1. 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 Optimization of the final focus stabilization The 9 th march 2010

2. 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 δ i and kicker strength k can be calculated via :  PID controller used :

3. 3 The initial status  The obtained results :

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

5. 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 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 :  The process is a delay (z -1 ) with a gain at a sampling period (Te = 0,02 s).

6. 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. 7 The context  The feedback scheme : Ground motion displacement CMS experiment (MG Data)  In open loop (feedback off) : The BPM measurement = the displacement at the CMS experiment filtered by the TMC table with an additional delay. ∆Y X : the filtered disturbance e-  The simulated layout : TMC Table A rigid QD0 Magnet on a rigid support

8. 8 The results DampingAmplification

9. 9 The results DampingAmplification

10. 10 The analysis  The gain of the sensitivity transfer function ( ∆y / X) :  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. Damping Amplification

11. 11 The principle of the developed 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.  The global scheme with feedback + feed-forward :

12. 12 The results  The obtained integrated RMS with FF + most optimized FB :  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 Without additional noise (Seismic sensor noise, BPM noise, disturbances on the magnet)

13. 13 The results  Another example of an obtained integrated RMS with FB + FF, (no noise) :  The global control (FB + FF) is more efficient.  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.

14. 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 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.  Some other considerations :

15. 15  Same example of an obtained integrated RMS with FB + FF, with additional noises :  The global control (FB + FF) still efficient.  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 Preliminary investigations

16.  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. 18 Conclusions  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.  Feedback :  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).  See the note “LAPP-TECH-2010-01-V2.pdf : Preliminary results of the analysis and of the optimization dedicated to the final focus stabilization”

19. Annexes

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