In active magnetic bearing (AMB) systems, stability is the most important factor for reliable operation. Rotor positions in radial direction are regulated by four-axis control in AMB, i.e., a radial system is to be treated as a multi-input multioutput (MIMO) system. One of the general indices representing the stability of a MIMO system is “maximum singular value” of a sensitivity function matrix, which needs full matrix elements for calculation. On the other hand, ISO 14839-3 employs “maximum gain” of the diagonal elements. In this concept, each control axis is considered as an independent single-input single-output (SISO) system and thus the stability indices can be determined with just four sensitivity functions. This paper discusses the stability indices using sensitivity functions as SISO systems with parallel/conical mode treatment and/or side-by-side treatment, and as a MIMO system with using maximum singular value; the paper also highlights the differences among these approaches. In addition, a conversion from usual xy axis form to forward/backward form is proposed, and the stability is evaluated in its converted form. For experimental demonstration, a test rig diverted from a high-speed compressor was used. The transfer functions were measured by exciting the control circuits with swept signals at rotor standstill and at its 30,000 revolutions/min rotational speed. For stability limit evaluation, the control loop gains were increased in one case, and in another case phase lags were inserted in the controller to lead the system close to unstable intentionally. In this experiment, the side-by-side assessment, which conforms to the ISO standard, indicates the least sensitive results, but the difference from the other assessments are not so great as to lead to inadequate evaluations. Converting the transfer functions to the forward/backward form decouples the mixed peaks due to gyroscopic effect in bode plot at rotation and gives much closer assessment to maximum singular value assessment. If large phase lags are inserted into the controller, the second bending mode is destabilized, but the sensitivity functions do not catch this instability. The ISO standard can be used practically in determining the stability of the AMB system, nevertheless it must be borne in mind that the sensitivity functions do not always highlight the instability in bending modes.

1.
Kanemitsu
,
Y.
,
et al.
, 1996, “
Japanese Proposal for International Standardization for Active Magnetic Bearing
,”
Proceedings 5th International Symposium on Magnetic Bearings
,
Kanazawa, Japan, August, pp.
265
270
.
2.
Matsushita
,
O.
,
Kanemitsu
,
Y.
,
Azuma
,
T.
, and
Fukushima
,
Y.
, 2000, “
Vibration Criteria Considered From Case Studies of Active Magnetic Bearing Equipped Rotating Machines
,”
Int. J. Rotating Mach.
1023-621X,
6
(
1
), pp.
67
78
.
3.
International Standard Organization
, 2004, “
Mechanical Vibration - Vibration of Rotating Machinery Equipped With Active Magnetic Bearings - Part 2: Evaluation of Vibration
,” ISO 14839-2.
4.
International Standard Organization
, 2006, “
Mechanical Vibration - Vibration of Rotating Machinery Equipped With Active Magnetic Bearings-Part 3: Evaluation of Stability Margin
,” ISO 14839-3.
5.
Ito
,
M.
,
Fujiwara
,
H.
,
Takahashi
,
N.
, and
Matsushita
,
O.
, 2004, “
Evaluation of Stability Margin of Active Magnetic Bearing Control System Combined With Several Filters
,”
Proceedings 9th International Symposium on Magnetic Bearings
,
Lexington, KY, August.
6.
Boyd
,
S. P.
, and
Barratt
,
C. H.
, 1991,
Linear Controller Design: Limits of Performance
,
Prentice-Hall, International
, Englewood Cliffs, NJ, pp.
110
112
.
7.
Fujiwara
,
H.
,
Takahashi
,
N.
,
Ito
,
M.
, and
Matsushita
,
O.
, 2005, “
Evaluation of Stability Margin of Active Magnetic Bearing Rotors Using Sensitivity Function
,”
Proceedings 3rd International Symposium on Stability Control of Rotating Machinery
,
Cleveland, OH, September.
You do not currently have access to this content.