RIKEN Accel. Prog. Rep. 50 (2017)

Ⅱ-9. Instrumentation

Development of control system for magnetic ﬁeld of the BigRIPS
separator with a feedback algorithm
Y. Shimizu∗1 D.S. Ahn,∗1 N. Fukuda,∗1 N. Inabe,∗1 K. Kusaka,∗1 M. Ohtake,∗1 H. Suzuki,∗1 H. Takeda,∗1Y. Yanagisawa,∗1 and K. Yoshida∗1

In = In−1 + ΔIn ,ΔIn = − KP (Bn − Bn−1 ) + KI ΔTn (Sn − Bn )KD(Bn − 2Bn−1 + Bn−2 ),−ΔTn

6.93 Tm → 7.00 Tm
7.07 Tm → 7.00 Tm

Bρ deviation (Tm)

0.06
0.04
0.02
0-0.02
-0.04
-0.06
-0.08
050

100150200

250300350Time (sec)
1 ×10
0.8
0.6
0.4
0.2
0-0.2
-0.4
-0.6
-0.8
-10-3

6.93 Tm → 7.00 Tm
7.07 Tm → 7.00 Tm+5×10-4 Tm+1×10-4 Tm−1×10-4 Tm−5×10-4 Tm

50

100

150200

250

300

350

Time (sec)where ΔTi is the sampling time, Si is the preset Bρ
value, and Bi is the measured Bρ value in the ith sampling. KP , KI , and KD , all non-negative, denote theparameters of the PID feedback algorithm corresponding to the proportional, integral, and derivative components, respectively. Note that the integral action
only responds to changes in the preset Bρ value because the proportional and derivative actions produce
a large unwanted spike when the preset Bρ value ischanged.3)
The magnetic ﬁeld is required to be changed andstabilized so that the position of the central particle in
the focal plane is set within 0.0±0.5 mm in 3 min. The
0.5 mm at the 5th focal plane of the BigRIPS separator corresponds to 6 × 10−4 Tm at 4 Tm. Thereforethe values of the parameters KP , KI , and KD were
optimized such that the magnetic ﬁeld is changed andstabilized within ±5 × 10−4 Tm in 3 min.
Figure 1 shows typical magnetic-ﬁeld responses ofthe 2nd dipole magnet of the BigRIPS separator asfunctions of time. The red and blue solid lines show
the results changed from 6.93 Tm and 7.07 Tm to7.00 Tm. Some overshoots remained because an NMR
probe could not work owing to a rapid change of magnetic ﬁeld in the beginning when the preset Bρ value∗10.08Bρ deviation (Tm)We have designed and constructed a new control
system for magnetic ﬁeld of the BigRIPS separator1)
at RIKEN. The absolute Bρ value was derived fromthe magnetic ﬁeld of a dipole magnet measured withan NMR probe and the central trajectory radius of
the dipole magnet determined from the magnetic-ﬁeldmap.2) A new control system has been designed to satisfy zero deviation between the preset and measured
Bρ values. Furthermore, the control system is required to show not only high stability but also highreproducibility within a reasonably short time, since
the settings of the BigRIPS separator are frequently
changed during an experiment.
In order to enhance the reproducibility of the Bρ
value of the dipole magnet, a new control system wasdesigned with a proportional-integral-derivative (PID)
algorithm.3) The output current In of the power supply
after the nth sampling is given by

RIKEN Nishina Center- 206 -Fig. 1. Typical magnetic-ﬁeld responses of the 2nd dipole
magnet of the BigRIPS separator as functions of time.
The bottom panel shows the plots enlarged around ±1×10−3 Tm.

was changed. However, they were negligibly small in
the BigRIPS tuning. The bottom panel of Fig. 1 shows
the plots enlarged around ±1 × 10−3 Tm. Dashed anddotted lines show the values of ±5 × 10−4 Tm and±1 × 10−4 Tm, respectively. The PID feedback system
successfully functions, and the magnetic ﬁeld is stabilized in 2.5 min within ±5×10−4 Tm. The ﬂuctuationsof the magnetic ﬁelds are limited within ±1×10−4 Tmafter 4 min.
A new control system for the magnetic ﬁeld of theBigRIPS separator with a PID feedback algorithm iscurrently operational well.
References
1) T. Kubo et al., Nucl. Instr. Meth. B 204, 97 (2003).
2) Y. Yanagisawa et al., RIKEN Accel. Prog. Rep. 41, 125(2008).
3) T. Kitamori, Journal of The Society of Instrument andControl Engineers, 19(4), 382 (1980).