This paper explains the control scheme that is to be used in the magnetic suspension mass comparator (MSMC), an instrument designed to directly compare mass artifacts in air to those in vacuum, at the United States National Institute of Standards and Technology. More specifically, the control system is used to apply a magnetic force between two chambers to magnetically suspend the mass artifacts, which allows for a direct comparison (i.e., a calibration) between the mass held in air and a mass held in vacuum. Previous control efforts that have been demonstrated on a proof-of-concept (POC) of this system utilized proportional-integral-derivative (PID)-based control with measurements of the magnetic field as the control signal. Here, we implement state-feedback control using a laser interferometric displacement measurement with a noise floor of approximately 5 nm (root-mean-square). One of the unique features and main challenges in this system is that, in order to achieve the necessary accuracy (relative uncertainty of 20 × 10−9 in the MSMC), the magnetic suspension must not impose appreciable lateral forces or moments. Therefore, in this design, a single magnetic actuator is used to generate a suspension force in the vertical direction, while gravity and the symmetry of the magnetic field provide the lateral restoring forces. The combined optical measurement and state-feedback control strategy presented here demonstrate an improvement over the previously reported results with magnetic field measurements and a PID-based control scheme.

References

1.
Jabbour
,
Z. J.
, and
Yaniv
,
S. L.
,
2001
, “
The Kilogram and Measurements of Mass and Force
,”
J. Res. Natl. Inst. Standards Technol.
,
106
(
1
), pp.
25
46
.
2.
Dushamna, S., and Lafferty, J. M.,
1962
, “
Scientific Foundations of Vacuum Technique
,”
Am. J. Phys.
,
30
(
8
), pp.
612
612
.
3.
Nater
,
R.
,
Reichmuth
,
A.
,
Schwartz
,
R.
,
Borys
,
M.
, and
Zervos
,
P.
,
2009
,
Dictionary of Weighing Terms
,
Springer
, Berlin.
4.
Picard
,
A.
,
Davis
,
R.
,
Gläser
,
M.
, and
Fujii
,
K.
,
2008
, “
Revised Formula for the Density of Moist Air (Cipm-2007)
,”
Metrologia
,
45
(
2
), pp.
149
155
.
5.
Newell
,
D. B.
,
2014
, “
A More Fundamental International System of Units
,”
Phys. Today
,
67
(
7
), pp.
35
41
.
6.
Mulhern
,
E.
, and
Stambaugh
,
C.
,
2016
, “
Characterization of the NIST Magnetic Suspension Mass Comparator Facility
,”
NCSLI Measure
,
11
(3–4), pp. 58–62.
7.
Mizushima
,
S.
,
Ueda
,
K.
,
Ooiwa
,
A.
, and
Fujii
,
K.
,
2015
, “
Determination of the Amount of Physical Adsorption of Water Vapour on Platinum–Iridium Surfaces
,”
Metrologia
,
52
(
4
), p.
522
.
8.
Davidson
,
S.
,
Berry
,
J.
,
Abbott
,
P.
,
Marti
,
K.
,
Green
,
R.
,
Malengo
,
A.
, and
Nielsen
,
L.
,
2016
, “
Air–Vacuum Transfer; Establishing Traceability to the New Kilogram
,”
Metrologia
,
53
(
5
), p.
A95
.
9.
Davidson
,
S.
,
2010
, “
Determination of the Effect of Transfer Between Vacuum and Air on Mass Standards of Platinum–Iridium and Stainless Steel
,”
Metrologia
,
47
(
4
), p.
487
.
10.
Jabbour
,
Z.
,
Abbott
,
P. J.
,
Liu
,
R.
, and
Williams
,
E.
,
2009
, “
A Magnetic Levitation Technique for the Simultaneous Comparison of Mass Artifacts in Air and Vacuum
,”
IEEE Trans. Instrum. Meas.
,
58
(
4
), pp.
878
883
.
11.
Benck
,
E. C.
,
Stambaugh
,
C.
,
Mulhern
,
E.
,
Abbott
,
P.
, and
Kubarych
,
Z.
,
2017
, “
Progress on Vacuum-to-Air Mass Calibration System Using Magnetic Suspension to Disseminate the Planck-Constant Realized Kilogram
,”
ACTA IMEKO
,
6
(
2
), pp.
70
74
.
12.
Stambaugh
,
C.
, and
Mulhern
,
E.
,
2016
, “
An FEM Analysis of the Magnetic Felds in the Magnetic Suspension Mass Comparator at NIST
,”
NCSLI Measure
,
11
(3–4), pp. 63–68.
13.
Beams
,
J. W.
,
Hulburt
,
C.
,
Lotz
,
W.
, Jr.
, and
Montague Jr
,
R.
,
1955
, “
Magnetic Suspension Balance
,”
Rev. Sci. Instrum.
,
26
(
12
), pp.
1181
1185
.
14.
Haynes
,
W. M.
, and
Stewart
,
J. W.
,
1971
, “
A Magnetic Densimeter for Low Temperatures and High Pressures
,”
Rev. Sci. Instrum.
,
42
(
8
), pp.
1142
1150
.
15.
Masui
,
R.
,
Haynes
,
W. M.
,
Chang
,
R. F.
,
Davis
,
H. A.
, and
Sengers
,
J. M. H. L.
,
1984
, “
Densimetry in Compressed Fluids by Combining Hydrostatic Weighing and Magnetic Levitation
,”
Rev. Sci. Instrum.
,
55
(
7
), pp.
1132
1142
.
16.
Fujii
,
K.
,
2004
, “
Present State of the Solid and Liquid Density Standards
,”
Metrologia
,
41
(
2
), p.
S1
.
17.
Wagner
,
W.
, and
Kleinrahm
,
R.
,
2004
, “
Densimeters for Very Accurate Density Measurements of Fluids Over Large Ranges of Temperature, Pressure, and Density
,”
Metrologia
,
41
(
2
), p.
S24
.
18.
McLinden
,
M. O.
,
Kleinrahm
,
R.
, and
Wagner
,
W.
,
2007
, “
Force Transmission Errors in Magnetic Suspension Densimeters
,”
Int. J. Thermophys.
,
28
(
2
), pp.
429
448
.
19.
Schoonover
,
R. M.
,
1982
, “
A Look at the Electronic Analytical Balance
,”
Anal. Chem.
,
54
(
8
), pp.
973A
980A
.
20.
Clark
,
J. W.
,
1947
, “
An Electronic Analytical Balance
,”
Rev. Sci. Instrum.
,
18
(
12
), pp.
915
918
.
21.
Beams
,
J.
,
1950
, “
Magnetic Suspension Balance
,”
Phys. Rev.
,
78
(
4
), p.
471
.
22.
Gu
,
J.
,
Kim
,
W-J.
, and
Verma
,
S.
,
2005
, “
Nanoscale Motion Control With a Compact Minimum-Actuator Magnetic Levitator
,”
ASME J. Dyn. Syst., Meas., Control
,
127
(
3
), pp.
433
442
.
23.
Trumper
,
D. L.
,
1990
, “
Magnetic Suspension Techniques for Precision Motion Control
,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA.
24.
Kim
,
W.-J.
, and
Trumper
,
D. L.
,
1998
, “
High-Precision Magnetic Levitation Stage for Photolithography
,”
Precis. Eng.
,
22
(
2
), pp.
66
77
.
25.
Stambaugh
,
C.
,
2017
, “
The Control System for the Magnetic Suspension Comparator System for Vacuum-to-Air Mass Dissemination
,”
ACTA IMEKO
,
6
(
2
), pp.
75
79
.
26.
MATLAB
,
2016
,
Version R2016a
,
The MathWorks
,
Natick, MA
.
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