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L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 1 / 27
Digital Signal Processing Approaches
for Varying Magnetic Field Measurements through a
Rotating Coils SystemL. Angrisani, R. Schiano Lo
Moriello L. Bottura, A. Masi
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 2 / 27
Outline Introductive notes Limitations of the standard Fourier analysis in
the presence of analog bucking Proposals:
Quadrature demodulation-based method Extrapolation-based method
Performance comparison in simulated conditions
Results in actual experiments Conclusions
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 3 / 27
Introduction
In superconducting magnets, dynamic effects like snapback can be estimated only through measurements in ramping conditions.
Due to current variation, field harmonics are both time and ramp rate dependent (e.g. decay phenomena).
The conventional Fourier analysis does not work properly. Being addressed to DC measurements, it assumes field harmonics to be constant during a coil turn.
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 4 / 27
Introduction
Increasing coil speed is often impracticable, and it could prove unsuccessful in the presence of high ramp rates of the current.
To measure varying magnetic fields through a rotating coils system, two new digital signal-processing methods are proposed.
They both assume continuous coil rotation.
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 5 / 27
The standard Fourier analysis
1,..,1,2
NiiNi
Magnetic flux as a function of the
angular position
Integration of Vcoil in the angular domain
Constant during a coil turn
Field Harmonics
][ DFT
15
11
)exp(Re)(n
nref
nn jnR
CK
1
12
nn
nref
n K
R
NC
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 6 / 27
Problems with the standard Fourier analysis
A periodic, magnetic flux characterized by constant envelope…..
0 5 10 15 20 25 30
10-15
10-10
10-5
100
Field harmonic order
Fiel
d ha
rmon
ic a
mpl
itude
[T
]T0;T0
T10BT;10;T1
)cos()(
42
55
331
5
1
BB
BB
nBkΦn
n
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 7 / 27
0 5 10 15 20 25 30
10-15
10-10
10-5
100
Field harmonic order
Fiel
d ha
rmon
ic a
mpl
itude
[T
]
The envelope of the main component (fundamental) increases linearly with the angular position, B3 and B5 being constant …..
T0;T0
T10T;10
T)1π20
()(
42
55
33
1
BB
BB
B
Imposed values
DFT results
Problems with the standard Fourier analysis
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 8 / 27
Hardware solution: analog bucking
0 5 10 15 20 25 30
10-20
10-15
10-10
10-5
Field harmonic order
Fiel
d ha
rmon
ic a
mpl
itude
[T
]
Problems with the standard Fourier analysis
Measurement problems with B5
still survive.
Measurement problems with B3
still survive.
0;0
T10T;10
T10)1π20
()(
42
65
53
31
BB
BB
B
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 9 / 27
Standard Fourier analysis characterization
LHC Cycle
Typical test current evolution
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 10 / 27
Standard Fourier analysis characterization
Raw DataCn(t)
Flux samples()
Cn expectedinstantaneous
Cn estimatedHarmonic
coefficients
Instantaneous vs. each turn
Average
Bn(t) An(t)
Best EstimatorsBn_avg and An_avg
For each turn
Absolute and relative errors|Bn-Bn_avg|
|Bn-Bn_avg|/Bn_avg|An-An_avg|
|An-An_avg|/An_avg
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 11 / 27
Standard Fourier analysis characterization
Difference greater than 1 unit for a 10A/s linear
ramp
4000 5000 6000 7000 8000 9000 10000 110000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8x 10
-3
R=10A/s
R=20A/s
R=30A/s
Absolute difference for B1
Current [A]
Ab
s(B
1-B
1 avg
)
[T
]
R=40A/s
R=50A/s
R=60A/s
R=70A/s
R=80A/s
R=90A/s
R=100A/s
Linear ramp: different ramp rates have been simulated
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 12 / 27
Standard Fourier analysis characterization
0 10 20 30 400
1
2
3
4
5x 10-5
Number of coil turns
abs[
(B1-
B1a
vg)
[T
]
B1
0 10 20 30 400
0.2
0.4
0.6
0.8
1x 10 -4
Number of coil turns
abs[
(B3-
B3a
vg)
[T
]
B3
Parabolic ramp
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 13 / 27
Standard Fourier analysis characterization
0 10 20 30 400
0.2
0.4
0.6
0.8
1
1.2x 10
-4
Number of coil turns
abs[
(B1-
B1a
vg)
[T
]
B1
0 10 20 30 400
0.5
1
1.5
2
2.5
3x 10 -4
Number of coil turns
abs[
(B3-
B3a
vg)
[T
]
B3
Exponential ramp
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 14 / 27
Proposal 1: quadrature demodulation-based method
Ф(t)
sin(2πft)
FIR
FIR
tg-1
x2
Unwrap
Phase
Modulus
cos(2πft)
)1(Kn
( )2
( )2
0 0.05 0.1 0.15 0.2
-300
-250
-200
-150
-100
-50
0
50FIR filter frequency response
Frequency [Hz]
Am
plitu
de
[dB
]
1800 2000 2200 2400
-2
-1
0
1
2
3
Time [s]
[Wb]
Magnetic flux and its envelope
Magnetic fluxFlux envelope
Residual C1 evaluation: digital bucking
Quadrature demodulation scheme
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 15 / 27
Sliding window FFT
Overlap ratio:
Flux samples()
I-Q Demodulation
Flux samples reconstruction
C2...C15=0
B1 estimation
STFT
STFT
+
-
Compensated Cn
Proposal 1: quadrature demodulation-based method
1N
N
1724 1734 1744 1754 1764 1774
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time [s]
Mag
neti
c fl
ux [
Wb]
Standard analysis
N points window
one sample
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 16 / 27
Proposal 1: typical results
Difference () between estimated and nominal
evolution of B1.
Comparison of the nominal evolution of B3 (green) to those
obtained through STFT (red) and demodulation+STFT (violet).
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 17 / 27
Proposal 2 : extrapolation-based method
For each angular position, the flux samples (red dots) acquired in the last four coil turns are used to extrapolate the flux samples related to the next turn for different sampling times (black dots).
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 18 / 27
Proposal 2 : extrapolation-based method
Time [s]
Mag
neti
c fl
ux
[Wb]
Time [s]Angle [rad]
Mag
netic
flu
x [
Wb]
Magnetic flux extrapolation
extrapolated flux samples
4 samples buffer
intersection plane
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 19 / 27
Performance comparison: linear ramp
( )2
1
1 N
n nn
Absolute RMS error X XN
10
20
30
40
50
1,00E-05
1,00E-04
1,00E-03
1,00E-02
Absolute
RMS error
[T]
Ramp Rate [A/s]
B1
Standard analysis
STFT
Extrapolation
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 20 / 27
Performance comparison: linear ramp
B5
B3
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 21 / 27
Performance comparison: parabolic ramp
B1-B7
A1-A8
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 22 / 27
Performance comparison: exponential ramp
B1-B7
A1-A8
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 23 / 27
Proposal 2: experimental results
Some measurements have been carried out on a reference, resistive magnetic dipole.
Continuous coil rotation has been assured.
Coil speed has been equal to 1 turn/s.
Different ramp rates have been considered: 5A/s, 10A/s, 20A/s.
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 24 / 27
Proposal 2: experimental results
As expected for the reference magnet measured, the first results seem to highlight that harmonic coefficients are independent of ramp rate.
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 25 / 27
Comparison
Blue trace: proposal 1
Black trace: proposal 2
The evolution versus time of harmonic coefficients gained from proposal 2 result smoother than those from proposal 1.
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 26 / 27
Conclusions Characterization of the standard Fourier analysis when
applied to compensated magnetic fluxes in non-stationary conditions.
A quadrature demodulation-based method for a reliable digital bucking has been proposed (proposal 1).
Harmonic coefficients are gained from the application of the standard Fourier analysis to digitally compensated flux samples.
An alternative method that extrapolates, for a given time instant, the flux value for each angular position in a coil turn has also been presented (proposal 2).
L.AngrisaniUniversity of Naples Federico II, ITALY
angrisan@unina.it
14th International Magnetic Measurement Workshop26-29 September 2005, Geneva, Switzerland 27 / 27
Conclusions Many tests in simulated dynamic conditions have been carried
out to assess and compare the performance of the proposed methods.
Proposal 1 allows more accurate estimate of harmonic coefficients, but B1, than that granted by standard Fourier analysis.
Proposal 2 performs much better even in the presence of high ramp rates.
The reduced computational burden of proposal 2 make real-time tracking of harmonic coefficients feasible.
The first results obtained in actual experiments seem to confirm the reliability of proposal 2.