Active cancellation of power supply ripple effects incontinuous wave superconducting radio frequency
cavities
Feng Qiu1,2,, Takako Miura1,2 , Toshihiro Matsumoto1,2 ,Shinichiro Michizono1,2 , Hiroaki Katagiri1 , Dai Arakawa1 ,Hiromitsu Nakajima1

Abstract
Digital low-level radio-frequency (LLRF) systems are used at the compact
energy recovery linac (cERL) test facility to stabilize the accelerating field
inside the radio frequency (RF) cavities. Proportional and integral feedback
controllers are implemented in the LLRF system to suppress the various
disturbances in the cavities. At cERL, the typical disturbances include microphonics detuning and high-voltage power supply (HVPS) ripples. These
two types of disturbances are reflected in the sum of sinusoidal fluctuations in
the RF phase. Recently, a real-time narrow-band active noise control (ANC)
approach which aims to reject the microphonics detuning of less than several
dozen Hz, was proved to be effective in cavity resonance control. We extend
this ANC method to the LLRF field control to suppress the RF ripples causedby the HVPS. In this paper, we present our experience of applying the ANC
algorithm to the LLRF system of the cERL facility at KEK. We confirmedthat high frequency ripples of up to 20 kHz can be well compensated by the
ANC method during the cERL beam-commissioning.
Keywords: LLRF, Active noise control, cERL, HVPS ripple

1
High Energy Accelerator Research Organization, 1–1 Oho, Tsukuba, Ibaraki 305–0801,
Japan
2
The Graduate University for Advanced Studies, Shonan Village, Hayama, Kanagawa
240–0193, Japan

Preprint submitted to NIM-A

December 10, 2019

1. Introduction
Field-programmable gate array (FPGA)-based digital low-level radiofrequency (LLRF) systems have been widely employed to regulate and control the accelerating field in various facilities such as the compact energy
recovery linac (cERL) at KEK. The cERL is a 1.3 GHz superconducting(SC) radio-frequency (RF) test machine that is operated in continuous-wave(CW) mode [1, 2]. As shown in Fig. 1, a total of six cavities have been installed in the cERL. The injector consists of one normal conducting buncher
cavity and three SC two-cell cavities (CAV1, CAV2 and CAV3). The othertwo nine-cell SC cavities (ML 1 and ML2) are installed in the main linac(ML). Various RF sources including two types of klystrons and two typesof solid state amplifiers (SSAs) have been adopted in the cERL. A 25 kW
klystron is used to drive the CAV1, while another 300 kW klystron is used
to drive the CAV2 and CAV3 with vector-sum (VS) control. The SSAs serveas the RF sources for the cavities in the ML.
In the ML of the cERL, the cavities are operated with a high loaded
Q (QL ) of approximately 1.0 × 107 , with a corresponding half-bandwidthof 65 Hz. The low cavity bandwidth makes the RF field very sensitive tothe microphonics detuning [3]. The proportional and integral (PI) feedback(FB) controller is not sufficient to suppress the microphonic effects in ourcase. In view of this situation, we integrated a disturbance observer (DOB)based control algorithm into the FB loops to speed up the system response to
the microphonics. The experimental results confirmed that the microphonics
detuning was well compensated by the “PI+DOB” control [2]. The cavities
in the injector are operated with a lower QL compared with the cavities in
the ML. The value of QL is approximately 1.2 × 106 for CAV1 and 0.5 × 106
for CAV2 and CAV3. The ripples in the klystron HVPS modulate the phaseof the klystron output and ultimately lead to a phase modulation of the
RF field in the cavity [4]. In the high voltage power supply (HVPS) of the
300 kW klystron, a ripples signal of approximately 300 Hz is observed. The
corresponding 300 Hz component in the RF phase of CAV2 and CAV3 canbe well suppressed by the “PI+DOB” control. However, a 20 kHz ripple
exists in the HVPS of the 25 kW klystron. Although this component will
be attenuated due to the low-pass characteristic of the cavity, it still limits
the phase stability that can be achieved in CAV1. This component cannot
be sufficiently suppressed by the large PI gains, since the large gains not
only increase the risk of an unstable system but also deteriorate the high28 kW SSA
25 kW Kly.

300
kWSSA
Kly.
8 kW
8 kW SSA 16 kW SSA

Vector-sum
Controlling

Dump~ 20 MeV

ML2

ML1

SC

SC
Nine-cell SC

Two-cell SC

Figure 1: Layout of cERL. The cavities and RF sources are shown in the figure. Theenergies and accelerating field in the cavities are also marked as well.

frequency noise level. Furthermore, the frequency of 20 kHz exceeds theeffective bandwidth of the DOB controller, which is usually less than 5 kHz
under FB operation [2].
Active noise control (ANC) technology has been widely used in electroacoustic or electromechanical systems to attenuate the low-frequency noisein situations where other methods are ineffective [5, 6]. In recent years,
narrow-band ANC-based control approaches have been successfully applied
at facilities such as European X-ray free electron laser (XFEL) and CornellBNL ERL test accelerator (CBETA) to reject microphonics with a cavity
resonance control system [7, 8, 9]. In these applications, the ANC controller
estimates the amplitude and phase of the sinusoidal microphonics detuning
and then cancels their effects with feedforward (FF) control. Since both themicrophonics and HVPS ripples are reflected by a sum of sinusoidal disturbances in the RF field, especially in the RF phase, this inspires us to extend
the narrow-band ANC algorithm to the LLRF field control to reject the
HVPS ripples. In this paper, Section 2 briefly introduces the LLRF system.
In addition, the measured HVPS ripple effects in CAV1 and CAV2&3 are presented in this section. In Sec. 3, we describe the principle of the narrow-band
ANC algorithm; some Matlab-based analysis is presented as well. Section 4
depicts the FPGA implementation of the ANC controller. Section 5 presents
3the results of this controller in the cERL beam-commissioning. Furthermore,
the comparison of ANC control and DOB control are discussed as well. Finally, in Sec. VI, we present a summary of our work.
2. Suppression of HVPS ripples by LLRF system
The simplified diagram of the digital LLRF system of the cERL is shownin Fig.2 [2, 4]. The 1.3 GHz RF signals from the cavities are down-converted
to 10 MHz intermediate frequency (IF) signals. The IF signals are sampled
in the next stage at 80 MHz and fed to a micro telecommunications computing architecture (µTCA) FPGA to execute the digital signal processing
algorithms. The in-phase and quadrature components (I/Q) are then extracted from the IF signal [10]. The VS signal is calibrated by calculating
the superposition of all the cavity pick-up signals. After being filtered bydigital low-pass filters, the I/Q components are compared with the reference
signal and the I/Q errors are calculated. Then, these I/Q errors are regulated by a PI FB controller. The regulated I/Q signals are added to the FF
models. The combined signals are fed to the I/Q modulator to modulate theRF signal from the master oscillator. Finally, the LLRF FB loop is closed
by means of a high power RF source, which drives the cavities. Embedded
Linux is installed in a Power-PC of the µTCA FPGA board. The experimental physics and industrial control system (EPICS) is installed in the Linuxsystem for communication control, and hence the board acts as an EPICS
input/output controller (IOC) [11, 12].
The RF system is subjected to various disturbances. In the cavities of
the cERL ML, the dominant disturbance under CW mode operation is microphonics due to the high QL of the cavities. In the cavities of the cERL
injector, besides microphonics, the HVPS ripple is another main disturbancethat deteriorates the RF stability, especially the RF phase stability [4]. The
measured HVPS ripples from the oscilloscope is shown in Fig.3(a). A 20 kHz
component is observed in the HVPS output of the 25 kW klystron; likewise,a 300 Hz component exists in the 300 kW klystron HVPS. This 20 kHz component is produced by the switching invertor-type power supply. The 300
Hz component is caused because the DC power supply uses a three phase
controlled thyristor rectifier. The peak-to-peak voltage fluctuation (∆Vk /Vk )of the above two components are ±0.05% and ±0.17%, respectively. The

4

HVPS

Down
Convertor

Analog filter

1300 MHz
Ripples

Kly

RF = 1300 MHz
FPGA
Clk ≈ 80 MHz
LTC2208
ADC

IF ≈ 10 MHz

ADC

IQ Mod.

LO ≈ 1310 MHz

SW1

I_Set
Vector sum Fil.
I
IIR
 cos sin 



sin

cos


 Q
IIR
Calib.
Q_Set

ADC

DIO (RF SW)
I_FF

PI

DAC

PI

DAC

I
Q

AD9783

Q_FF
Power PCLinuxEPICS IOCADC

AMC Card

Waveform

CommandFigure 2: Diagram of the LLRF system in the cERL at KEK. This figure shows the case ofindividual cavity control in which one klystron drives one cavity. In the case VS control,
multiple cavities will be driven by one klystron.

corresponding klystron phase fluctuation ∆θkly is expressed as [13]∆θkly = D

∆Vk
,
Vk

(1)

where D represents the voltage fluctuation coefficient for the klystron phasemodulation. This coefficient is determined by the klystron cathode voltage
Vk and the drift tube length L (the length between the input cavity andoutput cavity of the klystron). In our case, the value L is approximately
0.48 m for both the klystrons, and the operational Vk is 20 kV for the 25
kW klystron and 35 kV for the 300 kW klystron. According to Ref. [13],kthe value of D is approximately 13.0◦ / ∆V[%] for the 25 kW klystron andVk◦ ∆Vk
9.7 / Vk [%] for the 300 kW klystron. Accordingly, the corresponding phasefluctuations of the 25 kW klystron at 20 kHz and 300 kW klystron at 300
Hz are approximately ±0.65◦ and ±1.65◦ , respectively.
Figure 3 (b) shows the measured Fast Fourier Transformation (FFT) analysis of the klystron output phase. The amplitudes of the phase fluctuationof the corresponding components are 0.58◦ and 1.6◦ for the 25 kW klystron5

±0.050%~20 kHz±0.17%~300 Hz

(a)

2

0.8
Phase [deg]Phase [deg]20 kHz HVPS ripples
0.6
0.4
0.2
0
0

10

20
30
Frequency [kHz]

40

1
0.5
0
0

50

300 Hz HVPS ripples

1.5

0.2

0.4
0.6
Frequency [kHz]

0.8

1

(b)

Figure 3: (a): HVPS ripples measured from oscilloscope. (b) FFT analysis of klystron
output phase. The amplitude of the phase modulation is approximate 0.58◦ at 20 kHz forthe 25 kW klystron (left), and 1.6◦ at 300 Hz for the 300 kW klystron (right).

6

[degree rms]

A/A [% rms]

0.024
0.022
0.02

G2
0

20

0.02
G1
0.018
0.016

40

60

80

100

0

20

40

60

80

100

80

100

Kp

Kp

0.03

0.025

0.02

[degree rms]

A/A [% rms]

(a)

K2

0

20

40

60

80

0.03

0.025

0.02

100

K1
0

20

40

Kp

60

Kp

(b)

Figure 4: Gain-scanning result for (a): CAV1, (b): CAV2&3 (VS control). The subplots on
the left and right indicate the amplitude and phase stabilities, respectively. Before 2014,
G1 and K1 were determined as the optimal gains according to the phase performance.
From 2015 to present, G2 and K2 were selected as the operational gain to reduce the RF
trips.

0

Kp = G2

0.02

Kp = G1

0.015
0.01

−1

0.29 0.3

Phase [deg]Phase [deg]

10

10

0.005
20

20.2

20.4

−2

10

−3

0.31 0.32

−1

10

FF
Kp = K2
Kp = K1

−2

10

−3

10

0

0.06
0.04
0.02

0

FF

10

10
10

20

30

40

50

0

Frequency [kHz]

0.2

0.4

0.6

0.8

1

Frequency [kHz]Figure 5: FFT results of cavity phase in the case of FF operation (green), Kp = G2 or K2(blue) and Kp = G1 or K1 (red). The ripple effect always exists in all of these three cases.

7and 300 kW kystron, respectively. The results are in good agreement withthe value calibrated from Eq.(1).
High FB gains are required to suppress the ripples. To optimize the
PI gains in the FB loop, a gain scanning experiment was performed. The
optimal gains were determined according to the scanned performance curves.
Detailed information about this scanning process was presented in Ref. [14]and Ref. [15]. Under optimal integral gain (Ki ), which is approximately
1 × 105 in our case, the amplitude (left) and phase (right) stabilities asfunctions of proportional gain (Kp ) are illustrated in Fig. 4. The optimal
gain for phase is usually larger than the optimal gain for amplitude. One
possible reason is that disturbance such as microphonics and ripples mainly
influence the RF phase. To reject these disturbances in the RF phase, ahigher Kp is preferred. However, the high FB gains not only increase the riskof an unstable system but also increase the noise level of the high-frequency
components. Before the year 2014, the optimal gains were mainly determinedon the basis of phase performance, i.e., we selected G1 and K1 as the optimal
gains for CAV1 and CAV2&3. However, A few RF trips occurred in oursystem due to the high LLRF FB gain. These situations forced us to decrease
the gain from G1 and K1 to G2 and K2 after the year 2015. The gain G2 isselected as the operational gain of CAV1 mainly on the basis of amplitude
performance (we can achieve optimal amplitude stability under G2 ). The
gain K2 = 0.5 · K1 was determined for the operational gain of CAV2&3 to
make compromises between the amplitude stability and phase stability. The
RF trips due to the LLRF system were significantly reduced as presented in
Ref.[16].
Figure 5 compares the FFT analysis of the cavity phase under FF operation, FB operation with G2 (or K2 ) and FB operation with G1 (or K1 ). It
can be clearly seen that the 20 kHz and 300 Hz ripples still exist even underhigh gains G1 and K1 . If we continue to increase the gains to higher values,
the RF stabilities of both amplitude and phase become worse as shown in
Fig. 4.
3. Narrow-band ANC algorithm
ANC control is commonly used in electroacoustic and electromechanicalsystems to cancel unwanted noise. In this method, an anti-noise signal withthe same amplitude but opposite phase is generated by the ANC algorithm,
and then noise cancellation is realized with FF method [5, 7, 8, 9]. Usually, an8external reference detector is required to calculate the noise that needs to becanceled. In a special case of narrow band noise (e.g., sinusoidal noise), suchas microphonics or HVPS ripples, an internal reference may also be effective.
These facts provide a possibility to simplify the design of the system. In
European-XFEL, a narrow-band ANC method with an internal reference
was applied in the piezo-based resonance control system to reject the lowfrequency microphonics noise [7]. In CEBTA, an enhanced version of narrowband ANC algorithm, with adaptively tunes the control parameters, wassuccessfully implemented to suppress the microphonics detuning [8]. Sinceboth the microponics and HVPS ripples can be seen as a superposition ofsinusoidal signals, we were inspired to design a narrow-band ANC-based
method to reduce the ripple effects in our system.
Since the ripple effects are mainly concentrated in the RF phase, we only
consider the implementation of the ANC algorithm in the phase loop in thispaper for simplicity. Generally, one ANC unit cancels only one components.
Therefore, for the applications in Ref.[7] and Ref.[8], several ANC unites werecombined to suppress the microphonics which includes several components.
However, in our case, as shown in Fig. 5, the 20 kHz and 300 Hz ripples are
the dominant components for CAV1 and CAV2&3, respectively. This would
become more clear by investigating the accumulative phase RMS stability as
shown later in Fig.13. Therefore, we need only one ANC controller to cancel
the ripple effects.
In principle, the LLRF system is a muti-input muti-output system. Since
the Lorentz force detuning effect is not serious due to the CW mode operation, the microphonics detuning is well compensated by the resonancecontrol loop in the cavities of the injector. That is, the cavity is assumed to
be operated on-resonance in our system. Under this assumption, the LLRF
system for the phase loop control is considered as a single-input single-output
system.
Figure 6 shows the simplified model of the ANC control in combination
with PI control. If the cavity is operated on resonance, the cavity transfer
function Hcav (s) is simplified as
Hcav (s) =ω0.5,
s + ω0.5(2)where the parameter ω0.5 represents the cavity half-bandwidth. The transfer
function HT (s) = e−Td ·s represents the loop delay model in the system. In
our system, the loop delay Td is approximately 1 µs. Here, the model HP I
9d rp  t 

HT

cav

Hcav

set

H PI
err  n

e jntAdaptive Filteru  n

w [n]
n

LMS



Figure 6: Phase loop model of ANC-based controller in combination with PI controller.
The ANC controller is indicated by the grey block. The main components of the ANC
controller include an adaptive filter w(n) (indicated by red block) and an LMS algorithm(indicated by blue block).

represents the PI FB controller. It should be noted that in this paper, thePI controller is defined by its continuous-time form
Ki
.
(3)
s
The HVPS ripples at a specified frequency are expressed by a sinusoidal
signal drp (t) with a frequency ωrp , amplitude Arp , and phase φrp :HP I (s) = Kp +drp (t) = Arp sin(ωrp t + φrp ) .

(4)

The ANC controller is indicated by the grey block in Fig. 6. The oscillatorejωn t provides a pair of orthogonal signals sin(ωn t) and cos(ωn t), which areused as reference inputs for an adaptive filter w(n) with filter weights w1
and w2 . The value of ωn is selected based on the actual ripple frequency ωrp(e.g., 20 kHz and 300 Hz in our case). The orthogonal references are thenweighted and summed to produce the canceling signal u(t)u(t) = w1 · sin(ωn t) + w2 · cos(ωn t) .

(5)

By using the samples n = t/∆t to replace the parameter t, where ∆t is the
sampling duration, the canceling signal u(t) becomesu[n] = w1 [n] · sin[ωn ∆t · n] + w2 [n] · cos[ωn ∆t · n] .
10

(6)The adaptive weights w1 [n] and w2 [n] are updated by the least mean square(LMS) algorithm as follows:
w1 [n + 1] = w1 [n] + µ · ϕerr · sin[ωn ∆t · n − θn ] .

(7)

w2 [n + 1] = w2 [n] + µ · ϕerr · cos[ωn ∆t · n − θn ] .

(8)Here µ is the step size parameter of the LMS algorithm, and ϕerr represents
the cavity phase error, which is the difference between the cavity phase ϕcav
and phase set value ϕset . The parameter θn is the nominal phase responseof the original system (which is the system without ANC controller) at thefrequency ωn . Here, we use θn to compensate for the phase shift in the original
system. Assume that the actual phase response at ωn for the original systemis θp . Then, the stability condition is satisfied if the difference between θpand θn is less than 90◦ [5, 7, 8, 9]. The value of ωn can be easily predictedby the bode diagram. Since a ±90◦ error of ωn is acceptable, it is possible
to optimize ωn experimentally.
The steady state transfer function of this ANC controller from the error
ϕerr [n] to ANC output u[n] is [7, 8, 6]
Hanc (z) = µ ·cos(ωn ∆t − θn )z − cos(θn ).
z 2 − 2cos(ωn ∆t)z + 1(9)Figure 7 compares the closed loop transfer function from drp to the cavity
phase ϕcav in the case of PI individual control and “PI+ANC” control. In
the steady state, the transfer function of PI+ANC control is given by
Hcav · HT
Hdrp →ϕcav =.
(10)
1 + (HP I + Hanc ) · Hcav · HT
On the other hand, the transfer function of PI individual control is given by
Hcav · HT
Hdrp →ϕcav =.
(11)
1 + HP I · Hcav · HT
Here, the parameters in the cavity model Hcav are selected based on CAV1
(QL ≈ 1.2 × 106 ). The loop delay Td is supposed to be 1 µs as mentioned
above. The FB gain for Kp is selected as G2 . The parameter ωn is set to 20
kHz to suppress the ripples. As shown in Fig. 7, the ANC algorithm performs
like a notch filter and the center of the notch filter is defined by ωn .
Figure 8 shows the influence of µ and θn . The parameter µ determines
the bandwidth of the notch. The parameter θn may lead to an asymmetricmagnitude response. Regardless of the value of θn , there is a notch in thefrequency of ωn .
11

Magnitude [dB]-30

PI+ANC
PI
-35
-40
-45
-50
-55

-40
-50

1.99

2

-60

2.01
104

102

104

106

Frequency [Hz]Magnitude [dB]

Figure 7: Comparison of the closed-loop transfer function from drp to ϕcav in the case of
PI individual control (red) and “PI+ANC” control (blue). The ANC algorithm acts likea notch filter with the notch center defined by ωn .

-30
= 0.005,-40= 0.010,-50= 0.001,

19.94

19.96

19.98

20

20.02

20.04

n

= p

n

= p

n

= p

20.06

Magnitude [dB]

Frequency [kHz]
(a)
-30
-40

= 0.005,

-50
19.94

19.96

19.98

20

20.02

n

-

p

= 0.005,np= 0.005,

n

p

20.04

= 0 deg= -30 deg
= +30 deg

20.06

Frequency [kHz](b)
Figure 8: Magnitude of the closed loop transfer function in terms of different ANC parameters (a) µ and (b) θn . The parameter µ regulates the effective bandwidth of the ANC
controller, whereas the parameter θn affects the symmetry of the magnitude response.

12

From
cavityFF

SET
I/Q
cordiccav

I PI , QPI

PI
ϕerr
 set

To I/Q
modulator

Phase
Modulator I anc , Qanc

ANC

anc

Figure 9: Overall algorithm of “PI+ANC” control. The “Phase Modulator” model is used
to phase modulate the PI controller output with ϕanc . The I/Q signals path is indicatedby blue color.

4. FPGA implementation of the ANC controller
Since the structure of the narrow-band ANC algorithm is relatively simple, it can be implemented Iinside the FPGA in real-time. The combinationPIof the PI controller and the ANC controller is shown in Fig. 9. The cavity
I anc by the coordinate rotaphase ϕcav is extracted from the cavity I/Q signal
tion digital computer (CORDIC) algorithm. The CORDIC algorithm can
Qancthe rectangular coordinate
be used to realize a mutual transformation from(e.g., I/Q) to the polar coordinate
system (e.g., amplitude and phase). The
QPI
cavity phase error ϕerr is then obtained by calculating the difference between
ϕcav and the phase set value ϕset ; ϕerr is regulated by the ANC controller.
The processed phase signal ϕanc is used to modulate the PI controller output IP I and QP I using the “Phase Modulator” model. The structure of thismodel will be discussed in the following paper.
Figure 10 shows the structure of the ANC controller in FPGA. Theinternal reference signals sin[ωn ∆t · n] and cos[ωn ∆t · n] are generated by
CORDIC-based numerically controlled oscillator.
limit An additional phase offset
θn is introduced to compensate for theΣphase shift in thesystem
as discussed
anc
in Sec. 3. The regulated reference signals are then sent to the LMS algorithm
to update the filter weights w1 and w2 . The updateLMS
rules are given in (7)errsin
and (8) in Sec. 3. The ANC output phase is thencalculatedµ by the adaptive
Σ
1/z
cos“limit” modelw 1 is used to keep the ANC output infilter using (6). Here, thea bounded range in order to protect the system under abnormal cases (e.g.
w
the utilization of unreasonableµ1/z Σ  n θn or µ).2
The PI output signal need to be phase modulated by ϕanc . Suppose the
13

IPI

anc

I anc
Q anc
Q PI

Adaptive
Filter

err

limit

anc

Σ

cordicFrom
cavity

sin
cos

SET

LMS
µ
Σ

w1 1/z
n

w2I

1/z

PI , QPIΣµFF

To I/Q
modulator

Phase
Mod. I anc , QancPI
I/Q
cordicerr in FPGA.
ancadaptive filter and the LMS algoANC The
Figure 10: Structure ofcav
ANC controller
rithm are indicated by the the setred and blue blocks, respectively.

I PI

anc

I anc
Qanc
QPI

Figure 11: Structure of the phase modulator model in FPGA.

limit
14 Σ

sin
cos

w1
w

1/z

anc
LMS
µ
Σ

err

I/Q output of the PI controller is defined asIP I = Acos(α) ,QP I = Asin(α) .

(12)Then, the corresponding I/Q signal that phase modulated by ϕanc is givenby
Ianc = Acos(α + ϕanc ) = IP I · cos(ϕanc ) − QP I · sin(ϕanc ) ,(13)
Qanc = Asin(α + ϕanc ) = IP I · sin(ϕanc ) + QP I · cos(ϕanc ) .
It should be noted that, the value of ϕanc for ripples compensation isusually less than 2 degrees (actually, it is approximately 0.6 degree for
CAV1 and 1.7 degrees for CAV2&3); that means, we have cos(ϕanc ) ≈ 1
and sin(ϕanc ) ≈ ϕanc . Therefore, similar to that in Ref. [17], Eq. (13) issimplified into
Ianc ≈ IP I − QP I · ϕanc ,(14)
Qanc ≈ QP I + IP I · ϕanc .
The structure of the phase modulator model (“Phase Modulator” in Fig. 9)
in FPGA is illustrated in Fig. 11.
Finally, we summarize the utilization of the FPGA resources of the ANC
controller including the phase modulator model (Fig. 11) in Table 1. The
ANC control occupies a few registers due to the implementation of the
CORDIC algorithms.
Table 1: FPGA resource utilization of ANC controller

Block

Available

ANC controller[%]

Register

44800

1471

3.3%

DSP48Es

128

8

6.3%

Block RAM

148

0

0%

5. Results and Discussion
To validate the ANC control, we integrated the ANC controller into the
PI feedback loops in the µTCA-based LLRF systems of CAV1 and CAV2&3.
Table 2 lists the main parameters of the cavities and LLRF systems.
15

Table 2: LLRF and cavity parameters of CAV1, CAV2, and CAV3 in the cERL injector

Cavity

CAV1

CAV2

CAV3

Cavity Field (Eacc )∼ 5 MV/m∼ 5 MV/m∼ 5 MV/m

Beam Phase (Φb )

0◦

0◦

0◦

Loaded Q (QL )1.2 × 106

5.7 × 105

4.8 × 105

Cavity Bandwidth (ω0.5 )540 Hz1120 Hz1350 HzTime Delay (Td )

1 µs

1 µs

1 µs

Power Source

25 kW klystron

300 kW klystron (VS ctrl.)

PI Gains (Kp , Ki )(G2 , 0.6 × 105 )(K2 , 0.7 × 105 )Dominant Ripples

20 kHz300 Hz

To compare the PI individual control and “PI+ANC” control, we first
operate the LLRF system with PI individual control on CAV1. As shown in
Fig. 12 (a), the red curves give the amplitude and phase responses and theirs
corresponding FFT analysis of CAV1 under PI individual control. Here, theFB gain Kp was set to G2 . As expected, the 20 kHz ripple components
were easily found in the FFT analysis of the cavity phase. In the next step,after activating the ANC control (indicated by the blue curves in Fig. 12)
and keeping the PI control in the same condition as before, the 20 kHz
component in the cavity phase was well suppressed as shown in the FFTanalysis of Fig. 12 (a). For CAV2&3, a similar result can be found in Fig. 12(b); the 300 Hz component in the VS phase of CAV2 and CAV3 is almost
canceled out by the ANC control.
Comparisons of the cumulative RMS stabilities of CAV1 and CAV2&3
under PI individual control (red) and “PI+ANC” control (blue) are shownin Fig. 13 (a) and Fig. 13(b), respectively. From the amplitude cumulative
RMS stability curves (left side) in Fig. 13, it can be seen that the contributionof the 20 kHz ripple to the overall amplitude stability is almost negligible for
CAV1. The contribution of the 300 Hz ripple for CAV2&3 is about 8% in
both the control approaches. In principle, if we apply the presented ANC
method in both amplitude and phase loops (or I/Q loops), the ripple effects
in the amplitude can be rejected. In our application, since the ripple effects in
16

Phase [deg]

8000
7995

0

0.1

0.2
0.3
Time [ms]0.4
Phase [deg]

0
−20
−40

10

20
30
40
Frequency [kHz]50

Phase [deg]

5510
5500
5490

0

10

20
Time [ms]

30

−20
0.1

0.2
0.3
0.4
Frequency [kHz]

0
−0.1
−0.2
0
−2

10

PI
0.1

0.5

(b)

PI+ANC

0.2
0.3
Time [ms]0.4

20 kHz

−4

10

0

20
40
Frequency [kHz]

45.2
45
44.8

40

0

−40

0.1

(a)

Phase [deg]Amp. [a.u.]
Mag. [dB]
Amp. [a.u.]
Mag. [dB]

8005

0

−2

10

10

20
Time [ms]3040

300 Hz

−4

10

0

0.2
0.4
Frequency [kHz]Figure 12: PI individual control (red) vs “PI+ANC” control (blue) in 2018. The amplitude
and phase of the cavity field, and the corresponding FFT analysis are plotted. From top
to bottom: (a) CAV1, Kp = G2 and (b) VS of CAV2 and CAV3, Kp = K2 .

17[deg rms]

0.01
0

0

10

20

30

Frequency [kHz]

40

0.01
PI
PI+ANC

0

0

100

200

300

Frequency [Hz]

400

0

10

20

30

Frequency [kHz]

40

50

0.03
0.02

~300 Hz

~50%

0.01
0

500

~20 kHz

~30%

0.01

(a)

0.015

0.005

0.02

0

50

[deg rms]

A/A [% rms]
A/A [% rms]

0.02

0

100

200

300

Frequency [Hz]

400

500

(b)

Figure 13: Cumulative RMS amplitude (left) and phase (right) stabilities of (a) CAV1and (b) VS of CAV2 and CAV3 under PI individual control (red) and “PI+ANC” control(blue) in 2018. The contribution of the 20 kHz and 300 Hz ripples to the overall phase
RMS stability are 30% and 50%, respectively.

the amplitude are not as serious as those in the phase, we only implemented
the ANC algorithm in the phase loop to save FPGA resources. Therefore,
there is no improvement in amplitude performance. In all the cavities, theripple components significantly influence the phase stability. For CAV1, thecontribution of the 20 kHz ripple effects on the RMS phase stability is about
30% of the total stability. In the case of CAV2&3, the contribution of the
300 Hz ripple to the total stability is about 50%. The phase performance issignificantly improved after activating the ANC control. It should be notedthat the ANC algorithm is only effective for the frequency of interest (definedby ωn in the ANC controller). Other components such as 50 Hz and 150 Hz
in CAV2&3 are not sensitive to the ANC controller.
Table 3 summarizes the improvements of ANC control in comparison
with PI individual control. The phase performance in all of these cases are
improved by the ANC technique.
It is interesting to compare the ANC control with DOB control, which
is another advanced control method used in the cERL commissioning [2].
The basic architecture of the DOB control in combination with PI control is
18

Table 3: Performance of ANC control for the suppression of ripples during the cERL beamcommissioning in 2018.

Cavity

Kp

G2
CAV1
G1
CAV2&3Vector-sum

K2

MethodRF field stability∆A/A [% rms]

∆θ [◦ rms]

PI

0.015%

0.019◦

PI+ANC

0.015%

0.014◦

PI

0.016%

0.016◦

PI+ANC

0.016%

0.013◦

PI

0.014%

0.025◦

PI+ANC

0.014%

0.014◦

illustrated in Fig. 14. The definitions of the models Hcav , HT and HP I are
the same as those in Fig. 6. The model Hn−1 is the inverse transfer functionof the nominal cavity model Hn . A low-pass Q filter is connected with Hn−1
to make the overall combination Q · Hn−1 casual. By using Hn−1 , it is possible
to estimate the nominal system drive signal û. If the model Hn is sufficiently
precise, which means that Hn ≈ Hcav , the signal û is approximately equal
to the actual drive signal u. The signal uf is the filtered drive signal but
without disturbances. The model z −L is introduced here to compensate forthe loop delay Td . Therefore, we can obtain the disturbance estimation dˆby calculating the difference between û and uf . Finally, we remove dˆ fromthe drive signal to realize the disturbance rejection. In DOB control, thelow-pass Q filter determines the effective bandwidth of the controller [2, 18].
Detailed information about this DOB-based method can be found in Ref.[2].
Figure 15 compares the cumulative RMS stabilities of CAV1 and CAV2&3
under PI individual control (red) and “PI+DOB” control (blue). For consistency, the gain Kp was set to G2 and K2 for CAV1 and CAV2&3, respectively.
The cavity fields are approximately 3 MV/m for all of the 3 cavities. To evaluate whether we can remove the 20 kHz ripple by DOB control, we increase
the bandwidth of the Q filter in the DOB control to more than 5 kHz, whichis almost the highest value that can be achieved under the FB operation [2].
Since the 20 kHz ripples component is still beyond the effective bandwidthof DOB control, it is clearly seen in Fig. 15(a) that there is no improvement19

d rp  t 

HT

H cav

u

H PI
Set
DOB control

Q  H n1

d̂

Q

uf

û

zL

Figure 14: Simplified architecture of DOB control in comparison with PI control. The
DOB controller is indicated by the grey block. The disturbance drp can be estimated by
ˆ The effective bandwidth of the controller is determined by thethe controller output d.
lowpass Q filter.

in the phase performance at 20 kHz. For the low-frequency components ofless than several hundreds hertz, the phase performance is improved by DOB
control. For the frequency range from 1 kHz to 20 kHz, unfortunately, the
DOB control deteriorates the phase stability. The possible reason is that the
non-optimal bandwidth of the Q filter was chosen. For CAV2&3, we selected
a 2 kHz Q filter for the DOB control to remove the 300 Hz component asshown in Fig. 15(b). In contrast to ANC control, the DOB control is effective
not only for 300 Hz but also for other components such as 50 Hz and 150 Hz.
Since the dominant 300 Hz ripple effects are rejected, the phase stability of
CAV2&3 is improved from 0.026◦ rms to 0.015◦ rms by using the DOB control method. The result is comparable with that of the ANC controller (seeTable 3).
On comparing of these two controllers, it can be seen that the DOB control is valid in the low-frequency range (e.g., DC to several kHz), but theeffective bandwidth is limited by the stability requirements. For better performance, a system model is usually required in this control method [2, 18].
The ANC control is effective for the frequency components of interest withan infinite loop gain. Furthermore, we only need limited phase informationof the transfer function for the specified frequency, and a tolerance of up to±90◦ errors is acceptable in theory.
20[deg rms]

A/A [% rms]

0.03
0.02
0.01
0
0

10

20

30

40

0.02
0.01

~20 kHz

0

50

0

10

20

Frequency [kHz][deg rms]

A/A [% rms]

(a)
0.02
0.01

30

40

50

Frequency [kHz]0.03
PI
PI+DOB

0.02~300 Hz

0.01
0

0
0

100

200

300

400

0

500

100

200

300

400

500

Frequency [Hz]Frequency [Hz](b)

Figure 15: Cumulative RMS amplitude (left) and phase (right) stabilities of (a) CAV1and (b) VS of CAV2 and CAV3 under PI individual control (red) and “PI+DOB” control(blue) in 2015.

In the current ANC controller, the parameters such as θn , and ωn were
kept constant during the operation. However, after a long-term operation,these parameters may vary as the environment changes (e.g., temperaturedrifts). As future work, those parameters in the ANC controller can beadapted with the LMS algorithm [8]. In addition, we also plan to apply the
ANC technique in the resonance control system of the SC cavities in thecERL ML.
6. Summary
ANC control cancels the disturbances by generating an anti-noise signal
with equal amplitude but opposite phase. In European-XFEL and CBETA,
ANC-based methods have been successfully applied to cancel the microphonics detuning in the SC cavity with piezo tuner.
In the injector of the KEK-cERL, HVPS ripples of 20 kHz and 300 Hz
deteriorate the phase performance of the LLRF systems. The high-gain PI
control could not achieve the desired level of ripples suppression. Inspiredby the experience of European-XFEL and CBETA, we have integrated the21ANC-based algorithm in our LLRF system to damp the ripple components
in the RF phase. We demonstrated the effectiveness of this ANC method bysuccessfully canceling out the RF phase ripples during the cERL beam commissioning. In addition, we compared the performance of the ANC methodwith the DOB-based method. The DOB control method is a model-based
method, which is effective in the low-frequency domain with an effective
bandwidth (usually less than several kHz) that is limited by the stability
requirement. In contrast, the ANC control is efficient only for the frequency
component of interest, and it is applicable with very limited information
about the system model (i.e., correct θn ).
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24