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

2. LIGO-G060161-00-Z The Problem

3. LIGO-G060161-00-Z 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

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

5. LIGO-G060161-00-Z IIR Implementation

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

7. LIGO-G060161-00-Z STS Wit PS Geo F sts F Sup F PS F Geo + A B + + + + + + Output + + + K2K2 K1K1 ()() ()()  (  )=0 ()() ()() ()() Plant  + Ground Input Feedback Control Strategy

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

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

10. LIGO-G060161-00-Z Simple Implementation

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

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

13. LIGO-G060161-00-Z Closed Loop Response Closed Loop Equation Simplifying 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 XXX f = A filter XXX g = Ground to sensor TF XXX d = Actuator to sensor TF

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

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

16. LIGO-G060161-00-Z

17. *** SENSOR CORRECTION IS OFF ***

18. LIGO-G060161-00-Z 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?

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