J. Plasma Fusion Res. SERIES, Vol. 5 (2002) 463466

Gurrent Gontrol System for Superconducting
Coils of LHD
CHIKARAISHI Hirotaka, TAKAMI Shigeyuki, INOUE Tomoyuki, SATOW Takashi,
ISE Toshihumir and LHD Experimental Group
National Institute for Fusion Science, Toki 509-5292, Japan
lOsaka University, Suita, Osaka 565-0871, Japan(Received: ll December 2OO1 | Accepted: l7 May 2OO2)

Abstract
The LHD has six sets of large-scale superconducting coils and six dc power supplies to charge them.

For the current controllers of these power supplies, high accuracy of current control, fast response androbustness of system are required. This paper, therefore, describes the current control system for the LHD
dc power supplies. First, the outline of the power system is presented, and then, the current controllers for
the LHD are described. Finally, experimental results are presented and discussed in case ofcoil excitation
using these control systems. The results show the various characteristics for each control system andindicate it possible to control the system according to the requirements from a plasma experiment.

Keywords:
current control, Hrc control, inductance matrix, parameter estimation, superconducting coil, state variable

1. lntroduction

LHD superconducting coil has a current sensor and aThe LHD has twelve superconducting coils and six

local feedback loop, which control the actual voltage totrack the calculated voltage reference. With this local
loop, the error such as a voltage drop in the circuit or achange in line voltage is compensated, in order for thepower supply to work as an ideal controlled voltage
source. In the computer system to control all power
supplies, the current control scheme is described withstate vector as following:

dc power supplies to excite them.For these power
supplies, the following conditions were required; thesteady state c<lntrol error is less than 0.0l%o of the set
value, the current settling time for O.lvo of control error
is less than I second and the control system must be

robust against turbulence caused by the plasma
experiments. To resolve these requirements, somecontrol systems are studied, designed and tested.
In the following sections, the outline of the control
system for power supplies is introduced at first. Next,
the estimation of circuit parameters is described. Finally,#'"= A"'x"+"" l;:the controller design and experimental results areul= c"."".

presented.

2. Outline of the Power System". [;:

(1)

(2)

where .r" is a state vector, A., 8", C" and D" are thematrix of the control gains. f , l" and oj demote the cur-

Each power supplies are controlled by the computer
system shown as this figure. Each power supply for the@2O02 by The Japan Society of Plasma
C o rr e sp ondin g autho r' s e - mai I : hc hikara @ lhd. nifs. ac.j p

Science and Nuclear Fusion Research463

Chikaraishi H. et al., Current Control System for Superconducting Coils of LHD

rent reference, the actual coil current and the output

4. Pl Controller

voltage reference, respectively.

First, the P1 control scheme is designed for thissystem based on the state variables. Although thiscontrol scheme is simple, it has adequate performancefor the steady state current control. The current regulator
used in this system is formed as follows;

3. Parameter Estimation of Coil System
In the design of a control system, the electricalparameters of the superconducting coil system arerequired to determine the control gains mentioned

fat = kR" lQ: - i")dt + kL"(it - i")above. To estimate them, the inductance 2." wasmeasured from the coil terminals for all coils in various(3)

where L" is inductance matrix of the superconducting
coils, R" is resistance, and ft is the scalar control gain.

frequency. Figure I shows some frequency response ofthe self and mutual inductances. In this figure, HO, HM,HI. OV. IS and IV mean three helical coils and threepoloidal coils, respectively. The measured value is

From the equations, the control matrix in Equation (l)and (2) are evaluated as follows;

plotted in the figure. The lines show the results
calculated by a circuit model introduced later. To;

A"= 0, B"=?,1

describe this frequency response, we assumed that thecoil system has four coupled circuits to treat the induced

L"0C"= kR", D"= kcurrent flowing in the structural material. We
determined the circuit parameters by fitting to themeasured inductance as shown in Table I [2]. In thetable, Cl, C2, C3 and C4 are coupled circuits.

o -L"where U is a unit matrix. The step response of the coilcurrent is as following;l" = 1"6 * (l - e't') (rJ - lo)+ HOHO--o- HMHOHIHO-F+ OVHO--.- ISHOo"oao"U-where t = l/k is a characteristic time constant, i"6 is an

initial value of 1". From this equation, it is clear that theevery coil current has the same response and the balanceof the coil cunents are kept during the transient.
The control gain ft deciding the system response
has upper limit decided by the stability. This limit isdetermined due to the control theory as k < 2ttf.l4,
where /l is a cut-off frequency of a low pass filter
inserted to reduce noise.In the LHD power system, thef,

EJ

1oo

102

is selected as 0.87 Hz, therefore the upper limit of k
f tHzl 1o2

becomes 1.3.

The P control scheme is obtained by setting of R" =0 in the equation (3). In this P control, the steady stateFig. 1 Frequency response of inductance for LHD super-conducting coils.

Table 1 Estimated parameters of superconducting coil system of LHDa) Coil inductance matrix l,[HjHOHMHIOVNryc1C2c3C4@)

HOHMHIOVISIVClC2C3
1.206 t.052 0.466 0.355 0.231
t.2M
1.279 1.156 0.4& 0.335 0.238
1.049
1.154 t.2ffi 0.462 0.325 0.238
0.458
0.456 0.455 1.258 0.285 0.144
o.329
0.329 0.329 0.284 0.953 0.25r
o.233
0.233 0.234 o.t42 0.250 0.744
0.875
0.858 0.767
000000
0.840 0.550 0.430
0.706
0.692 0.657000000
0.485 001.343

464

0.874 0.648
0.858 0.96
0.767 0.611
0.670 0.840
0.405 0.550
0.278 0.453

100l0000

0.706 4.24
0.692 4.240.657 4.21-0.140 0.485

0000
00t00-o.15-o.15

Chikaraishi H. et al., Current Control System for Superconducting Coils of LHD

f able 2 Comparison of the current control system

Size of .r"

6Numbers of parameters

84PPI
k=0.1 ft=0.1
6t2338684156

Steady state control error

0.lVo

O.0lVo <O.OlVo <O.0lVo <O.0lVo

Response time constant

10sControl schemeP

t=0.1lsls

H-(1)H*(2)

t't55

9,016

<0.3s

<0.3s

control error ie = it - i" remains as following;i"= (kL")-t .R" . iJ(s)In this system, L may become about 0.01% of lj when ft= 1.0 because the orders of R" and L" are 10-a and 1,respectively.

Table 2 shows the system size and somecharacteristic parameters for each control system. Thel1-(1) and l1o(2) controllers are described later. When

890

900 t

[r]

910

we use the P control, ft = I is necessary to satisfy therequirements for control effor and response time asshown in the table. Figure 2 shows a ramp response of
the P controller with ft = 1. In this figure, the HO
current reference is swept and the other current
references are kept constant. The HO current traces its
reference with I s delay and the disturbance of the other92O

Fig. 2 Ramp response of the power supply when P controller with k= 1 is applied.

111

currents are less than 24. With this result, the\t\Q)independent cunent control for each coils are confirmed.

ltC)

For the P1 controller, a similar result is observed.
Figure 3 shows the reaction caused by the plasma

I11ri961950

961 900

850

current when the P controller with k = 0.1 is used. In
this figure, the reaction is observed only on HI coilbecause the fast changing of the magnetic flux is shieldby the HI coil current. For the P controller with ft = 1.0
and PI controller, the experiments with a plasma are not

Fig. 3 Reaction caused by a plasma current. Pcontroller
with k= 0.1 is used.

executed yet.

5. H- Gontroller
In the PI controller mentioned above, the control
gain is limited by the stability requirement, which means
the response time constant cannot become so small. The--H€r -; -;!_o,-/1- design scheme is one of the solutions to managel

both the robustness and fast response. We designed two
types of F1- controller for the LHD power system [3].
One, aiming H*(2), realizes the robustness and fastresponse, but its size is large as shown in Table 2. The
other, aiming H*(l), is compact rather than the former
one. These controllers realize the high accuracy and thefast response for the current control as shown in TableI'rtel. oI-Ft -r- r\,-i\OEEi

2150230$1M-l50260
t [s] 50250
Fig. 4 Ramp response of the power supply when F/".(1)control is applied.

2. Figure 4 shows a ramp response of the I1-(1)5O24Ocontroller. For the f/-(2) controller, a similar response
is observed. When this figure is compared with Fig. 3, it465

Chikaraishi H. et al., Current Control System for Superconducting Coils of LHD

6. Summaryis clear that the F1- control realizes the better responsethan P or P.I controller. Figure 5 shows the reaction
caused by a plasma current with the F1-(l) control. ThisThis paper describes the current control system inthe LHD dc power system. To design the current

figure shows that the shielding effect by HI coilcontroller, the electrical parameters of the coil systemare estimated and some types of the controllers arebecomes weak, because the control response is much
faster than the P control. For the f1o(2) controller, theplasma experiments is not executed yet.

designed. The test results show that these controllers arestable and satisfied requirements. The reaction causedby the plasma current is different for each controlsystem, and the effect of different control response to
the plasma characteristics will be studied.

61cEOlr,*...

-HOHM

References
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HI1245-1256 (1999).

$#*

t21 H. Chikaraishi et al., lTth International conf. on

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t3l T. Ise er al., PESC 96 Record.2Tth Annual IEEE

Power Electronics Specialists Conf., pp. 1099-2640 tlsl 2660

2680

1Fig. 5 Reaction caused by a plasma current. H-(1) control is applied.

466

104 (1996).