Fast Orbit Feedback

Fast Orbit Feedback - BPM to PS

Yuke Tian

Control Group, Accelerator Division

Photon Sciences Directory

Brookhaven National Lab

EPICS Collaboration Meeting, BNL, 2010

Outline

• NSLS-II orbit feedback system requirements• Fast orbit feedback system architecture

• Overall architecture• BPM FOFB data measurement• BPM FOFB data delivery – fiber SDI link• FOFB calculation – compensation for each eigenmode• Corrector setpoints to power supply system

• Progress • Summary


NSLS-II orbit feedback system requirement

Energy 3.0 GeVCircumference 792 mNumber of Periods 30 DBALength Long Straights 6.6 & 9.3mEmittance (h,v) <1nm, 0.008nmMomentum Compaction .00037Dipole Bend Radius 25mEnergy Loss per Turn <2MeV

Energy Spread 0.094%RF Frequency 500 MHzHarmonic Number 1320RF Bucket Height >2.5%RMS Bunch Length 15ps-30psAverage Current 300ma (500ma)Current per Bunch 0.5maCharge per Bunch 1.2nCTouschek Lifetime >3hrs

NSLS-II technical Requirements & Specifications



Long ID Short IDDispersionRegion

Lattice function for one cell



5

,,

'

'

105/

1.0

1.0'1.0

1.0'1.0

pp

yy

xx

yxyx

yy

xx

my 3In short insertion, , hence must hold orbit stable to m3.0Orbit stability requirements can be met using orbit feedback.


NSLS-II orbit stability requirement


Long term - Years/MonthsGround movementSeason changes

Medium - Days/HoursSun and MoonDay-night variations (thermal)Rivers, rain, water table, windSynchrotron radiationRefills and start-upSensor motionDrift of electronicsLocal machineryFilling patterns

Short - Minutes/SecondsGround vibrationsTraffic, Earth quakes Power suppliesInjectorsInsertion devicesAir conditioningRefrigerators/compressorsWater coolingBeam instabilities in general

Noises source need to be suppressed


NSLS-II orbit feedback system requirementTypical noises source frequency in light source


NSLS-II orbit feedback system requirementBeam motion from long term group motion

Floor motion around the ring. Maximum movement is 107 µm, and the RMS around the ring is 36 µm.

Electron beam motion (vertical) without feedback loop; maximum is 600 µm.

Lihua Yu


Orbit feedback system architectureOverall architecture: slow and fast correctors


Fast orbit feedback system in one cell

Orbit feedback system architecture


NSLS-II two tier device controller architecture


Cell 1

Cell 2

Cell 3

Cell 16

Cell 30

Cell 29

Storage Ring

Cell 15Cell 17

SDI linkSDI link




NSLS-II FOFB latency/bandwidth

● BPM group delay: less than 50 us (estimate)

● BPM data from 8 BPMs transferred to cell controller: 3.5us

● BPM data distribute among the storage ring 6us (12us if one link broken)

● FOFB calculation with separate mode compensation: 3.5us

● Set power supply by PS SDI link: 5.4 us (11us if one link broken)

● Fast corrector PS bandwidth (10 degree phase shift): 8KHz

● Corrector magnet/chamber bandwidth: 1KHz

(measured with Inconel beampipe, 10 degree phase shift)

BPM FOFB data measurement



Joseph Mead

BPM FOFB data measurement



Kiman Ha

BPM FOFB data delivery – fiber SDI link



Joseph De Long

FOFB calculation – compensation for each eigenmode


• Fast orbit feedback system is a typical multiple-input and multiple-output (MIMO) system. For NSLS-II, there are 240 BPMs and 90 fast correctors. Tranditional singular value decomponsition (SVD) based FOFB treats each eigenmode the same.

• The reality is, a MIMO system will have different frequency response for different eigenmode and thus it is desirable to design different compensation to each eigenmode.

• The challenge is to finish the large computation within the time budget of FOFB system.

• NSLS-II FOFB system takes advantage of our two-tier communication structure and the parallel computation capability of FPGA to do the compensation for each eigenmode in FPGA.



A simple SISO feedback system

Controller

C(z)

Plant

H(z)

)(tx )(ty

)()(1

)()(

)(

)(

zHzC

zHzC

zX

zY



Fast orbit feedback system algorithm (MIMO system)

Controller

R-1=VΣ-1UT

Accelerator

R=UΣVT

d

goldd

11 MxNxMxN dR

11

1 MxNxMNx dR

Compensator

(PID etc)

R: response matrix

R-1: reverse response matrix

FOFB baseline algorithm

Offline operation: kick each corrector measure all BPM and get response matrix R

calculate R-1 with SVD

(10KHz) operation: measure/distribute all BPM data calculate corrector setpoints

set correctors



FOFB baseline calculation

11

1 MxNxMNx dR 11

Mxrowii dR th

N

N

NTUVR

.

1....

1

1

,..., 2

1

2

1

2111

Each of the corrector setpoint is calculated from a 1xM vector and Mx1 vector multiplication. If 8 BPM/cell, M=240.

For each corrector plane


Orbit feedback system architecture Problems for baseline algorithm

The ill-conditioned response matrix will cause numerical instability Solution: 1) Truncated SVD (TSVD) regularization: sharp cut off 2) Tikhonov regularization

N

N

N

N

NTUVDR

.

1....

1

1

,..., 2

1

2

2

22

22

2

21

21

1

2111

11

1 MxNxMNx dR 11

Mxrowii dR th Each of the corrector setpoint is calculated from a 1xM vector and Mx1 vector

multiplication. If 8 BPM/cell in NSLS-II, M=240. Total: ~240 MAC.

For each corrector plane






Orbit feedback system architecture Problems for baseline algorithm

To suppress high frequency contribution to the integrated amplitude, it is desirable to compensate each mode in frequency domain . So far, all the FOFB has an assumption that each mode has the same frequency response (same bandwidth).

UT Accelerator

R=UΣVT

d

goldd

Qi(z-1)id V


Compensation for each eigenmode


dzqdUzqV

N

N

N

N

NT

.

)(

1....

1

1

,...,)( 2

1

1

2

2

22

22

2

21

21

1

2111

21

21

2

11

1

21

)(

.

)(

)(

,...,

dzQ

dzQ

dzQ

n

N

: Compensator for mode i. )( 1zQi

:eigentspace components of dd ii

d

Calculation with the compensation for each mode



1. Calculate the eigenvector components (d1,d2,…dN) for BPM displacement

Total calculation: 1xM vector times Mx1 vector. Do this N times (for each ). This is N times larger calculation than gain-only FOFB calculation. For NSLS-II, N=90. Total MAC: 240 * 90 = 21,600

2. For each , design compensation .

3. Output modes (V) times . 1xN vector times Nx1 vector.

Challenge: need to finish the calculation within a few microsecond.

FPGA is perfect for this task. It can carry out the calculation (Matrix calculation and DSP compensation) in parallel.

1)1( MxxMii dd i

id )( 1zQi

ii dzQ )( 1

1Mxd

Calculation with the compensation for each mode


Implementation of fast orbit feedback Calculation with the compensation for one mode

Dual

Port

RAM

Dual

Port

RAM

Dual

Port

RAM

MUX

X Compensation

(PID, Notch filter etc) +

From control system

From control system

Eigenvector

Eigenvector

Select Active

Eigenvector

BPM dataFrom SDI link


Implementation of fast orbit feedback


Single mode component compensation (floating point module)



Single mode component compensation (floating point module)

Simulated BPM data Simulated input matrix Single mode component

Single mode component with compensation



Single mode component compensation (compare fixed point and floating point module)


SystemGenerator: floating point with fixedx point




Single mode component compensation (compare FPGA fixed point and Matlab floating point calculation)

Calculation difference for single mode component

Calculation difference for single mode component with compensation



Single mode component compensation (FPGA hardware co-simulation and Matlab floating point calculation)

Implementation of fast orbit feedbackCompare FPGA hardware co-simulation results and Matlab floating point calculation


Implementation of fast orbit feedbackFlexible frequency compensation in FPGA for each eigenmode


60Hz notch filter 200KHz low path filter


Calculation for corrector setting (one plane)

One mode Total

Speed (240+12)*10 = 2520ns 2520 + (90+8)*10 =3500ns

Accuracy <10ppm <10ppm

BRAM Resource (Virtex5FX70)

1% of BRAM 33% of BRAM

DSP Resource Depend on the compensation design.

Need lots of DSP resource to compensate for all eigenmodes.

Virtext5 (Virtex 6) provides many DSP resources to achieve single mode

compensation requirement.


Corrector setpoint to power supply system


Master

(PSC master,

Cell controller)PSC PSC

PSC

PSC PSC

PSC PSCPSC PSC

PSC

TX RX TX RXTX RX TX RX

RX TX RX TXRX TX RX TX

RX TXRX TX RX TX

TX RXTX RX TX RX

Power supply SDI link

RX TX

TX RX

RX TX

TX RX TX RX

RX TX

TX RX

RX TX


Redundant 100Mbps link to deliver FOFB calculation results (corrector setpoints) to PSC

Dynamic ID assignment

Flexible package size

Simply cabling between PSCs and cell controller.

Progress


BPM – finished first revision

SFP for fiber SDI link

RF signal inputs

V5 FPGA

4 ADC channels

256MB DDR2

GigE to EPICS IOC

Progress


Cell Controller – finished first revision

SFP for fiber SDI link

V5 FPGA

256MB DDR2

16 isolated TTL inputs

12 50Ohm TTL outputs

4 analog outputs2 PS SDI links

GigE to EPICS IOC

Progress


Power supply controller – in production

1 = JTAG connectors – Programming to FPGA and CPLD.

2 = RS232 port – Communication to PC for diagnostic and software development.

3 = DDR2 memory modules – PS diagnostic data, CPU memory.

4 = SDI connectors – Communication between PSC master (or cell controller) and PSC slaves.

5 = Fiber transceiver – Communication with PSI.

6 = Ethernet connector – Communication to EPICS IOC for PSC master.

7 = FPGA (Spartan3A)

8 = CPLD(8a) & SPI memory(8b) – Dual boot and remote programming functions.

7a1

2

3

4

5

6

8a

8b

7

Progress

• BPM hardware (DFE and AFE) passed the first revision. The second revision is underway.

• Cell controller (DFE and IO board) passed the first revision. • BPM FOFB data measurement is tested with lab simulated data and real

beam data.• BPM FOFB data delivery (fiber SDI link) is tested. • FOFB calculation is tested. • Power supply SDI link is tested. • Power supply controller is in production.• We are working on the FOFB system integration. It includes integration

of BPM, cell controller and power supply controller units.


Summary

• NSLS-II tow tier structure provides fast and deterministic data transfer for BPM data (BPM to cell controller), and power supply setpoints (cell controller to power supply controller). Cell controller is the central data concentrator/generator that has all the necessary data for FOFB calculation and needs no extra data shuffling. All BPM and power supply data bits are put “on wire” once.

• NSLS-II FOFB is taking advantages of the two tier structure and the parallel computation capability of FPGA to implement a unique FOFB algorithm that can carry compensation for each eigenmode. NSLS-II will be the first facility to implement such FOFB approach.

• NSLS-II FOFB hardware, firmware and software design will be fully open to the community. For more hardware and firmware details, please go to tomorrow’s “Open Hardware Development Workshop”.



Acknowledgments• FOFB algorithm

Lihua Yu Igor Pinayev• BPM/ Cell controller development

Kurt Vetter Joseph Mead Joseph De Long Kiman Ha Alfred Dellapenna Yong Hu Guobao Shen Om Singh Bob Dalesio• PSC and PS design

Wing Louie John Ricciardelli George Ganetis

Fast Orbit Feedback - BPM to PS Yuke Tian Control Group, Accelerator Division Photon Sciences Directory Brookhaven National Lab EPICS Collaboration Meeting,

Documents

feedback loop maximum

multipleoutput mimo

bpm data

cell controller

link broken fofb calculation

ps sdi link

fast corrector ps bandwidth