LLRF study in cERL

Feng QIU
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Study at cERL

Main Content
LLRF system

The 300 Hz Fluctuation

Gain Scanning

Future Plan

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Study at cERL (2013), F. QIULLRF system
Main function of LLRF systems.
I.
II.

Stabilize the RF field (I&QFeedback) .
Minimize the cavity input power(Tuner Feedback).

 cosθ sinθ A⋅ 
 − sinθ cosθ  cosϕ(t ) sinϕ(t) A(t ) ⋅  − sinϕ(t) cosϕ(t ) Closed-loop operation ( Feedback) isrequired to stabilize the RF field.
Requirement: 0.1% RMS for amplitude
and 0.1 deg. RMS for phase [1].

1 .Higher gain (Larger K(s)) corresponds to higher disturbance suppression. However, too high gains may result of unstable.

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Study at cERL (2013), F. QIU

300 Hz Fluctuation (Inj. 2&3, Buncher)
The 300 Hz fluc. at Inj2&3 (FB2) and Buncher (FB0) cavity during CL/OL operation.
The Inj1 (FB1) LLRF system doesn’t not has evident dominant components.
Amp.

Pha.

Pha. (FFT)Bun.
300 Hz Fluc.

Inj.1

No dominant

Inj.2&3

300 Hz Fluc.

4Study at cERL (2013)

Fluctuation at 300 Hz (Source)
The Power supply is the probable source of the 300 Hz component.
The RF fluctuation agrees well with the PS fluctuation (suppose 10 deg /HV%, thenthe 20mV fluctuation in PS will lead to 10 deg×(100×25mv/15V) = 1.67 deg ).
According to current controlling parameter (KI=10, KP=0), the 300 Hz component
is suppressed by ~10 dB (~3 times), not enough.
300 KW Kly. High Voltage

Fluc. @ 300 Hz

Buncher

Inj2&3 (VS)∆A/A

-43.5 [dB]

-46 [dB]∆θ

0.9 [deg.]

1.6 [deg.]

Closed loop

∆A/A-54 [dB]

-56.5 [dB]

(KI=10, KP=0)∆θ0.3 [deg.]

0.5 [deg.]

Open loop

Scope
FFTOpen-loop

1.6 deg.

Cavity input (OL)Suppressed

Closed-loop

0.5 deg.

Cavity5 Pick up (CL)

Clear to see that the300 Hz component issuppressed by CL
operation.
Study at cERL (2013), F. QIUGain scanning (300 Hz suppression)
Gain-scanning: Scanning (changing) different proportional gain KP and integral
Gain KI (@ 2 MV/m for security) to find out the optimal gains .
The 300 Hz component is suppressed by high gains.
Suppression of 300 Hz component
About 20 dB suppression
when increasing
proportional gain KP by 9times (KI=0).

Meas. vs. Sim.
Meas.
We can also analyze thesuppression of the 300 Hz
component by simulation,
the results agree well witheach other.

Sim.

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Study at cERL (2013), F. QIUGain scanning (Critical gains)
Too high gains would result of loop-unstable. We can evaluate the critical(Maximum) gain by both KI=0, KP gain-scanning.
Critical Gain of FB1 is about
250 (Oscillation @ Gain 250)
Critical Gain of FB2 is about 90(Oscillation @ Gain 90)

Inj. 1The difference of thecritical gain is main
dominated by thebandwidth of the cavity.

Inj. 2&3

Too High Gain case!
Stb

Inj1

Inj2

Inj3

QL [2]

1.2e6

5.8e6

4.8e6

Oscillated, dangerous!
Bandwidth [kHz]

1.1

2.25

2.7

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Study at cERL (2013), F. QIUGain scanning (Buncher)
It is clear to see the optimal gains (optimal KP and KI) of the buncher cavity
according to the scanning map.
For the buncher cavity, the performance is dominated by the integral gains (KI)due to it is normal cavity (QL=2.1e4 [2]).

Scanning Map [3]Performance @ 7MV/m
The amplitude and phase stability
can be 0.045% RMS and 0.055 deg.
RMS, respectively.

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Study at cERL (2013), F. QIUGain scanning (Inj. 1)
The dominant gain in Inj1 is proportional gain (KP).
High gain controlling can be realized due to its narrow bandwidth.

KI=const., KP scanningOpt.
KP= const., KI scanning
Performance @ 7MV

The amplitude and phase stability of Inj1
can be 0.01% RMS and 0.02 deg. RMS,
respectively.
9Study at cERL (2013), F. QIUGain scanning (Inj. 2&3)
Both KI and KP have influenced the performance.
Because there is 300 Hz component in Inj. 2&3, Higher KI would suppressedthe 300 Hz more effective.
KI=const., KP scanning

KP= const., KI scanning
Performance @ 7MV

The amplitude and phase stability of Inj1
can be 0.012% RMS and 0.02 deg. RMS,respectively.
10Opt.

Study at cERL (2013), F. QIUFuture Plan
How to eliminate the 300 Hz fluctuation in the power supply (not by increasing
the controlling gain but by hardware itself).
How to change the controlling parameter safely (KI, KP, SETA, SETP, etc.)?
What is the limitation of every parameter?
Vector-sum controlling problem in the Inj. 2&3 (FB2).

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Study at cERL (2013), F. QIU

Reference[1] T. Miyajima, “Beam Commissioning of Energy Recovery Linacs”, IPAC’13,Shanghai, May 2013, FRXBB201[2] S. Sakanaka et al. “Progress in Construction of the 35-MeV Compact Energy
Recovery Linac at KEK” IPAC’13, Shanghai, May 2013, WEPWA015[3] F. QIU et al. “Evaluation of the Superconducting LLRF System at cERL inKEK”. IPAC’13, Shanghai, May 2013, WEPEM015

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Study at cERL (2013), F. QIU

Question?
Thank you very much for your attending

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Study at cERL (2013), F. QIUGain scanning (definition)
Gain scanning: determine the optimal controlling gains (@ 2MV foe security).
Definition of the integral and proportional gains .
I. FPGA input parameter KP and KI.
II. Digital Gain Kp and Ki.
III. Analog Gain kp and ki.
IV. Real Gains: ASet/(ASet-AMeas.)

Gains

Integral

Proportional

FPGAKIKP

Dig.

Ki=KI/218

Kp=KP/27

Ana.

ki=Ki/TS(1)kp=Kp

Real≈ ki*Gop(2)≈ kp*Gop
FFkp(analog)
kp
DAC

KI&KP (FPGA) vs. Ki&Kp (dig.)ki(analog)∫ki1/sLoop
delay

CavityKi (dig.) vs. ki (ana.)

Kly/IOTGop

ki&kp (ana.) vs. real gain ASet/(ASet-AMeas.)
1 .TS is FPGA sampling clock period (TS= 1/162.5e6 in cERL LLRF system)
2. Gop is the open-loop gain (Gains from FF to SEL(Fil) during the open-loop operation. For the Inj1 and Inj2&3, Gop ≈ 1 (0 dB).)

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Study at cERL (2013), F. QIUFluctuation at 300 Hz (Sim.)
According to current controlling parameter (KI=10, KP=0), the 300 Hz component
is suppressed by ~10 dB (~3 times), not enough.

10 dB suppression@ 300 Hz (with KI=10, KP=0)
Fluc. @ 300 HzBuncher

Inj2&3 (VS)∆A/A

-43.5 [dB]

-46 [dB]∆θ

0.9 [deg.] Diff. 1.6 [deg.]

Closed loop

∆A/A

-54 [dB]-56.5 [dB]

(KI=10, KP=0)∆θ0.3 [deg.]

0.5 [deg.]

Open loop

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Study at cERL (2013), F. QIUGain scanning (300 Hz Sim.)The 300 Hz fluctuation would be suppressed by higher gains.

Pick up
The transfer function
from the disturbanceto the Pcik up in theclosed loop

Disturbacne

Low Gain

KI=0 case

300 HzHigh Gain

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Study at cERL (2013), F. QIUGain scanning (High Gain Sim.)Too high gains would result of loop-unstable. We can evaluate the critical gain
by both KI=0, KP gain-scanning and bode diagram simulation.
Critical Gain of FB1 is about
250 (Oscillation @ Gain 250)
Critical Gain of FB2 is about90 (Oscillation @ Gain 90)

17Stb

Inj1

Inj2

Inj3

QL

1.2e6

5.8e6

4.8e6

BW [kHz]1.12.25

2.7

Study at cERL (2013), F. QIUGain scanning (Performance)
Gain-scanning experiment is implemented in 2MV/m condition, it is also inagreement well with 7 MV/m case.
Our requirement: 0.1% for amplitude, 0.1 deg for phase. Satisfying (FB0&1&2).

Stb

Bun.

Inj1

Inj2&3(VS)∆A/A [%]

0.045

0.010.012∆θ [deg]

0.055

0.02

0.02
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Study at cERL (2013), F. QIU