Low Level RF feedback loop design CSEM-EIC/EOn/Sep02 1 Main - - PowerPoint PPT Presentation

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Low Level RF feedback loop design CSEM-EIC/EOn/Sep02 1 Main - - PowerPoint PPT Presentation

May 24, 2023 397 likes •545 views

Low Level RF feedback loop design CSEM-EIC/EOn/Sep02 1 Main variables the instantaneous phase deviation of the bunch from the synchronous phase. R the variations of the beam radius rf the RF frequency b the variations of the beam

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SLIDE 1

CSEM-EIC/EOn/Sep02 1

Low Level RF feedback loop design

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SLIDE 2

CSEM-EIC/EOn/Sep02 3

Main variables

ϕ the instantaneous phase deviation of the bunch from the synchronous phase. δR the variations of the beam radius ωrf the RF frequency δωb the variations of the beam frequency ϕb the phase of the beam with respect to the RF

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SLIDE 3

CSEM-EIC/EOn/Sep02 4

Transfer functions

B scaling factor, ωs the synchronousfrequency.

2 2 2 2 2 2

) ( ) ( ) (

s rf rb s rf R s rf

s s s B s b R s B s s s B ω δω δω ω δω ω δω ϕ

ω ϕ

+ = = + = = + = =

tt Phase and radial system synchronization system

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SLIDE 4

CSEM-EIC/EOn/Sep02 5

Phase and radial loop

  • U

x x b R y U k x x x x dt d

s s s s

D C B A s

        +                 =         =         +                 − =         1 1

2 1 2 1 2 2 1

  • ϕ

ω

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SLIDE 5

CSEM-EIC/EOn/Sep02 6

Discrete representation, pole placement

Add an integral action Set of gains Feedback:

      − = 1

sdiscr sdiscr

C A F

[ ]

int

K K K

R ϕ

( )

Z K R K K U

R int

− + − = ϕ

ϕ

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SLIDE 6

CSEM-EIC/EOn/Sep02 7

Pole placement

Poles of a 3rd order Bessel filter Non overshooting behaviour 200 Hz (20 ms)

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SLIDE 7

CSEM-EIC/EOn/Sep02 8

Feedback structure

Cascaded implementation plus antiwindup

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SLIDE 8

CSEM-EIC/EOn/Sep02 9

Closed loop response

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.2 0.4 0.6 0.8 1 1.2 x 10

  • 3

Phase and radial loop response time [s] Radius and its reference [m] 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

  • 2

2 4 6 8 10 12 Phase and radial loop response time [s] Phase [deg]

10 10

1

10

2

10

3

10

4
  • 50

50 100 150 freq, [Hz] mag, [dB] 10 10

1

10

2

10

3

10

4
  • 300
  • 250
  • 200
  • 150
  • 100
  • 50

freq, [Hz] phase [deg]

1 mm step

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SLIDE 9

CSEM-EIC/EOn/Sep02 10

Synchronization

Beam rigidly phase with its reference ϕb - ϕref = ϕset Phase reference can be incremented at each clock cycle Output of the phase detector: sawtooth corresponding to the freq difference

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SLIDE 10

CSEM-EIC/EOn/Sep02 11

Synchronization

Force the output of the phase detector to a ct value during acceleration using an offset (Moving reference)

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SLIDE 11

CSEM-EIC/EOn/Sep02 12

Synchronization

Moving reference Error: diff between an extrapolated rf phase and the

  • ref. Allows the closing of the synchron
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SLIDE 12

CSEM-EIC/EOn/Sep02 13

State space model

         + = = + = = = =

rf s rf s s b b b

s s x s x s x ω ω ϕ ω ω ω ω ω ϕ

2 2 3 2 2 2 2 1

1

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SLIDE 13

CSEM-EIC/EOn/Sep02 14

Loop gains

After going to discrete, set of gains: Using pole placement

( )

∫ − − + + − = ) (

int b ref b b

K K K K U

b b

ϕ ϕ ϕ ω ϕ

ϕ ω ϕ

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SLIDE 14

CSEM-EIC/EOn/Sep02 15

Closed loop behaviour

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.2 0.4 0.6 0.8 1 1.2 1.4 Synchronization loop response tim e [s] Beam phase and its reference [rad] 10 10

1

10

2

10

3

10

4
  • 50

50 100 150 freq, [H z] mag, [dB] 10 10

1

10

2

10

3

10

4
  • 300
  • 250
  • 200
  • 150
  • 100
  • 50

freq, [H z] phase [deg]