Orbit feedback robustness tests and System identification for FACET

1. Orbit feedback robustness testsandSystem identification for FACET Jürgen Pfingstner 29th of February 2012

2. Outline • Orbit feedback robustness • Static accelerator imperfections • Controller parameter errors • Conclusions • System identification at FACET • Principle • Algorithms • Results • Conclusions

3. 1. Orbit feedback robustness

4. Orbit feedback system for ML and BDS

5. 1.1 Static accelerator imperfections

6. Static RF errors

7. Static QP strength errors

8. Actuator scaling errors 30% error => 0.5% lumi. loss

9. BPM scaling errors 1% error => 0.5% lumi. loss

10. 1.2 Controller parameter errors

11. Errors in the used orbit response matrix due to ground motion (input/output directions)

12. Controller gain variations Δfi

13. Gain factors fi Mode 189 • Smooth distribution of the fi would be preferable for the robustness • Why are some patterns that create small BPM readings so important?

14. Investigation of mode 189 SF1, SD0 SD4, SF5, SF6

15. General sextupole kick • Angel y without sextupoles • Angle with sextupoles • Angle with sextupoles and kick in between them • 1.) Effect of the mode: • Luminosity loss via beam size growth in y plane, due to a correlation x’y • Corresponds to coupling from the x to the y plain in the FD • -> Sextupoles • 2.) Possible explanation: • Setup [-I] -x2 x3 x1 x2 S1 S2 Uncorrected geometric aberrations

16. Possible future work • 1.) Orbit feedback: • Robustness improvement by searching in a measured response matrix for the mode 189 and a. Assign a high gain to it b. Correct the problem with a different system, e.g. tuning knobs. 1.) Tuning (from discussion with Andrea, Daniel): • Maybe a possibility to use BPM readings as a tuning signal instead of luminosity • Maybe also other effects at the IP can be assigned to a BPM pattern • Correlation studies could be interesting

17. 2.System identification at FACET

18. 2.1 Principle Estimation algorithm • Goal: • Fit the model system in some sense to the real system, • using u(t) and y(t) • Ingredients • Model assumption • Estimation algorithm • System excitation Real-world system R(t) Excitation u(t) y(t) • ... Input data (actuators) • … Output data (BPM readings) • … real-world system (accelerator) • … estimated system

19. 2.2 Algorithms • Modified RLS can “forget” older values to learn time-changing systems. • Derivatives (easier to calculate) • - Stochastic approximation (SA) • - Least Mean Square (LMS) • Model: • Task: Find R from many known measurements yk and excitations uk . • Least squares solution: (pseudo-inverse) • LS calculation can be modified for recursive calculation (RLS):

20. 2.3 Results

21. Excitation level vs. emittance growth

22. RLS no noise, 63 corr.

23. RLS with noise, 63 corr.

24. RLS only one corrector, noise

25. RLS more excitation with noise

26. 2.4 Conclusions • Full orbit response matrix R cannot be identified in acceptable time with an parasitical excitation • Reasons: • Low BPM resolution • Slow actuator dynamics • Alternative scenarios • 1) Identification of a subset of correctors with higher excitation. • This could be helpful to get necessary information for BBA • 2) Identification of only 1 or 2 correctors for diagnostics purposes

27. Thank you for your attention!

28. LMS and SA algorithm, noise, 190 corr., Δεx=2%