NSLS-II Fast Orbit Feedback with Individual Eigenmode Compensation Yuke Tian, Li Hua Yu Accelerator Division Photon Science Directory Brookhaven National

NSLS-II Fast Orbit Feedback with Individual Eigenmode Compensation

Yuke Tian, Li Hua Yu

Accelerator Division

Photon Science Directory

Brookhaven National Lab

EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011

Outline

• NSLS-II orbit feedback system• Technical requirements and specifications• NSLS-II site field vibration measurement• Slow and fast corrector locations

• Fast orbit feedback with individual eigenmode compensation• Typical fast orbit feedback algorithm• NSLS-II FOFB algorithm with individual eigenmode compensation• Comparison of the two algorithms• Solving the calculation problems from two directions

• NSLS-II fast orbit feedback implementation• Summary


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


NSLS-II site field vibration measurement


Slow and fast corrector locations

Even Cell

Odd Cell


Let’s design a FOFB system


BPM

BPM

BPM

BPM

BPM

BPM

BPM

BPM

PS Controller

PS Controller

PS Controller

PS Controller

PS Controller

PS Controller

Orbit feedback calculationBPM data

Tx/Rx BPM data

around the ring

Tx/Rx BPM data

around the ring

Corrector setpoint

BPM

BPM

BPM

BPM

BPM

BPM

BPM

BPM

PS Controller

PS Controller

PS Controller

PS Controller

PS Controller

PS Controller

Orbit feedback calculationBPM data Corrector setpoint

Can we make a clean architecture ?


1. Try to deliver BPM data to a place that orbit calculation module have directly access. Don’t shove data around too much.

2. Similarly, try to deliver corrector setpoint from a place that orbit calculation module have directly access.

3. Looks we need a place that can:

Receiver local BPM data;

Tx/Rx BPM data to/for other cell;

Carry out FOFB calculation;

Tx corrector setpoints to PS control system.

Cell Controller !

Controller

R-1=VΣ-1UT

Accelerator

R=UΣVT

d

goldd

Compensator

(PID etc)

11

1 MxNxMNx dR R-1: reverse response matrix

11 MxNxMxN dR R: response matrix

Typical fast orbit feedback algorithm

The ill-conditioned response matrix will cause numerical instability.

Solution: 1) Truncated SVD (TSVD) regularization 2) Tikhonov regularization


N

N

N

N

NTUVDR

.

1....

1

1

,..., 2

1

2

2

22

22

2

21

21

1

2111

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.

11

1 MxNxMNx dR 11

Mxrowii dR th For each corrector plane

Typical fast orbit feedback algorithm


NSLS-II FOFB algorithm – 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. The BPMs and correctors are coupled together. One BPM reading is the results of many correctors. One corrector kick can also affect many BPM readings. It is difficult to design a compensator for all noises with different frequencies.

• It is desirable if we can decouple the BPM and corrector relationship so that the MIMO problem can be converted into many single input single output (SISO) problems, for which control theory has many standard treatments.

• Fortunately, SVD already provides a solution: it projects the BPMs input into the eigenspace, where each component is independent. We can design many SISO type compensators (one for each eigenmode) and apply the standard SISO control theory to treat each eigenmode problem in frequency domain without affecting other eigenmodes.


(z)Q000

....

00(z)Q0

000(z)Q

Q(z)

N

2

1

c1, c2, …, cN is the input projections in the eigenspace.

Q1(z), Q2(z), …, QN(z) is the compensator for each eigenmode.

We want to prove that Q1(z), Q2(z), …, QN(z) only corrects the corresponding eigenmode in eigenspace without affecting other eigenmodes.

UT

d

c

Accelerator

R=UΣVT

e

golddQ(z) Σ -1 V

NSLS-II FOFB calculation – compensation for each eigenmode


UT

d

c

Accelerator

R=UΣVT

e

golddQ(z) Σ -1 V

In cycle n, )e(n)d(n)(Uc(n) T Q(z)c(n)V)( 1n

1)e(n)Q(z)c(n)(VVU1)d(n 1T

1)e(nUQ(z)c(n)1)d(n 1)e(nUQ(z)c(n)1)d(nU1)c(n TT

1)e(nU

(n)c

....

(n)c

(n)c

(z)Q000

....

00(z)Q0

000(z)Q

1)(nc

....

1)(nc

1)(nc

T

N

2

1

N

2

1

N

2

1

The pure effect of Qi(z) is on the ith eigencomponent.The noise signals are also decoupled into the eigenspace. This gives us freedom to suppress the noises in eigenspace using SISO control theory.

IVVVV TT IUUT Since,

NSLS-II FOFB calculation – compensation for each eigenmode


Decpoupling or not ? Calculation compare

Calculation Amount Without Decouping With Decouping

One corrector strength (one plane)

M+k =243 N(M+N+k)= 29970

90 corrector strength (one plane)

N(M+k) = 21870 N*N*(M+N+k) = 2697300

11

1 )( MxNxMNx dRzQ For each corrector plane, M multiplication and accumulation(MAC), followed by k MAC for corrections.

Calculation (one plane): One corrector : M+k N correctors: N*(M+k)

Without decoupling:

)e(n)d(n)(Uc(n) T Q(z)c(n)V)( 1n

With decoupling:It takes NxM MAC to decouple the inputs into eigenspace.

It takes N*k MAC for N compensators in each eigenmode. It takes N*N to get one corrector strength. Calculation (one plane): One corrector: N*(M+N+k) N correctors: N*N*(M+N+k)

Assume N=90, M=240, k=3:

Assume 50us of 10Khz FOFB time is used for the caluclations: N*N*(M+N+k)/50us=5.400 GMAC/s.

For doing two plane FOFB in 10us: 5.4*5*2= 54 GMAC/s

The high end DSP chip gives about 200-300 Millions floating point operations (MFLOP).


Solving the calculation problems from two directionsDistributed FOFB system: two tier communication

30 cells in

the storage ring

All the BPM data is delivered to all the 30 cell controller within 12us, cell controller only needs to calculate the local corrector strength. This distributed architecture reduces the calculation by factor of 30.


Solving the calculation problems from two directionsFPGA’s powerful DSP performance

FPGA ‘s DSP power is mainly gained through the parallel computation capability. The parallelism increases FPGA DSP power (vs genetic DSP or CPU) by a factor of more than 2000 (Virtex 6).

Standard DSP/CPU process: sequential

FPGA’s fully implementationOne of the DSP48 block in FPGA


Solving the calculation problems from two directionsFOFB calculate in FPGA:

UT

d

c

Accelerator

R=UΣVT

e

golddQ(z) Σ -1 V

ed

U1T X

U2T X

UNT X

1c

2c

Nc

V1

VN

X

V2 X

XΘ N

Θ 2

Θ 1

Q1(z)

Q2(z)

QN(z)

NSLS-II FOFB Model


Solving the calculation problems from two directionsFOFB calculate amount in FPGA:

ed

U1T X

U2T X

UNT X

1c

2c

Nc

V1

VN

X

V2X

X Θ N

Θ 2

Θ 1

Q1(z)

Q2(z)

QN(z)

)e(n)d(n)(Uc(n) T Decoupling into eigenspace:

All components c1(n), c2(n), …, cN(n) is calculated in parallel (M MAC)

Compensation for each eigenmode: Q(z)c(n)The k step compensations are done in parallel. (k MAC)

Corrector strength calculation: Q(z)c(n)V)( 1nAll corrector strength is calculated in parallel: N MAC

The total calculation is reduced to: M+N+k = 240 + 90 + 3 = 333 MAC. FPGA will finish it within a few us.


NSLS-II FOFB Implementation

ed

U1T X

X

X

1c

2c

Nc

V1 X

X

XΘ N

Θ 2

Θ 1

Q1(z)

Q2(z)

QN(z)

RAMBPM data

From SDI link

Control System

(EPICS IOC)

Download through GigE interface

RAM

MUX

RAM

U2T

UNT

RAM

MUX

RAM

RAM

MUX

RAM

MAC

MAC

MAC

MAC

MAC

MAC

RAM

MUX

RAM

V2

RAM

MUX

RAM

VN

RAM

MUX

RAM

To PSC

To PSC

To PSC


Floating point calculation vs fixed point calculation: FPGA computation is usually fixed point calculation,

the quantization errors should be carefully controlled so that the calculation is accurate.


FPGA fixed calculation block

Matlab floating point calculation



Decoupling calculation errorError with PID calculation for one eigenmode


Status


• The hardware design (PCB, chassis) for BPM, cell controller and PSC are all done. PSC is in production stage. BPM and cell controller are in the first article of production stage.

• BPM and PSC FPGA firmware, EPICS drivers and database development are all done. All cell controller blocks (SDI, FOFB etc) are all. The cell controller integration is in progress.

• Since we have the fast fiber SDI to deliver data around the ring, cell controller’s SDI link will also be used as fast machine protection system that deliver critical system (such as the vast valve signal from vacuum system) around the ring within much less than 1ms. This latency is impossible for PLC to achieve.

Open source hardware


Want it ? You got it.



• We like to open the hardware we designed at BNL to the community. These includes all the PCB design, the FPGA firmware design and the EPICS IOC (driver, database) design. We welcome any suggestions and cooperation from the community.

PSC

PSI



• The digital front end (DFE) board (Virtex6 FPGA) can be used as a common platform for many systems since it provides the basic common elements such as large memory (1 GB DDR3), embedded CPU, Gigbit Ethernet port to EPICS IOC, high speed SDI link(use 2 of the 6 available SFPs), and many user IOs (>160) to the user daughter board.

BPM Cell ControllerShare the same DFE



BPM control panel and raw ADC data



BPM turn-by-turn data and 10KHz FOFB data



BPM 10Hz slow acquisition data

• NSLS-II’s stringent emittance requirements need a efficient fast orbit feedback system. The two tier communication structure and the FPGA-based fast orbit feedback calculation architecure is designed for achieve the requirments.

• Algorithm with individual eigenmode compensation is proposed. The typical MIMO feedback problem is converted into many SISO problems. This algorithm enables accelerator physicists to correct the beam orbit in eigenspace.

• We compared the calculations for FOFB with and without individual eigenmode compensation. We found that the proposed NSLS-II FOFB algorithm needs a large amount of calculations. However, benifited from NSLS-II FOFB architecure, the challenge can be conquered.

• We expect a successful application of the NSLS-II FOFB algorithm during the NSLS-II commissioning and daily operation.

• BNL like to open all the designs to the community as part of the open source hardware initiative.

Summary


Acknowledgments

• FOFB algorithmIgor PinayevSam Krinsky

• BPM/ Cell controller development : Kurt Vetter

Joseph MeadKiman HaAlfred Dellapenna

Joseph De LongYong Hu

Guobao Shen Om Singh Bob Dalesio• PSC and PS design:

Wing Louie John Ricciardelli George Ganetis


Documents

NSLS-II Fast Orbit Feedback with Individual Eigenmode Compensation Yuke Tian, Li Hua Yu Accelerator Division Photon Science Directory Brookhaven National