nsls-ii fast orbit feedback with individual eigenmode compensation yuke tian, li hua yu accelerator...
TRANSCRIPT
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
NSLS-II site field vibration measurement
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
Slow and fast corrector locations
Even Cell
Odd Cell
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
Let’s design a FOFB system
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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 ?
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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.
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
(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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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).
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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.
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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.
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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.
NSLS-II FOFB Implementation
FPGA fixed calculation block
Matlab floating point calculation
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
NSLS-II FOFB Implementation
Decoupling calculation errorError with PID calculation for one eigenmode
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
Status
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
• 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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
Want it ? You got it.
Open source hardware
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
• 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
Open source hardware
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
• 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
Open source hardware
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
BPM control panel and raw ADC data
Open source hardware
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
BPM turn-by-turn data and 10KHz FOFB data
Open source hardware
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011
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
EPICS Collaboration Meeting, Hsinchu, Taiwan, June, 2011