A DISTURBANCE-OBSERVER-BASED CONTROLLER FOR LLRF
SYSTEMS
F. QIU#, D. ARAKAWA, Y. HONDA, H. KATAGIRI, T. MATSUMOTO, S. MICHIZONO, T.
MIURA, T. OBINA, KEK, Tsukuba, Ibaraki 305-0801, JapanS. B.WIBOWO, SOKENDAI (the Graduate University for Advanced Studies), Tsukuba, JapanINTRODUCTION
At KEK, a 3 GeV energy recover linac (ERL) lightsource is proposed. For the demonstration, a compact ERL(cERL) was constructed as a prototype machine for the 3GeV ERL project [1,2]. The cERL, which is a 1.3 GHz
superconducting (SC) project, consists of an injector partand a recirculating loop part. Three two-cell cavities, called
Inj. 1, Inj. 2, and Inj. 3, were installed in the injector, andtwo main nine-cell cavities were installed in therecirculating loop. To fulfill the required beam quality, theRF field fluctuations should be maintained at less than
0.1% (in amplitude) and 0.1° (in phase) in the cERL. Field
programmable gate array (FPGA)-based digital low-level
ratio frequency (LLRF) systems were developed toimplement the RF field control [3].
In the LLRF systems of the cERL, disturbance signals
such as 50-Hz microphonics and 300 Hz high-voltage
power supply (HVPS) ripples will severely limit theperformance of the LLRF systems [3]. Furthermore, during
beam commissioning, the beam loading can be seen as
another disturbance. In principle, these disturbance signals
can be rejected or suppressed by applying highproportional and integral (PI) gains in the feedback (FB)
control; however, the PI gains are limited by the loop delay.
In the cERL, during the beam commissioning, we foundthat the PI gain is not sufficient in the presence of large
disturbances. In view of this situation, we present a
disturbance observer (DOB)-based approach that aims to____________________________________________#qiufeng@post.kek.jp

LLRF SYSTEM
A simplified block diagram of the cERL LLRF system isshown in Fig. 1. The 1.3-GHz cavity probe signal is downconverted to a 10-MHz intermediate frequency (IF) signal.
The IF signals are sampled at 80 MHz by 16-bit ADCs andthen fed into the FPGA. The baseband and quadrature (I/Q)
components are extracted from the IF signal with a non-IQ
method. In the next stage, the I/Q signals are comparedwith their set values, and the errors are calculated. Theerrors are regulated with a PI controller and then addedwith a feedforward (FF) table. Finally, the combined signal
is fed into the I/Q modulator via the 16-bit DACs toregenerate the 1.3-GHz RF signal. This regulated RF signal
will be used to drive the high-power source, which drives
the cavities [6,7].
1300 MHzLO ≈ 1310 MHz

Kly. / SSAAnalog filter

Pre. Amp.

RF = 1300 MHz

SW1FPGAI_Set

Clk ≈ 80 MHz
LTC2208
ADC

IF ≈ 10 MHz

ADC

IQ Mod.

Digital low-level radio frequency (LLRFs) systems havebeen developed and evaluated in the compact energy
recovery linac (cERL) at KEK. The required RF stabilities
are 0.1% rms in amplitude and 0.1° rms in phase. Theserequirements are satisfied by applying digital LLRF
systems. To further enhance the control system and makeit robust to disturbances such as large power supply (PS)ripples and high-intensity beams, we have designed anddeveloped a disturbance observer (DOB)-based control
method. This method utilizes the RF system model, which
can be acquired using modern system identification
methods. Experiments show that the proposed DOB-based
controller is more effective in the presence of highdisturbances compared with the conventional proportional
and integral (PI) controller. In this paper, we present thepreliminary results based on the experiments with DOBbased controller.

control an LLRF system subject to large disturbances [45].
In this paper, we first introduce the LLRF system in thecERL, and then describe the principle, design, andimplementation of this DOB-based approach. Finally,
preliminary results are used to compare the proposed DOB
control and the previous PI control in the cERL beamcommissioning.

Down
Convertor

Abstract

Calibration
 cos sin sin cos I

FilterIIR

DIO (RF SW)
I_FF
CalibrationPI cos sin sin cos PI

Q IIR
Vector Sum

DAC I
DAC

Q

AD9783

Q_FF
Q_Set

ADC
ADC

AMC Digital Feedback CardPower PC
LinuxEPICS IOC

Waveform

CommandFigure 1: Schematic of the LLRF system in the cERL.

DOB CONTROLThe basic idea of DOB control is shown in Fig. 2(a) [45]. Here, Gp(s) and Gn(s) represent the transfer function ofthe actual plant (e.g., cavities and RF devices) and thenominal mathematical model. Signals d and de represent
the real disturbance and the disturbance estimate,respectively. Signal FF represents the FF table output.
From Fig. 2(a), it is clear that the disturbance estimate decan be expressed byFFdPlantFFGp  sdPlantGp  sFilQ sInvG n 1  s 

Inv + FilQ  s  Gn1  s dededPlant

DelayGp  se  sTd

FilQ s

Inv + File  sTn

Q  s  Gn1  s de(b)

(a)

FF(c)

Figure 2: Evolution of DOB control. From left to right: (a) the basic structure of DOB control, (b) DOB control withQ filter, (c) DOB control with Q filter and delay compensation unit.
de    d  Gp  s  Gn1  s    .

(1)

If the the inverse nominal model Gn-1(s) (which can beacquired by applying system identification [6,7]) issufficiently accurate, the signal de is a good estimate of the
disturbance signal d; i.e., the disturbance signal can beobserved and then reproduced if we know the systemmodels very well. Therefore, after removing the signal defrom the FF table (see Fig. 1), the disturbances arecompensated.
In practice, a Q filter is usually required as shown in Fig.
2(b). The main function of the Q filter is to make the
combined transfer function Q(s)Gn-1(s) a casual system thatis physically realizable (the Gn-1(s) is usually anti-casual inpractice). The selection of the Q filter is one of the key
issues in the DOB controller design. References [4-5]describe good Q filter candidates. In the cERL LLRF
system, our selection is a second-order filter as given inQ s 1

 s  1

2.

(2)

The time delay is another issue that needs to beconsidered. Suppose parameter Tn is an estimate of theactual time delay Td, then as shown in Fig. 2(c), an extra
delay model is added in the DOB controller to compensate
for the time delay of the system. From Fig. 2(c), it is clearthat we can update the disturbance estimate de as

Figure 3: Integration of DOB control and PI control. The
presented DOB controller is indicated by the red block.
The closed-loop Bode plots with and without DOB
control are shown in Fig. 4. Here, we select the two mostcritical transfer functions in the system to analyze, which
are the disturbance d and the noise n, to the cavity pick-up
y (d→y and n→y). The location of each signal is given inFig. 3. The Q filter in the DOB controller is specified
according to (2), with a 5-kHz cutoff bandwidth.
Figure 4(a) indicates that the proposed DOB control
shows great superiority in disturbance rejection comparedwith the PI control, especially for the frequency range fromDC to 10 kHz. This is also the most attractive advantage of
the DOB control. Figure 4(b) shows that there is no
obvious difference in noise suppression for these twoapproaches.

de    d  Gp  s  e sTd Gn1  s  Q  s    Q  s  e sTn . (3)Therefore, on the basis of (3), if the system model issufficiently accurate, and the filter Q(s) outputs 0 dB in thefrequency band of interest, which covers the classic
disturbance frequencies (e.g., DC to 1 kHz), the signal deis a good representation of the actual disturbance d.

ANALYTICAL STUDY
The integration of the DOB controller and the previous
PI feedback system is shown in Fig. 3. The DOB-based
controller is indicated by the red block. The switch SW2 in
the figure control the enable/disable operation of the DOB
controller.

Figure 4: Closed-loop system response comparison of PI
control and “PI+DOB” control. From left to right: (a)Disturbance to cavity pick-up (d→y); (b) Noise to cavity
pick-up (n→y).

EXPERIMENT ON CERL BEAM
COMMSIIIONING
We have developed this DOB-based controller in an
FPGA and demonstrated it in the digital LLRF system ofthe injector. The main parameters of the RF system andcavities are listed in Table 1. In the HVPS of the 300 kW
klystron, which drives Inj. 2 and Inj. 3, the 300 Hz
component is one of the main disturbances. On the otherhand, in the presence of the high-intensity beam current
under burst mode operation, beam loading is anotherimportant disturbance. We will present each of these twocases separately.
Table 1: LLRF and Cavity Parameters of the Injector
CavityInj. 1

Inj.2

Inj.3

Cavityvolt. (Vc)

0.7 MV

0.65 MV

0.65 MVBeam
phase (φb)

0°

0°

0°

Ctrl
methodIndividual

Vector-sum control

Powersource

20 kW kly.

300 kW kly.

Loaded Q(QL)

1.2 × 106

5.7 × 105

Beam-loading Compensation
During the cERL beam commissioning, a 1 mA beam
current is operated for approximately 1 ms in burst mode.
The beam loading here can be considered as a disturbance.
The PI control is not sufficient to compensate for the beamloading effect in the beam commissioning; therefore, weapply the proposed DOB control to compensate for thebeam-loading effects.
Figure 6 shows the results of the beam-loading
compensation experiment under 1.6 ms, 800 µA (peakvalue), and a 5 Hz beam pulse. Results of the PI control(blue) and the PI+DOB control (red) on both Inj.1 and Inj.
2&3 (vector sum) are compared in Fig. 6. It should be
mentioned that the Q filter here is identical to the one
employed in the HVPS rejection experiment. The
improvement in the DOB control is evident in bothcavities, as shown in Fig. 6. The beam loading iscompensated for successfully in the presence of the DOBcontrol.

4.8 × 105

HVPS Ripple Rejection
Figure 5 compares the PI control (blue) and the PI+DOB
control (red) for the LLRF systems on Inj. 2 and Inj. 3. It
should be mentioned that the PI gains, which are optimized
with a gain-scanning experiment [7], are identical in boththe control approaches. The second-order IIR filter, whichis the discrete form of (2), with 5 kHz bandwidth, isselected as the Q filter. Fast Fourier transform (FFT) results
demonstrate that the 300-Hz HVPS ripples are clearlyrejected after applying the DOB control. The amplitude
and phase stability improve from 0.03% and 0.029° to
0.026% and 0.018°, respectively.

Figure 6: Measured RF field for the amplitude (left) andthe phase (right) in the cavities of the injector in thepresence of 800-µA beam loading. Red and blue
waveforms in each subplot represent the PI control and thePI+DOB control, respectively. From top to bottom: (a) Inj.
1, (b) Inj. 2&3.

SUMMARY
During the beam cERL commissioning, the LLRF
system performance is limited by several types ofdisturbances, mainly the 300-Hz HVPS ripples and beamloading. The previous PI control is not sufficient to reject
these disturbances. In this study, a DOB-based control
approach for disturbance rejection was developed. Both the300 Hz HVPS ripples and beam loading are successfullycompensated for with this DOB-based approach. In thispaper, we presented the idea and the preliminary results ofthis approach.

REFERENCES

Figure 5: FB control (blue) vs. FB+DOB control (red). RF
field performance in amplitude and phase is plotted as wellas their FFT analysis. From top to bottom: (a) waveform,(b) FFT.

[1] N. Nakamura et al., “Present status of the compact
ERL at KEK,” Proc. IPAC2014, Dresden, Germany(2014).
[2] S. Sakanaka et al., “Construction and commissioningof compact-ERL Injector at KEK,” Proc. ERL2013,
Novosibirsk, Russia (2013).

[3] T. Miura, “Performance of RF systems for compact
ERL injector at KEK,” Proc. ERL 2013, Novosibirsk,
Russia (2013).
[4] C.J. Kempf et al., “Disturbance observer andfeedforward design for a high-speed direct-drive
positioning table,” IEEE Trans. Contr. Syst. Technol.,7(5), Sept. (1999).
[5] T. Umeno and Y. Hori, “Robust speed control of dc
servomotors using modern two degrees-of-freedom
controller design,” IEEE Trans. Ind. Electron., vol. 38,
no. 5, pp. 363–368 (1991).
[6] F. Qiu et al., “Digital filters used for digital feedback
system at cERL,” LINAC14, Geneva, Switzerland(2014).
[7] F. Qiu et al., “Evaluation of the superconducting
LLRF system at cERL in KEK,” IPAC13, Shanghai(2013).