B. Caron, G. Balik, L. Brunetti LAViSta Team

1. Optimization of the final focus stabilization B. Caron, G. Balik, L. Brunetti LAViSta Team LAPP-IN2P3-CNRS, Université de Savoie,Annecy, France& SYMME-POLYTECH Annecy-Chambéry, Université de Savoie, Annecy, France The 9th march 2010

2. The initial status • The previous developments done by Daniel : - Daniel Schulte “Some Comments on feedback and feed-forward at the IP”. - Juergen Pfingstner “Ground motion control problems for CLIC”. • Expected beam-beam offset due to quadrupole slice offsets δi and kicker strength k can be calculated via : • PID controller used :

3. The initial status • The obtained results :

4. Our developed method • A dedicated feedback (FB) with a optimized method • A developed approach with a feedback + a feed-forward (FF) • The methods • The obtained results • The analysis

5. The system • The feedback scheme of the system : ∆Y: the displacement of the beam which needs to be controlled (BPM post collision). X: the disturbance which corresponds to the mechanical excitation of the QD0 magnet. → The transfer function between the mechanical displacement of this QD0 magnet and the beam can be modeled by a constant matrix. W: the noise of the sensor (BPM noise) is added to the beam displacement... Kb: The computed action (which is applied thanks to a kicker). • The process : - The dynamic of the process is due to the frequency of the beam train.- The obtained displacement of the beam is proportional to the injected current. • The process is a delay (z-1) with a gain at a sampling period (Te = 0,02 s).

6. The controller • The closed loop transfer function (sensitivity transfer function) : • We have considered a standard structure of controller : The goal is to reduce the RMS(0) (at 0 Hz) of ∆y(z-1). In order to find the best controller that minimize RMS(0), we have used the followings steps : - Estimation of the PSD of the measured ground motion signal : X(z-1)=Z(x(t)) - Scanning the parameter space of the controller. - Computation of the PSD of the obtained output using : - We keep the parameter set of the controller that gives the minimum RMS(0).

7. The context • The feedback scheme : • The simulated layout : A rigid QD0 Magnet on a rigid support e- ∆Y • In open loop (feedback off) : The BPM measurement = the displacement at the CMS experiment filtered by the TMC table with an additional delay. X : the filtered disturbance TMC Table Ground motion displacementCMS experiment (MG Data)

8. The results Damping Amplification

9. The results Damping Amplification

10. The analysis • The gain of the sensitivity transfer function (∆y / X) : Damping Amplification • The controller is efficient on a bandwidth of frequencies which is limited by the sampling time of the process output. • If the PSD of the disturbances is not steady, the controller will not be the most optimized one. • This feedback can be coupled with a feed-forward approach.

11. The principle of the developed feed-forward • The global scheme with feedback + feed-forward : • An open-loop FF controller is not able to deal with: - even very small difference between FF controller and TMC table. - low drift of the output of the FF controller (a very small DC component) . - all other differences between real world and the FF controller • The parameters of the feed-forward filter is adapted in real time in order to adjust its action in function of: - the BPM measurement. - the measurement of the ground motion. - the computed action of the feedback.

12. The results • The obtained integrated RMS with FF + most optimized FB : • Without additional noise (Seismic sensor noise, BPM noise, disturbances on the magnet) • The control is efficient, but it could be improve. • The best controller for FB is not the best controller when FF is added • A global optimization with FF + FB has to be done

13. The results • Another example of an obtained integrated RMS with FB + FF, (no noise) : • The feedback controller has only one integrator and is optimized mainly around 5-20 Hz • The feedback allows to obtain an improvement at low frequencies without too much important amplification at high frequencies. • Then, the feed-forward success to improve the results even at low frequencies and at high frequencies. • The global control (FB + FF) is more efficient.

14. Some important comments about results and simulation • At time t=0 the controller is not adapted • The filter parameters converge to a set able to minimize the output but not toward the TMC table parameters • Some other considerations : • Some improvements have to be done in order to deal with other neglected mechanical dynamics (work in progress) • The parameters drift of the FF controller is possible due to very low output signals (numerical problems, noises, too low excitation of the adaptive algorithm). • The FF could be temporarily unstable • Precision and dynamic of seismic noise measurement. • Influence of the dynamic of the beam before final focus. • Behavior of the BPM due to the dynamic of the parameters adaptation (the peak to peak is much more important during this transient). • Final positioning of the seismic noise measurement. • Stability of the PSD of the seismic noise.

15. Preliminary investigations • Same example of an obtained integrated RMS with FB + FF, with additional noises : • We have tested the influence of white noise (WN) on all measurements : • A variance of the WN equals to 3% of the peak to peak of the BMP is admitted • A variance of the WN equals to 1e-6 of the peak to peak of the ground motion measurement is admitted • The global control (FB + FF) still efficient.

16. Preliminary investigations • Ex : The global scheme (FB + FF) with the DAC / ADC and a neglected mechanical dynamic : • In this case : - ADC (Guralp) : 18 bits.- ADC (BPM) : 16 bits.- DAC (kicker) : 26 bits. • The resolution of the ADC/DAC depends on the required specification of the stabilization. (and the use of amplifiers)

17. Preliminary investigations • Ex : The global scheme (FB + FF) with the DAC / ADC and a neglected mechanical dynamic : • A neglected dynamic has no influence on the results. • The required resolution of the ADC/DAC is very important in order to avoid a deterioration of the results.

18. Conclusions • Feedback : • An optimized controller has been developed and allows to obtain a very low displacement of the beam. • It depends on the knowledge of the disturbance PSD. • See the note “LAPP-TECH-2010-01-V2.pdf : Preliminary results of the analysis and of the optimization dedicated to the final focus stabilization” • Feedback + feed-forward : • A feed-forward approach has been carry out. • This method improves the results. • This method requires a less accurate knowledge of the disturbance on magnets. • Future prospects : • Add more realistic neglected dynamics and noises in order to test and tune the robustness of the adaptive algorithm of the ff controller. • Take into account the transfer function of the sensor and the noise of the sensors (Guralp + BPM).

19. Annexes

20. Annexes No noise, FB optimized

21. Annexes With noise, FB optimized

22. Annexes No noise, FF+FB optimized

23. Annexes With noise, FF+FB optimized

24. Annexes With noise, FF+FB optimized +converter