BPM/Corrector Layout - ADOS

Status of SLS Instrumentation and Achievements in Coupling Control

TIARA-SVET kick-off Meeting 23-24/02/11

BPM/Corrector Layout

sector

8 8

14

Quadrupole

Sextupole

Dipole

for FEMTO straight

+1 BPM/Correctors

U19

W128

��

Horizontal / Vertical Correctors

BPMs

• The SLS Storage Ring is divided into 12 sectors.

• Pairs of 6 BPMs and 6 horizontal/vertical Dipole Corrector Magnets are distributed over one Sector (+1

BPM/Correctors set for FEMTO straight).

• The Corrector Magnets are implemented as extra windings on the Sextupoles, the BPMs are adjacent to

the Quadrupols (nonzero orbit in a quadrupole field leads to a dipole kick).

Michael Boge 2



How is the Closed Orbit corrected ?

• Sliding Bump - Phase advances between Correctors 0◦ < ∆φ < 180◦, Correctors 1,2,3 allow to zero

the orbit in BPM 2 near Corrector 2. 1 opens “Orbit Bump”, 2 provides kick for 3 to close it again.

Continue (“Slide”) with 2,3,4 to zero orbit in BPM 3 ... iterate until orbit is minimized in all BPMs !

Corrector BPM

12 3

12

3

Orbit Bump

4

< 180 deg∆Φ

• MICADO - Finds a set of “Most Effective Correctors”, which minimize the RMS orbit in all BPMs at

a minimum (“most effective”) RMS Corrector kick by means of the SIMPLEX algorithm. The number

of Correctors (= iterations) is selectable.

• Singular Value Decomposition (SVD) - Decomposes the “Response Matrix”

Aij =

√βiβj

2 sin πνcos [πν − |φi − φj |] containing the orbit “response” in BPM i to a change of

Corrector j into matrices U ,W ,V with A = U ∗ W ∗ V T . W is a diagonal matrix containing the

sorted Eigenvalues of A. The “inverse” correction matrix is given by A−1 = V ∗ 1/W ∗ UT .

SVD makes the other presented schemes obsolete !-)

Michael Boge 3



Corrector/BPM Response Matrices

73 hcm 5 0 -5

010

2030

4050

6070

mon index0

1020

3040

5060

70

hcm index

-15

-10

-5

0

5

10

15

73 vcm 10 5 0 -5

-10

010

2030

4050

6070

mon index0

1020

3040

5060

70

vcm index

-15

-10

-5

0

5

10

15

Aij =

√βiβj

2 sin πνcos [πν − |φi − φj |]

• “Response Matrix”: Differences from the “Closed Orbit” (“Difference Orbit”)

due to a kick of corrector i are recorded at BPM positions j = 1..73.

• νx = 20.44 (≈3 BPMs/Correctors per unit phase, φ =∫ s

01/β(s)ds)

• νy = 8.74 (≈9 BPMs/correctors per unit phase)

Michael Boge 4



SVD Eigenvalues

0.001

0.01

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80

rms/m

ax o

rbit [

mm

] a

nd

w[in

de

x]

index of w[index]

whhorbit

wvvorbit

• Range of Eigenvalues 0.5 < W < 500

• Eigenvalue Cutoff @ i0 (Wi = 0 for i > i0) determines the minimum achievable RMS Orbit and

Corrector Strength after Correction → “MICADO” like: the largest Eigenvalues correspond to the

“Most Effective Corrector” patterns

• No Cutoff corresponds to “Matrix Inversion”. The RMS Orbit after Correction is Zero !

Michael Boge 5



Inverse Corrector/BPM Response Matrices

73 hcm 0.5 0

-0.5

010

2030

4050

6070

hcm index0

1020

3040

5060

70

mon index

-1

-0.5

0

0.5

1

73 vcm 0.5 0

-0.5

010

2030

4050

6070

vcm index0

1020

3040

5060

70

mon index

-1

-0.5

0

0.5

1

A−1

ij = (V ∗ 1/W ∗ UT )ij

• A−1

ijis a sparse “tridiagonal” matrix (3 large (+1 small) adjacent coefficients are nonzero since BPM

and Corrector positions are slightly different)

→“Sliding Bump Scheme” iteratively inverts A

• A−1

ijcontains global information although it is a “tridiagonal” matrix !

→ Implementation of a Fast Orbit Feedback (FOFB)

Michael Boge 6



How to correct Off-Energy Orbits ?

• In the case of “strong focussing” (b) the Orbit Deviation @ a location s is given by

x0(s) = D(s)∆p/p0 with ∆p = p − p0, D(s) denotes the Dispersion. ∆L/L0 = αc∆p/p0 with

the so-called “Momentum Compaction Factor” αc = 1/L0

∫ L0

0D(s)/ρ(s)ds (≈ 6 · 10−4 at the

SLS)

• p variations due to “Path Length” ∆L/L0 (thermal or modelling effects) changes have to be corrected

by means of the RF Frequency f with ∆f/f = −αc∆p/p0 and NOT by the Orbit Correctors !

→ Fit ∆p/p0 part of the Orbit using SVD on a 1 column response matrix containing dispersion values Di0

@ the BPMs and change the RF frequency by −∆f to correct for ∆p/p0 !

Michael Boge 7



Orbit Correction Loop

��

��

Off−Energy OrbitCorrection

Orbit Correctionbased on InvertedResponse Matrix

Removal from

Using Frequency

Corrector Pattern

Dispersion Pattern

Michael Boge 8



Fast Orbit Feedback - Schematic View

A-L = Submatrices of A -1PC

measured

theoretical

A

B

CD

E

F

G

H

I

J

K

L Response Matrix A

= Signal Processors

Fast Link 40Mb/s

PC

= SVD Engine

Slow Link

1Mb/s

Slow Link

or

• Dedicated Signal Processors perform Matrix Multiplications in parallel !

Michael Boge 9



Fast Orbit Feedback - Digital BPM System

Closed Orbit:

Mode for All Machines

in Different Operation

Only One BPM System

Turn−by−Turn:

Vital for

Commissioning

Turn−by−Turn:

PSI +

Closed Orbit Mode −> Fast Orbit Feedback

µ

1 MSample/s, <20 mµ

4 KSample/s, <0.8 m~300 nm <100 Hz

Michael Boge 10



Fast Orbit Feedback - Detail

Michael Boge 11



Fast Orbit Feedback - Performance

100

102

104

−20

−15

−10

−5

0

5

hor. open loop transfer function

frequency [Hz]

am

plit

ude [dB

]

BW 1 = 355 Hz

BW 2 = 2014 Hz

measuredfit

100

102

104

−20

−15

−10

−5

0

5

ver. open loop transfer function

frequency [Hz]

am

plit

ude [dB

]

BW 1 = 827 Hz

BW 2 = 2010 Hz

measuredfit

100

102

104

−800

−600

−400

−200

0

200

frequency [Hz]

phase [deg]

measuredfit

100

102

104

−600

−500

−400

−300

−200

−100

0

100

frequency [Hz]

phase [deg]

measuredfit0 dB point @ 100 Hz

Michael Boge 12



Slow/Fast Orbit Feedback - System Integration

peratoroco

BPM

Server

TRACY

Server

Client

Event

Event

@ 3Hz

Poll

CORBA Server

CorrectorsBPMs

Client

Feedback

FB Log

ClientModel Server

Console

Server

CDEV

BPMFast Orbit Feedback

LowLevel Hardware

EZCA Server

FOFB

De

dic

ate

dV

ME

/DS

P

Le

ve

lU

NIX

Ho

sts

Event

@ 0.5Hz

Event

@ 1Hz

@ 1Hz

• Development within a Client-Server (Common Object Request Broker CORBA) environment

• Hard Correction (“Matrix Inversion” on the Model based Response Matrix using SVD)

• BPM Datasets @ 3 Hz, average over 3 successive Datasets => ≈ 1 Hz correction rate (toggle between

x/y plane => 2 s for full cycle)

Michael Boge 13



Slow/Fast Orbit Feedback - Operator Interface

oco(Mode=RI,co; Server=slsbd8; Domain=slsac.psi.ch)

Feedback ON Mode FOFB active

Tklogger(Group=slsbd; Server=slsbd8; Domain=slsac.psi.ch)

Reference Orbit

EVENT

Blinking !!!

POLL

Daq ON !!!

Continue !!!

Stop FeedbackStart FeedbackCorrect

Michael Boge 14

Documents

BPM/Corrector Layout - ADOS