SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

TESLA Cavity driving with FPGA controller

TESLA Cavity driving with FPGA controller

Tomasz Czarski

WUT - Institute of Electronic Systems

PERG-ELHEP-DESY Group

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

• Low Level RF system introduction• Superconducting cavity modeling• Cavity features• Recognition of real cavity system• Cavity parameters identification• Control system algorithm• Experimental results

Main topics

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Functional block diagram of Low Level Radio Frequency Cavity Control System

DOWN-CONVERTER

250 kHzVECTOR

MODULATOR

CAVITY ENVIRONSANALOG SYSTEM

FPGA CONTROLLER FPGA I/Q DETECTOR

KLYSTRON

PARAMETERS IDENTIFICATION SYSTEM

MASTER OSCILATOR1.3 GHz

CONTROL BLOCK

PARTICLE

FIELDSENSOR

COUPLER

DAC ADC

DIGITAL

CONTROL SYSTEM

CAVITY RESONATOR and ELECTRIC FIELD distribution

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Superconductive cavity modeling

dv/dt = A·v + ω1/2·R·iA = -ω1/2+i∆ω

vn = E·vn-1 + T·ω1/2·R·in-1 E = (1-ω1/2·T) + i∆ω·T

State space – continuous and discrete model

Input signal

I(s)↔i(t)

RF current

I(s–iωg)

RF voltage

Z(s)∙I(s–iωg)

Output signal

Z(s+iωg)∙I(s)↔v(t)

Low pass transformationZ(s+iωg) ≈ ω1/2·R/(s +ω1/2– i∆ω)

half-bandwidth = ω1/2 detuning = ∆ω

CAVITY transfer function

Z(s) = (1/R+ sC+1/sL)-1

Modulation

exp(iωgt)

Demodulation

exp(-iωgt)

Analytic signal: a(t)·exp[i(ωgt + φ(t))]

Complex envelope: a(t)·exp[iφ(t)] = [I,Q]

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Cavity features

Fie

ld

sen

sor

Cou

ple

rParticle

Carrier frequency

Pulse timeRepetition

timeField

gradientBeam pulse repetition

Average beam current

1.3 GHz 1.3 ms 100 ms 25 MV/m 1µs 8 mA

Resonance frequency

Characteristic resistance

Quality factorHalf-

bandwidthDetuning

ω0 = (LC)-½

2π·1.3 GHz

ρ = (L/C)½

520 Ω

Q = R/ρ

3·106

ω1/2 = 1/2RC

2π·215 Hz

∆ω = ω0 - ωg

~ 2π· 600 Hz

Cavity parameters: resonance circuit parameters: R L C

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Algebraic model of cavity environment system

Internal CAVITY model

Outputcalibrator

Input offsetcompensator

Inputcalibrator

+

u v

Inputoffset phasor

u0

Inputdistortion factor

D C

C’

+ u’0

D’

Inputphasor

Outputphasor

External CAVITY model

v’k = Ek-1·v’k-1 + C·C’·D·[u0 + D’·(u’k-1 + u’0)] – C·C’·(ub)k-1

v’

u’

Outputdistortion factor

FPGA controller area

Internal CAVITY modelInternal CAVITY model

CAVITY environs

vk = Ek-1·vk-1 + uk-1 - (ub)k-1

E = (1-ω1/2·T) + i∆ω·T

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Functional black diagram of FPGA controllerAnd control tables determination

I/Q DETECTOR

FEED-FORWARDTABLE

+

GAINTABLE

– +

CALIBRATIONCALIBRATION

&FILTERING

F P G A C O N T R O L L E R

SET-POINTTABLE

C O N T R O L FEED-FORWARD SET-POINT

FillingCavity is driven in resonance condition

i(t) = Io·exp(iφ(t))dφ(t)/dt = (t)

v(t) = i(t)·R(1– exp(-ω1/2·t))

FlattopEnvelope of cavity voltage is stable

i(t) = V0·(1-iΔω(t)/ω1/2)/R v(t) = V0 = V0·exp(iΦ0)

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Cavity parameters identification idea

External CAVITY model

vk = Ek·vk-1 + F·uk-1 Ek = (1-ω1/2·T) + i∆ωk·T

Time varying parameters estimation by series of base functions:

polynomial or cubic B-spline functions

Linear decomposition of time varying parameter x: x = w * y

w – matrix of base functions, y – vector of unknown coefficients

Over-determined matrix equation for measurement range:

V = W*z

V – total output vector, W – total structure matrix of the model

z – total vector of unknown values

Least square (LS) solution: z = (WT*W)-1*WT*V

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Functional diagram of cavity testing system

CAVITY SYSTEM

CONTROLLER

CONTROL DATA

PARAMETERSIDENTIFICATION

CAVITY MODEL ≈

MEMORY

FPGA SYSTEM

MATLAB SYSTEM

vu

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Feed-forward cavity drivingCHECHIA cavity and model comparison

0 500 1000 1500 2000-10

-5

0

5

10

15

20

25

30

time [10-6 s]

Cavity output envelope [MV]

quality factor = 3.02e6

smooth line - MATLAB model noisy line - CHECHIA cavity

filling

flattop

decay

0 500 1000 1500 2000-20

-15

-10

-5

0

5

10

15

20

25

time [10-6 s]

Klystron output estimation [mA]

Feed-forward table - dashed line

0 500 1000 1500 2000

-1.5

-1

-0.5

0

0.5

time [10-6 s]

Phase of Cavity and Klystron output estimation [rad]

0 500 1000 1500 2000-200

-100

0

100

200

300

400

500

600

700

800

time [10-6 s]

Detuning monitoring [Hz]

supposed detuning

estimated detuning

MATLAB

CAVITY

Klystron

Controller

IQM

IQM

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

Feedback cavity drivingCHECHIA cavity and model comparison

0 500 1000 1500 2000

-5

0

5

10

15

20

25

time [10-6s]

Cavity output envelope [MV]

filling

flattop

decay

0 500 1000 1500 2000-15

-10

-5

0

5

10

15

20Klystron output [mA]

time [10-6s]

time [10-6s]

0 500 1000 1500 2000

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8Phase of cavity and klystron output [rad]

time [10-6s]time [10-6s]

0 500 1000 1500 2000-200

-100

0

100

200

300

400

500

600Cavity detuning [Hz]

time [10-6s]

CavityKlystron

supposed detuningestimated detuning

IQM

IQM

SPIE - WARSAW, August 30, 2005 Institute of Electronics Systems, ELHEP Group

• Cavity model has been confirmed according to reality

• Cavity parameters identification has been verified for control purpose

CONCLUSION