LLRF Low Level Applications Study · 14/10/2008 FLASH Seminar, Zheqiao Geng 11 Measurement at ACC1-- Change the set point gradient 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-50 0 50 Full system

LLRF Low Level Applications Study

FLASH SeminarZheqiao Geng

14.10.2008

14/10/2008 FLASH Seminar, Zheqiao Geng 2

Outline

Introduction to low level applications (LLA) System phase and system gainCavity parameters measurementAdaptive feed forwardFuture plan for LLA


Introduction to low level applications


LLA Introduction

Low level applications is a collection of work concern to the software of

Locating near front end hardware (in FPGA, DSP or front end CPU)

Running fast (intra-pulse or pulse-pulse)


Two focuses of LLA

Algorithms: Principle to perform measurement and optimizationImplementation: Multi-processor, distributed software, real time


Algorithm Study:System phase and system gain


Goals

Measure the system phase and system gainStudy the influence to the feedback system by

the system phase


DefinitionSystem Phase: The phase difference between Vsum and Vdac in steady stateSystem Gain: The amplitude ratio between Vsum and Vdac in steady stateWith P controllerLoop Phase = System phaseLoop Gain = System Gain * Feedback GainAssume the system is Linear


Measurement of system phase and system gain

During RF flattop, the cavity is approximately in steady state, so

This method only works when there is no beamThe RF flattop should be flat (close to steady state)System phase and system gain change during the flattop due to the cavity detuning changes

)_/_(_ outDACsumVectoranglePhaseSystem =

)_/_(_ outDACsumVectorabsGainSystem =


Measurement at ACC1-- Change the feedback gain

10 20 30 40 50-5

0

5

Gain Setting

Sys

tem

Pha

se /

deg

10 20 30 40 501.6

1.65

1.7

1.75

Gain Setting

Sys

tem

Gai

n

10 20 30 40 500

5

10

Gain Setting

Am

plitu

de R

MS

Erro

r / %

10 20 30 40 500

0.2

0.4

0.6

0.8

Gain Setting

Pha

se R

MS

Erro

r / d

eg

With only feedback, without feed forward

System phase and system gain are measured by averaging the flattop

With smaller gain, the flattop is bad, approximation to steady state will have larger error


Measurement at ACC1-- Change the set point gradient

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-50

0

50Full system phase (from DAC to VS) / deg

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-2

0

2Phase shift from DAC to klystron output / deg

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-50

0

50Phase shift from klystron output to VS / deg

Set point amplitude / MV/m

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 101

1.5

2Full system gain (from DAC to VS)

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 101.69

1.7

1.71x 10-4 Gain from DAC to klystron output

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 100.8

1

1.2x 104 Gain from klystron output to VS


5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-100

-50

0

50

100

150

200


Det

unin

g at

dec

ay /

Hz

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 100

1

2

3x 10-3


Am

plitu

de e

rror

5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 100

0.5

1

1.5


Pha

se e

rror /

deg

With feedback and feed forward

The klystron of ACC1 is quite linear

The definition of system phase and system gain includes the cavity detuning effect


System phase and feedback stability

( )ωω

ωΔ−+

=js

sG2/1

2/1

θjgesH =)(

( )θωωω

ωωj

I

Ie

gePjsjssV

sVPsHsG

sV

2/12/1

2/1)(

)()()(1

1)(

+Δ−+Δ−+

=

+=

[ ] 0Re 2/12/1 >+Δ− θωωω jgePj

Pg

gP1cos

0cos2/12/1

−>⇒

>+

θ

θωω

⎥⎦⎤

⎢⎣⎡ ++− angleDetuningangleDetuning _

2,_

2ππ

The stable area of system phase is


Measurement at ACC1-- System phase and feedback stability

With feedback and feed forward on

The loop phase is changed in negative way by about 70 degree

With feedback and feed forward on

The loop phase is changed in positive way by about 80 degree


System phase and steady state error

0 50 100 150 200 250 300 350 400-1.5

-1

-0.5

0

0.5

1

System Phase / deg

Ste

ady

Sta

te A

mpl

itude

Erro

r with

Loo

p G

ain

of 1

00 /

%

Amplitude Error VS System Phase

0 50 100 150 200 250 300 350 400-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

System Phase / deg

Ste

ady

Sta

te P

hase

Erro

r with

Loo

p G

ain

of 1

00 /

deg

Phase Error VS System Phase

System Phase Optimization:

• Keep system phase in the stable range

• Select system phase to be 0 for minimizing the steady state phase error (amplitude error is non-avoidable for feedback but can be compensated by feed forward)


Measurement at ACC1-- System phase and steady state error

With only feedback, without feed forward

-20 0 20 40

-20

0

20

40

60System phase measurement / deg

System phase setting / deg

-20 0 20 401.52

1.54

1.56

1.58System gain measurement / deg


-20 0 20 401

1.5

2

2.5Amplitude error / %


-20 0 20 400

0.2

0.4

0.6

0.8

1Phase error / deg



System phase and system gain drift

0 1000 2000 3000 4000 5000 6000-19

-18

-17

-16

-15

-14

-13

-12

-11

-10

Time / 7s

Sys

tem

Pha

se /

deg

Ten-hour Measurement of ACC1 System Phase

0 1000 2000 3000 4000 5000 60001.785

1.79

1.795

1.8

1.805

1.81

1.815

1.82

1.825

1.83

Time / 7s

Sys

tem

Gai

n

Ten-hour Measurement of ACC1 System Gain

0 1000 2000 3000 4000 5000 60000.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Time / 7s

Am

plitu

de E

rror (

RM

S) a

t Fla

ttop

/ %

Ten-hour Measurement of ACC1 Amplitude Error

0 1000 2000 3000 4000 5000 60000

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

Time / 7s

Pha

se E

rror (

RM

S) a

t Fla

ttop

/ deg

Ten-hour Measurement of ACC1 Phase Error

Measured during 1:00am, 17.08.2008 to 11:00am, 17.08.2008.


Algorithm Study:Cavity parameters measurement


Goals

Measure loaded Q of the cavityMeasure detuning of the cavityMeasure beam phase and amplitude in each cavity


Cavity equation used for parameters measurement

( )

0

0

2/12/12/1 2

ZQrC

IRVCVjdt

dVbLforc

c

ω

ωωωω

⎟⎟⎠

⎞⎜⎜⎝

⎛=

+=Δ−+


Forward and reflected signal directivity correction

0 200 400 600 800 1000 1200 1400 1600 1800 2000-3

-2

-1

0

1

2

3

4

5Forward signal without directivity correction

IQ

0 200 400 600 800 1000 1200 1400 1600 1800 2000-0.5

0

0.5

1

1.5

2

2.5x 10

-3 Forward signal with directivity correction

IQ

The forward signal with directivity correction will be used as the cavity driving signal in the cavity equation

mearefmeaforref

mearefmeaforfor

dVcVV

bVaVV

__

__

+=

+=


Forward and reflected signal directivity correction

0 50 1004.8

4.9

5

5.1x 10-4 Amplitude of a

0 50 1001.6

1.65

1.7

1.75x 10-4 Amplitude of b

0 50 1006.5

7

7.5

8

8.5x 10-5 Amplitude of c

0 50 1002.945

2.95

2.955

2.96x 10-3 Amplitude of d

0 50 10041

42

43

44Phase of a / deg

0 50 1000

1

2

3

4Phase of b / deg

0 50 100142

144

146

148

150Phase of c / deg

0 50 100-158.7

-158.6

-158.5

-158.4

-158.3Phase of d / deg

100 times calibration of the directivity coefficients


Loaded Q and detuning measurement-- Intra-pulse, without beam

0 200 400 600 800 1000 1200 1400 1600 18000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 106 Loaded Q during RF pulse

Measurements are sensitive to the cavity driving signal calibration

Large error during the filling time

Relative measurements can be used to detect the system status change

0 200 400 600 800 1000 1200 1400 1600 1800-100

-50

0

50

100

150Detuning / Hz


Loaded Q and detuning measurement-- Pulse to pulse, at RF decay

0 10 20 30 40 50 60 70 80 90 1003

3.01

3.02

3.03x 106 Loaded Q at decay part

Measurement times

0 10 20 30 40 50 60 70 80 90 10020

30

40

50

60Detuning at decay part / Hz

Measurement times

QL: 0.2% RMS

Detuning: 5 Hz RMS


Beam measurement-- Calibration of the Toroid signal

The beam induced cavity driving voltage can be derived by the Toroid signal multiplied by a complex coefficient

toroidbbL VCIR ⋅=

( ) bLforcc IRVCVj

dtdV

2/12/12/1 2ωωωω +=Δ−+


Beam measurement-- Calibration of the Toroid signal

0 500 1000 1500-1

0

1

2

3

4Toroid signal

0 500 1000 1500-6

-4

-2

0

2Beam induced driving signal = Toroid * Cb

0 500 1000 15000

1

2

3

4

5

6x 106Loaded Q measurement with beam

0 500 1000 1500-100

-50

0

50

100

150Detuning measurement with beam / Hz

IQ


Beam measurement-- Pulse to pulse fluctuation

0 10 20 30 40 50 60 70 801.6

1.65

1.7

1.75

Measurement times

Am

plitu

de o

f Cb

0 10 20 30 40 50 60 70 80-180

-175

-170

Measurement times

Pha

se o

f Cb

/ deg

1.3% RMS

1.4 degree RMS


Use cases of cavity parameters

Detect the QL exceptions, such as quenchProvide detuning information to piezo controlDetect the detuning exceptionsCalibrate the vector sumDenoise the cavity probe signal in real time…


Denoise the cavity probe signal with Kalman filter in real time

The cavity model are formed by:

Loaded Q curve during the RF pulse

Detuning curve during the RF pulse

Beam curve during the RF pulse

Cavity equations

The model is linear and time varying.

0 200 400 600 800 1000 1200 1400 1600 1800-2

0

2

4

6

8

10

12

14Cavity probe signal

500 520 540 560 580 600 620 640 660 680 700

13.45

13.5

13.55

13.6

I flattop zoom

originalfilteredmodel prediction

500 520 540 560 580 600 620 640 660 680 7001.6

1.7

1.8

1.9

2

2.1

Q flattop zoom

originalfilteredmodel prediction


Algorithm Study:Adaptive feed forward


Goals

Identify the systemStudy the adaptive feed forward algorithm based on inversed system model


Calibrate the klystron signal as vector sum effective driving signal

The vector sum can be viewed as the output of an effective single cavity

The cavity equation will still work for the effective single cavity

The driving signal to this effective single cavity can be derived from the klystron output signal by multiplying a complex constant

0 500 1000 1500 2000-5000

0

5000

10000

15000

20000Vector sum

IQ

0 500 1000 1500 2000-2

-1

0

1

2

3

4Effective cavity driving derived from klystron output

IQ


Vector sum effective single cavity model

0 200 400 600 800 1000 1200 1400 1600 1800 20000

100

200

300

400

500Half bandwidth during the RF pulse / Hz

0 200 400 600 800 1000 1200 1400 1600 1800 2000-200

-100

0

100Detuning during the RF pulse / Hz

Time / us

0 100 200 300 400 500 600 700 800 900 10001.3

1.4

1.5

1.6x 10

-4 Gain from DAC to vector sum driving

0 100 200 300 400 500 600 700 800 900 1000-5

0

5

10

15Phase shift from DAC to vector sum driving

Time / us

AFF:

Vector sum error Driving signal correction (system model)

Driving system correction Feed forward correction (DAC to driving signal gain)


Adaptive feed forward algorithm-- Procedure

For each iteration:

Get the initial feed forward correction table from last pulse: FF_CORR0 = DAC – FF0

Measure the vector sum error of this pulse

Inverse the system model, calculate the corresponding feed forward correction signal FF_CORR1

Get and update the new feed forward correction table of this iteration: FF_CORR = FF_CORR0 + FF_CORR1

Analysis:

With open loop operation: normal adaptive feed forward algorithm

With closed loop operation: feedback signal will also be taken into account


Adaptive feed forward algorithm-- Principle

( ) bLdsumsum IRVCVj

dtdV

2/12/12/1 2ωωωω +=Δ−+

Cavity equation

We expect

( ) bLdsetset IRVCVj

dtdV

2/12/12/1 2ωωωω +′=Δ−+

So the new driving signal can be calculated based on

( ) dsumsum VCVj

dtVd

Δ=ΔΔ−+Δ

2/12/1 ωωω


AFF test at ACC1 (Open loop)


AFF test at ACC1 (Closed loop)


Future plan for LLA


Plan for LLA work

Continue developing algorithmsSystem phase and system gainCavity parameters measurementAdaptive feed forwardSystem status analysisException detection and handlingSystem performance estimation

Implement and test the LLA algorithms in the SIMCON development system at ACC1


Thank you for attention!

Documents

LLRF Low Level Applications Study · 14/10/2008 FLASH Seminar, Zheqiao Geng 11 Measurement at ACC1-- Change the set point gradient 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-50 0 50 Full system