Orbit Feedback Control

Ralph Steinhagen , Orbit Feedback Control - Prototyping at the SPS 1

Orbit Feedback Control

A. Controller

B. I. data acquisition II. control algorithm III. sending the corrections to the machine IV. Performance of the feedback

C. ToDo‘s

Prototyping at the SPSResults from the studies of the LHC Orbit Feedback

Ralph Steinhagen, AB-OP-SPS


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


Data Acquisition at 100 Hz

Manipulating, measuring and correction the orbit at 100Hz:

excitation:

feedback:

zoom:


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“


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


Data Acquisition – Gaps in Acquisition

found gaps in data stream acquisition:

Systematic, load independent (T~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

Load dependent systematic


What Happens When Data Is Lost:

Packet is dropped:

the max. frequency one can correct drops and the feedback is unstable for former stable frequency:

Load dependent systematic

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)


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. ):

d

.. refmon xxx

)( 2nO

xMd

M


Controller in PCR – Space Domain

Simulated distorted orbit

Computed SVD correction

Corrected orbit (distorted +SVD)

Simulation wit MAD:


Controller in PCR – Space Domain

added additional 2 cods on both sides to close the solution

-> local SVD solution

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

effect of the closed SVD solution on the global Orbit


Controller in PCR – Time Domain

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):

d

m-dim.

m: #monitors; n: #correctors

n-dim.

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)


Controller in PCR – Response Functions

SVD: GSVD=e-s(aij) ~O(n2) ms(aij): pseudo inv. Matrix

PIC: GPIC=(Kp – Ki/s) Kp: proportional gain

Ki: integral gain

BPM: GBPM=Ci e-s(aij) Ci: Calibration factor

Physics: GPhysic=(bij) (bij): response matrix of the machine (MAD, linear optics)

PC:

+ computed model of G(s)

G(s) is the combined response function of the power converter (PC), PC-controller and its connected load (SPS cod - magnet)


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 (SPS~ 0.5s <-> LHC~ 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)


PC - Response and Stability

G(s) can be reconstructed from the observed amplitude and phase response

1

2log20A

AMagnitude

reference

response


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

additional delay

Distortion due to step-by-step processing of buffered data.

overflow

desired stable signal


Controller- Response and Stability

a stable feedback system must fit two criteria:

1. 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).

2. phase: !

the phase is determined by:

• the used circuit (L,R and C)

• the overall delay of the system

d= f (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)

2


Controller- Performance

The response function of the whole feedback system was measured:

ramp

injection at 26 GeV

450 GeV

no feedback:

with feedback:

with feedback (zoom):


Controller- Performance

10 Hz sampling

20 Hz sampling

100 Hz sampling

50 Hz sampling

Reasonable correction stability (high beta) for f << 1 Hz (limited by BPM noise):

x ~ 30 (20) m


Controller- Performance Example

Limited by hfrq. BPM noise

will later be reduced by a filter


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


Controller- Response and Stability

instable

Stableperformance ~ 1- cos()

our delay ~ 5ms


Data Acquisition – Power Spectrum BPM

With additional signal


Dummy

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Orbit Feedback Control

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