Orbit Feedback Control

1. Orbit Feedback Control Prototyping at the SPS Results from the studies of the LHC Orbit Feedback Ralph Steinhagen, AB-OP-SPS • Controller • I. data acquisition II. control algorithm III. sending the corrections to the machine IV. Performance of the feedback • ToDo‘s Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

2. Data Acquisition in BA5 • Acquired additionally the common SPS monitor data • Increased sampling frequency of the electronic up to 100 Hz(!): very nice! The sampling frequency should be at least 20-30 times higher than the highest frequency one wants to correct Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

3. Data Acquisition at 100 Hz Manipulating, measuring and correction the orbit at 100Hz: excitation: feedback: zoom: Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

4. Data Acquisition - Calibration • cross-callibration with standard SPS monitors • slope: will later be applied as a calibration factor in the acq. system, direct correlation to the calibration of the SPS monitors • now: through time changing calibration factors-> further investigation Slope for BPM.517 = 0.8 instead of „1“ Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

5. Data Acquisition - Intensity Dependency • Shift of mean orbit after changing the intensity (scraping) of the beam. Examples: Begin: I ~ 3-6 E11 End: I ~ 1-2 E11 Start of scraping Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

6. Data Acquisition – Gaps in Acquisition Load dependent systematic • found gaps in data stream acquisition: Systematic, load independent (DT~230ms every 26 s 4 s): not acquired/send? loss due to OS architecture? load dependent: dropped packets due to network architecture (10BaseT) dropped/not received packets cause a decrease of the effective sampling frequency -> decrease of max. correction frequency -> cause for instabilities • delay from measurement to delivering the packet is small but needs to be known and precisely defined Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

7. What Happens When Data Is Lost: Load dependent systematic Packet is dropped: the max. frequency one can correct drops and the feedback is unstable for former stable frequency: • One can prevent this by: • reducing the max. frequency (low pass filter) -> worse performance (factor 2n, n = # of consecutive lost packets) • polynomial interpolation of BPM reading (continuous, n- times differentiable) -> high complexity (increase of delay -> decrease of max. frequency) Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

8. Controller in PCR • Controller works in two domains: space domain & time domain • space domain (x/y over s): Problem: find the appropriate corrector strength to minimize the deposition of the closed orbit with the respect to the reference orbit: Chosen solution: Singular Value Decomposition (SVD): • small corrector strength • easy method of eliminating singular solution (Eigenvalue problem) • main complex calculation of the pseudo inverse Matrix need to be done only once for a certain set up, then the correction can be done through a simple matrix multiplication (fix. ): Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

9. Controller in PCR – Space Domain Corrected orbit (distorted +SVD) Computed SVD correction Simulated distorted orbit Simulation wit MAD: Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

10. Controller in PCR – Space Domain • added additional 2 cods on both sides to close the solution -> local SVD solution effect of the closed SVD solution on the global Orbit • the ring outside of the selected area is not affected by the solution • opens the possibility to do ‚parallel‘ parallel MD (parasitic) • test for the future: e.g. faster stabilisation of the beam in the collimation section than a global correction Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

11. Controller in PCR – Time Domain n-dim. m-dim. m: #monitors; n: #correctors time domain (x/y over t): Problem: find the appropriate corrector strength to minimize the deposition of the changing closed orbit. Chosen solution: 1rd order: feedback loop with a Proportional Integral Controller (PIC): • slower but good to compensate steady state errors (known and unknown) induced by errors of other components in the system (LHC) • good for keeping a certain solution (orbit position) Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

12. Controller in PCR – Response Functions Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

13. Power Converter • The feedback server send its correction via Ethernet back to the power converter (PC) in BA5. • Why prototyping at the SPS when the main part (PC+magnets) seem to behave completely different (tSPS~ 0.5s <-> tLHC~ 120s)? • It is possible to decompose and later recombine the whole systems response function and to exchange the response of the SPS PC-magnet combination (GSPS(s)) with the response function for the LHC PC-Magnets combination (GLHC(s)). • With this simple exchange of functions one can accurately predict the feedback behaviour with a real LHC-PC and load. • But this function needs to be modelled and MEASURED !! • This measurement could be performed in two month – we hope !! Replaced by GLHC(s) Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

14. PC - Response and Stability G(s) can be reconstructed from the observed amplitude and phase response reference response Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

15. PC – Accessing the Grid via UDP/10BaseT Buffering of packets in network infrastructure and servers causes distortion, additional delay and overflows to next cycle segment. Effect very common in each part of the controller and is load depended (interfering of realtime and non-realtime data streams) -> faster processing of packets and no buffering of data packets where necessary desired stable signal overflow additional delay Distortion due to step-by-step processing of buffered data. Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

16. Controller- Response and Stability • a stable feedback system must fit two criteria: • the desired controlled frequency has to be below the bandwidth of the system. The bandwidth is determined by L,R (and C) of the PC circuit (1rd order) and its controlling algorithm (2nd order). • phase: ! • the phase is determined by: • the used circuit (L,R and C) • the overall delay l of the system • dj= l 2pf (increases linear with the frequency) • e.g. a total delay of 0.1 s limits the control system to f = 2.5Hz • -> the delays have to be as small as possible and for the lag compensation well defined (constant) Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

17. Controller- Performance 450 GeV ramp injection at 26 GeV The response function of the whole feedback system was measured: no feedback: with feedback: with feedback (zoom): Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

18. Controller- Performance 20 Hz sampling 10 Hz sampling 50 Hz sampling 100 Hz sampling Reasonable correction stability (high beta) for f << 1 Hz (limited by BPM noise): Dx ~ 30 (20) mm Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

19. Controller- Performance Example Limited by hfrq. BPM noise will later be reduced by a filter Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

20. To-do‘s: End 2003 -> 2004 • Input: • reducing dead times and packet drops • changing of calibration factors need to be understood and suppressed • Controller: • space domain: ‘final’ strategy for LHC (global<->local), optimising the local SVD correction • time domain: multidimensional lag compensation (1-dim. -> Smith predictor, modelling of response functions and algorithms, optimising with filter) • Output: • Measurement of the frequency response of LHC PC with a standard load • All: • the response function for each component needs to be precisely known and deterministic (!!) • reliability of the systems needs to be enhanced • scaling of the solution which works in the SPS to the dimension of the LHC • model should as always be proven by experimental results Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

21. Controller- Response and Stability instable Stable performance ~ 1- cos(j) our delay ~ 5ms Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

22. Data Acquisition – Power Spectrum BPM With additional signal Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS

23. Dummy Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS