DEVELOPMENT OF ITERATIVE LEARNING AND DISTURBANCEOBSERVER-BASED LLRF CONTROL SYSTEM FOR INTERNATIONAL
LINEAR COLLIDERFeng Qiu∗ , Shinichiro Michizono, Toshihiro Matsumoto, Takako Miura,KEK, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
Sigit Basuki Wibowo, Na Liu
The Graduate School for Advanced Studies, Kanagawa 240-0193, Japan
Abstract
This paper shows the development of a iterative learning
control (ILC) combined with a disturbance observer (DOB)based control for the digital low-level radio-frequency(LLRF) system of international linear collider (ILC) project.
The motivation of this study is to compensate for the repetitive (or predictable) and unpredictable disturbances in theradio-frequency (RF) system such as beam loading, Lorentz
force detuning (LFD) and microphonics. Results in a cavity
simulator-based test bench demonstrate the possibility of thepresented control approach. We have a plan to further generalize this approach to LLRF systems at superconducting
test facility (STF) and future ILC project.

and KEK superconducting test facility (STF) [6]. However,
ILC algorithm is incapable of reject the unpredictable disturbances such as microphonics. In view of this situation,
disturbance observer (DOB) based control method is introduced to suppress the microphonics effects. DOB control
was successfully applied in the LLRF system of the compact
energy recovery linac (cERL) test facility at KEK [2]. It is
proved that the DOB control is effective for both repetitive
and unpredictable disturbances. This motivate us to designa control algorithm which combined the advantages of ILCand DOB, and both of the repetitive and unpredictable errors are expected to be canceled in the combined controlapproach.

INTRODUCTIONITERATIVE LEARNING CONTROLThe International Linear Collider (ILC) is an proposed
electron and positron collider facility for precisely investigating the Higgs boson, dark matter, and possible extra
dimensions. A total of 400 radio frequency (RF) stations,each was equipped with 39 superconducting (SC) RF cavities
driven by a 10 MW multi-beam klystron, will be establishedin ILC [1]. These cavities are operated in the pulse modewith 1.65 ms pulse duration, and 5 Hz repetition rate. Theparticle beam is then accelerated by the high gradient RF
field in the RF cavities. In order to achieve high beam quality, the RF field fluctuation should be maintained at less than
0.07% (RMS) for the amplitude and 0.35◦ (RMS) for thephase, respectively [1]. In accelerators, LLRF systems areapplied to stabilize the RF field.
The LLRF systems in a pulse mode machine are disturbed
by various of disturbances [2]. Typical disturbances areclassified into two categories: repetitive (or predictable)
disturbances and unpredictable disturbances. Repetitive disturbances such as Lorentz force detuning (LFD) and beamloading, are repeated in the system with 200 ms period. The
unpredictable disturbances such as microphonics varies frompulse to pulse.
The repetitive disturbances can be removed by iterative
learning control (ILC) [3–5]. In this control strategy, the error information gathered from the last cycles was estimatedand used to improve the current cycle. ILC algorithm requires the system to perform the same action over and overagain with high precision. This requirement can be fulfilled
in a pulse mode operation accelerators such as ILC facilityILC algorithms were originally developed for robot learning and training in [7]. Considering a discrete-time system
G p in the j-th trial(x j (k + 1) = Ax j (k) + Bu j (k).
(1)
y j (k) = C x j (k)∗ qiufeng@post.kek.jp

Here, the matrices A,B, and C describing the discrete-timesystem in the state space and x j (k), u j (k), and y j (k) are
the state, control, and output variables, respectively. The
subscript " j" and "k" represents the iteration index and timeindex, respectively.
A widely used ILC learning algorithm is given by
u j+1 (k) = Q I LC u j (k) + L(e j (k)) .
(2)
Here, Q I LC and L are defined as Q-filter and learning function, respectively. The signal e j represents the error signal.
Figure 1 has illustrated the learning process of the ILC
algorithm used in a LLRF system with pulse mode operation(e.g. LLRF system at ILC project). The learning process ofILC algorithm is illustrated in Fig. 1. In the j-th trial, thecavity error signal e j (k), is learned by the learning function
L. The result L(e j ), is added to the j-th control signal,
u j (k). The combined signal is filtered by Q I LC to enhance
the robustness of the algorithm. The output signal is thenupdated by the filtered signal. In the j + 1 th trial, the cavity
signal is detected at first, and then is compared with thegiven reference signal r to calculate the new error signal,
e j+1 (k). This algorithm is repeated from pulse to pulse, andthe tracking accuracy is improved in this iterative process.

u j k Controlu1  k 10e0  k 

e1  k 1kSample

kSampleu j k jej k Erroru0  k 0ej k jLOutput

j+1

ju j 1  k 

QILCdj+1

y j 1  k ke j 1  k j+1

kGp

Iterationjr

Iteration

Figure 1: Learning process of ILC algorithm.
The simplest way is to defined L in (2), as a proportional
gain k p . In this case, the learning updated algorithm in (2)is simplified by
u j+1 (k) = Q I LC u j (k) + k p e j (k) .
(3)
Algorithm shown in (3) is also named P-type ILC. In ourstudy, we have applied a P-type ILC at first because its ease ofdesign and implementation. Many advanced ILC algorithms
have been proposed including higher order ILC (HOILC),
H∞ -based ILC, plant inversion-based ILC and optimizationbased ILC [3–5]. In our paper, we have selected the plant
inversion-based ILC algorithm due to its fast convergencerate. The algorithm of plant inversion-based ILC can beexpressed byu j+1 (k) = Q I LC u j (k) + G−1(4)n e j (k) .
Here, G n represents the nominal model of the actual system
G p . The learning function in this case is L = G−1
n . Furthermore, to avoid the model uncertainty and enhance therobustness, a low-pass Q I LC is employed.

DOB-BASED CONTROLDOB control was originally proposed in [8]. The disturbance observer is capable to estimate the repetitive andunpredictable disturbances of the system. If the estimateddisturbances is with high accuracy, it is possible to cancel
the real disturbances with the estimate. The structure ofthe DOB control is shown in Fig 2. Signals c, ε, d, and dˆrepresent the control, plant input, disturbance, and disturbance estimate, respectively. Models G p and G n represent
the transfer function of the real system and nominal systemmodel (G n ≈ G p ). The Q-filter Q DOB here is a low-passfilter which makes the Q DOB G−1
n physically realizable. According to Fig. 2, the disturbance estimation is given by [2]dˆ = Q DOB (ε + d)G p G−1
n −ε .

(5)

In the cERL beam commissioning, this DOB control
method is demonstrated by successfully compensating thebeam-loading, as well as by successfully suppressing thepower supply ripples and microphonics [2].

cdPlantGp  s FilQDOB  s Inv + Fil
QDOB  s  Gn1  s d̂Figure 2: DOB control with Q-filter.

COMBINED CONTROLLER
In our design, we incorporate the ILC algorithm, as well as
DOB control with the traditional proportional (P) feedbackcontroller. The overall control block diagram is given byFig. 3. As discussed above, we have designed two typesof ILC algorithm: P-type ILC and plant-inversion ILC inthe combined controller. It should be mentioned that in theplant-inversion ILC case, the learning function L is not equalto G−1n any more. The overall system need to be considered
and the ILC algorithm is modified by [5]hiLCu Ij+1(k) = Q I LC u Ij LC (k) + Tu−1 e j (k) .
(6)
Where Tu represents the close loop transfer function matrix
from the ILC control signal u Ij LC to the plant output f (k).
The learning function is now defined as L = Tu−1 .

EXPERIMENT ON CAVITY SIMULATOR
The control algorithm in Fig. 3 is demonstrated in a realtime cavity-simulator based test bench [9]. Main components of the simulator include cavity base-band models for
fundamental mode and parasitic modes, a mechanical modelof the LFD and model for beam current. The unpredictabledisturbance model (e.g. microphonics) is also taken into
account in our simulator. The cavity simulator is implemented in a field programmable gate array (FPGA) which isconnected with digital LLRF systems. It is possible to test
the function of the presented algorithms with the the cavity
simulator in the absence of the real SC cavities. In the experiment, we select the cavity and RF parameters mainly based

LQILC  z 
SWILC Algorithmr k ek u j1  k ILC

FFKPf k uc k Gp k d̂  k 

DOB Ctrl.
SWdisturbance e sTd

reason is the limitation of the Q DOB bandwidth in the DOB
control. In the "P+ILC" case, there is a deviation in the phase
due to the unpredictable microphonics and beam fluctuations.
In the "P+DOB+ILC" case (red), the LFD and beam-loading
effects is perfectly compensated, as well as the microphonics.
Figure 5 compares the convergence rate of the P-type ILC(blue) and plant inversion-based ILC (red). According to Fig.
5, the plant inversion-based ILC convergences at a faster rate
than P-type ILC. This improvement is very important in areal beam operation.

zL0.07

QDOB  z f k 

QDOB  z  Gn  z 1∆A/A[% rms]

ej k Memoryu ILCk jLearning

Memory

0.05
0.04
0.03

Figure 3: Overall model of “P+DOB+ILC” control. The
presented ILC algorithm and DOB control are indicated byblue and red block, respectively.
on the KEK-STF project (Q L ≈ 4.6 × 106 , pulse duration ≈1.65 ms, repetition rate = 5 Hz).

Amp. [counts]

4

1.405

10000

x 10

1.4

5000
1.395
10.5

1

1.5

2
2.5
time [ms]

1.2

3

1.4

Phase [deg]

1015

20
2530
Iteration [counts]

354045Figure 5: Comparison of convergence rate of the P-type ILC(blue) and plant inversion-based ILC (red).

SUMMARY

1.63.540.5

REFERENCES[1] ILC, “ILC Technical Design Report”, http://www.
linearcollider.org/ILC/?pid=1000895

PP+DOB
P+ILC
P+DOB+ILC
Reference

0−0.505

We have presented a "P+DOB+ILC" control strategy thataims to reject both of the repetitive and unpredictable disturbances in LLRF system. Experiments on cavity simulator demonstrate that the stability of the LLRF system isimproved after implementing the presented approach. We
hope to extend these control strategy to the real pulse mode
operated accelerators like STF and ILC.

15000

00P−type ILC
Plant Inversion ILC

0.06

0.5

11.5

22.5
time [ms]33.5[2] F. Qiu et al. “Application of disturbance observer-based control in low-level radio frequency system in a compact energy
recovery linac at KEK”, in PRSTAB,18, 092801(2015).

4Figure 4: Comparison of P control (blue), "P+DOB" control(black), "P+ILC" control (green) and "P+DOB+ILC" control(red).
Figure 4 compares the cavity pick-up signal under four
different control methods including traditional P control(blue), "P+DOB" control (black), "P+ILC" control (green)and "P+DOB+ILC" control (red). In the cavity simulatorpart, we have introduced a nearly on-crest beam current
with ±10% fluctuations, as a result, beam loading effects
mainly appears in the amplitude of the pick up signal. In
all of these four approaches, we maintain the P parameterssame (loop gain ≈ 150). The beam loading effect and themicrophonics is almost compensated by "P+DOB" control
except in the head and end of the beam current. The main

[3] C. Schmidt, Ph.D. thesis, Technische Universität HamburgHarburg, 2010.
[4] Bristow, Douglas A et al., “A survey of iterative learning control”, IEEE Control Systems 26.3 (2006): 96-114.
[5] Shu-Wen Yu, Ph.D. thesis, University of California, Berkeley ,2011.
[6] H. Hayano, “Superconducting accelerator sevelopment at STFfor ILC”, in Proc. 12th Annual Meeting of Particle Accelerator
Society of Japan, Tsuruga, Japan, Aug. 2015, pp. 164–168.
[7] M. Uchiyama, “Formation of high speed motion pattern ofmechanical arm by trial”, in Trans. Soc. Instrument Contr.
Engineers, vol. 14, no. 6, pp.706-712, 1978.
[8] K. Ohishi,“Microprocessor controlled dc motor for load insensitive position servo system”, in IEEE Trans. Ind. Electron,
Vol. 34, pp.44-49,1987.
[9] Tomasz Czarski et al., “ TESLA cavity modeling and digital implementation in FPGA technology for control systemdevelopment”, in NIMA, 548(3) (2005)