaptive FIR Filters(Gradient Minimization) Control Path Feed Forward Sensor Adaptive Path HEPI Geophones HEPI BSC Adaptive FIR Filter Wednesday 10:10am (SEI) LIGO-G060161-00-Z G

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