FPGA-BASED LOW LEVEL CONTROL OF CERN’S LINAC 3 CAVITIES

Javier Serrano

CERN, Geneva, Switzerland

Summary

ContextThe problemTraditional analog solutionsThe LRFSC cardControl system designImplementation and results

Ions in the LHC

ECR

RFQLINAC

3

LEIR

PSSPS

LHC

Pb27+

upgradedto 200 A

Linac Repetitionrate 200ms to

400ms

4.2 MeV/nucl

StripperPb27+ to Pb54+

50 A Energy rampingcavity to be added

72 MeV/nucl

5.9 GeV/nucl

177 GeV/nucl

Accumulation of9x108 ions in two

bunches every 3.6s(to 4 LHC bunches)

StripperPb54+ to Pb82+

4 bunchlet pairs(to reduce SPS tune shift)

every 3.6s

Accumulation of 8 to 13LEIR/PS batches, deliveryof 32 to 52 bunches to the

LHC per cycle

592 bunches of 0.7x108 ions per ringfilling time: ~10min/ring

Luminosity: ~ 1027cm-2s-1

The problem

The amplitude A and phase φ of the RF electric field in a cavity are subject to external perturbations (50 Hz power, temperature, the beam…).

A feedback system is needed to control it, i.e. measure it, compare it and adjust it.

A

ωt

φ

I

Q

x(t) = A cos(ωt - φ)orx(t) = I cos(ωt) + Q sin(ωt) withI = A cos(φ)Q = A sin(φ)

φ

A

Overview of feedback system

CAVITY

Pickup

Solid state amplifier

Controller

Forward

Reflected

Cavity

Set Points from Control RoomQ

I

Analog demodulation

X

x(t)

LO (Local Oscillator)

Low passfilter

Low passfilter A

φ

Phase detector has limited range and exhibits AM to PM coupling.

X

X

LO0º

90º

Low passfilter

x(t)

Low passfilter

I

Q

Both paths must be identical: perfect splitter, perfect 90º, etc.

Digital IQ demodulation

XLow pass

filter

x(t)

LO (Local Oscillator) ADC

clkFPGA

xd(t)

FPGA implements multiplication by sine and cosine tables and digital low pass filtering.

If clk’s frequency is exactly four times that of xd(t):

De-mux

xs(t)

xs(t) +/-1

+/-1

LPF

LPF

I

Q

One single analog path

LRFSC card block diagram

14A/D20.256 MHz

BPF

81.024 MHz

14A/D20.256 MHz

BPF

81.024 MHz

14A/D20.256 MHz

BPF

81.024 MHz

IQ

2x2

IsetQset

IrFwdQrFwd

ICav

QCav

PID

IrRef QrRef

IrCavQrCav

Q

L

Amp

(-fAmp)

IlrnQlrn

IeCavQeCav

ResonanceControl

Algorithm

IFwd

QFwd

IRef

QRef

IRefQRef

IFwdQFwd

IOutQOut

DAC101.28 MHz

BPF

81.024 MHzLO

101.28 MHzReflected

101.28 MHzForward

101.28 MHzCavity

101.28 MHzOutput

81.024 MHz

162.048 MHz

Sin Cos

20.256 MHzBPF

14

IpreQpre

2x2

A B C DABCD

A B C DABCD

PI

PILPF LPF

|IQ|

|IQ|

AB

AB

-++-

os os

RAMRAM

S.P.RAM

F.F.RAM

DiagnosticTest Point

IQ RAM

40.512 MHz

DUALCHANNEL

DAC

To FrontPanel

To VME

Diagnostic Output (1 of 4)

FPGAXilinx

XC2V2000

IQ

2x2

IQ

2x2DigitalFilter

RF EnvelopeOutput (-20 dBc)

ICav

QCav

ICav QCav

RFON/OFF

ToPLD

BEAMON/OFF

ToPLD

FASTPROTECT

ToPLD

20.256 MHzClock

ToPLD

40.512 MHzClock

ToPLD

81.024 MHzClock

ToPLD

DAC

100 kHz

±5V signal

AD6645WJ HMJ-5

WJ AH31

WJ AH31 AD9755

18x256k SRAM6.4 ms of full IQ data

AMPAMP

The LRFSC card

Control system design: the cavity model

20

2 2s

2σ C(s)

s

s

σ C(s)

2

2

)C(j

|)C(j|

dB3

0

2

|)C(j|

dB3

2

)C(j

Transfer functions:

RF I and Q

Control system design: methodology

1. Plot frequency response of open loop system (PI controller followed by cavity).

2. Set KI/KP = so that the controller zero cancels the cavity pole. This gives us one equation.

3. The other equation needed comes from the requirement that the cabling delay should represent 45° at the frequency where the open loop gain is 1. This gives a total phase margin of 45°, ensuring global stability.

s

K K I

P

PI Controller

s Cavity

F-sTe

ForwardDelay

R-sTe

ReverseDelay

OutputSetPoint

I(s) O(s)

+-

+

Control system design: implementation

Digital PI using rectangular rule for integration.

28 bit integrator with anti-windup.Saturation preferred to scaling

throughout except in IQ Modulator.Data paths vary between 14 and 41 bits

inside the design. Tradeoff between speed and accuracy.

HW/SW interaction

RF ON

400 s200 ms

VME InterruptPowerPC VME master writes control information and reads back diagnostics

Results

Trace Kp Ki(kHz)

f -3dB

(kHz)

f -3dB

(kHz)*

f 0dB

(kHz)

f 0dB

(kHz)*

1 (top) 10.25 227.6 472 468 390 386

2 (middle) 9.25 205.1 425 425 322 336

3 (bottom) 8.0 177.3 359 360 200 246

Theory Experiment

Thanks!