An Air-Gap-Flux-Oriented Vector Controller For Stable Operation of Bearingless Induction Motors
An Air-Gap-Flux-Oriented Vector Controller For Stable Operation of Bearingless Induction Motors
Abstract—A bearingless induction machine has combined the strong flux distribution of a revolving magnetic field in
characteristics of an induction motor and magnetic bearings. It is the air gap between the stator and rotor [6], [7]. Thus, the
known that the magnetic suspension of the rotor becomes unstable information of the instantaneous orientation and amplitude of
at over load operation, particularly in transient conditions.
A novel air-gap-flux-oriented vector control scheme has been the revolving magnetic field is required in a controller of the
proposed to operate the bearingless induction motor during the bearingless motors. If there is an error in the field orientation,
high torque acceleration period. It has been found that there is an for example, the direction of a generated radial force has twice
optimal flux orientation for complete decoupling in radial force the angle error with respect to the radial force reference. If
generation. Test results in a laboratory bearingless induction correct amplitude and orientation of the revolving magnetic
motor validates the performance efficacy of proposed controller
at overload conditions. field are obtained in the controller, then the generated radial
force corresponds to the radial force reference in both direction
Index Terms—Bearingless motor, magnetic bearing, vector and amplitude. Thus, the vector control of the bearingless
control.
induction motor is necessary.
A direct field-oriented controller for induction-type bearing-
I. INTRODUCTION less motors was proposed [8]. On the other hand, an indirect
field-oriented controller has been proposed by the authors [9],
M AGNETIC bearings have been used in machine tools,
turbo-molecular pumps, compressors, blowers, com-
pact generators, and flywheels [1]–[4]. However, conventional
[10]. Successful operations in loaded conditions as well as tran-
sient conditions have been shown up to the rated values. It has
magnetic bearings have significant dimensions, and require a been experimentally learned that the magnetic suspension be-
number of windings as well as many single-phase inverters. comes stable with a slight increase in the reference value of rotor
resistance [10]. The increase in the results in the fact that
Bearingless motors, i.e., a hybrid of electrical motor and
an air-gap flux vector , rather than a rotor flux vector , is
magnetic bearings, have been expected to reduce dimensions,
aligned to a flux reference which is generated in the con-
number of inverters and associated cost. In induction-type
troller as a feedforward flux reference. The increase in is
bearingless motors, it was shown that only 0.0056 times of
not effective in overload operation in transient conditions. The
a motor VA is required for radial force control windings [5].
magnetic suspension becomes unstable during high torque ac-
This result indicates possible cost reduction in a bearingless
celeration because of significant variations in with respect
induction motor.
to . This fact suggests an application of air-gap-flux-oriented
In the radial positioning of the bearingless motors, radial
vector controller for the bearingless induction motor [11], [12].
forces are generated based on the feedback signals of radial
In this paper, an air-gap-flux-oriented vector controller has
displacement sensors detecting the movements of the rotor
been built. Successful operation at twice the rated torque current
shafts. The radial forces are generated taking advantage of
is shown experimentally. In addition, a universal field-oriented
controller is also applied to realize perfect decoupling of radial
Paper IPCSD 99–108, presented at the 1999 Industry Applications Society forces in two perpendicular axes. It is found that better perfor-
Annual Meeting, Phoenix, AZ, October 3–7, and approved for publication in
the IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS by the Electric Machines mance can be obtained with a slight lead angle in flux vector
Committee of the IEEE Industry Applications Society. Manuscript submitted rather than . The reasons for this fact are discussed.
for review June 1, 1999 and released for publication February 24, 2000. This
work was supported by the Ministry of Education, Science and Culture through
a Grant-in-Aid for Scientific Research. II. SYSTEM CONFIGURATION
T. Suzuki and A. Chiba are with the Department of Electrical Engi-
neering, Science University of Tokyo, Chiba 278-8510, Japan (e-mail:
A. Principle of Radial Force Generation
j7399621@ed.noda.sut.ac.jp; chiba@ee.noda.sut.ac.jp). The basic winding configurations of an induction-type bear-
M. A. Rahman is with the Faculty of Engineering and Applied Science,
Memorial University of Newfoundland, St. John’s, NF A1B 3X5 Canada ingless motor are shown in Fig. 1. Two sets of three-phase wind-
(e-mail: rahman@engr.mun.ca). ings are wound in the same stator slots. One is the four-pole
T. Fukao is with the Department of Electrical and Electronic Engi- windings for the production of motoring torque. It is called the
neering, Tokyo Insititute of Technology, Tokyo 152-8552, Japan (e-mail:
tfukao@ee.titech.ac.jp). motor winding. The other is the two-pole windings for con-
Publisher Item Identifier S 0093-9994(00)04775-7. trolling the rotor radial position in the air gap. This is referred
0093–9994/00$10.00 © 2000 IEEE
1070 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 36, NO. 4, JULY/AUGUST 2000
(1)
1072 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 36, NO. 4, JULY/AUGUST 2000
The air-gap flux is given as By dividing the right-hand side of equation (11) by , one
obtains
(4)
(5)
(13)
Stator current and slip speed are determined as follows.
When it is assumed that an air-gap flux is perfectly aligned
with the axis, (5) reduces to Similarly, using (2), (3), (7), and (9) one can obtain the fol-
lowing expression:
(6)
(14)
and using (5) and (6), one can write
By dividing both sides of (14) by , the expression for ,
(7) can be obtained as
(8)
The air-gap-flux-oriented vector controller scheme is based
on (13) and (15). The three-phase reference currents are pro-
In (3), slip speed is defined as
duced through the – axis transformation and transfor-
(9) mation which are identified in block of Fig. 5.
(11) (13-a)
where where
or (12)
SUZUKI et al.: AN AIR-GAP-FLUX-ORIENTED VECTOR CONTROLLER 1073
From (15),
(15-a)
(15-b)
(17)
(18)
Test results are shown in Fig. 9 with turn ratio “ ” and ra-
dial force references. From this figure, it is shown that the ra-
dial force reference of -axis component does not vary with the
turn ratio “ ” However, the -axis component varies with the
Fig. 8 shows the system configuration of a vector controller turn ratio “ ” That is to say that the coupling between the two
with turn ratio “ .” This controller was originally proposed in perpendicular axes causes interference in the radial force refer-
[11], however, phase lead and lag block position has been opti- ences. When turn ratio “ ” is set to 1.04, decouple of the radial
mized. When the turn ratio “ ” is equal to 1, is equal to . force can be realized.
This system at “ ” will correspond to the air-gap-flux-ori-
ented vector controller shown in Fig. 6.
V. DISCUSSION OF PHASE SHIFT OF THE FLUX
It is shown by experiment and simulation that the air-gap-
flux-oriented vector controller is effective to make the mag- REFERENCE VECTOR
netic suspension stable in acceleration tests. However, it is quite The radial force is produced by using active unbalance of
possible that the air-gap-flux-oriented vector controller can not flux density of the air gap between the rotor and stator. There-
completely decouple to radial force components. Thus, the sta- fore, it is assumed that the magnetic suspension becomes stable
tionary load tests will be required to indicate the most suitable with the air-gap-flux-oriented vector controller. However, it is
flux reference vector for decoupling the radial forces. shown experimentally in Fig. 9 that successful decooupling of
The experimental machine is constructed from two units; one the radial forces takes place at turn ratio “ ” , but not
is called Motor 1, and the other is called Motor 2. Motor 1 is at the usual value of “ ” . Digital simulations in Matlab
driven as a motor and Motor 2 is driven as a generator. There- software carried out to determine how the flux reference vector
fore, Motor 1 is loaded with stationary load via Motor 2. move with variations of turn ratio “ .” Fig. 10 shows results of
The radial force references , are measured at no-load digital simulation. The standard value of phase lead angle of the
condition. These radial force references are considered as a stan- air-gap flux is based on flux reference generated in a con-
dard value. troller. It is evident from Fig. 10 that the phase angle of is
SUZUKI et al.: AN AIR-GAP-FLUX-ORIENTED VECTOR CONTROLLER 1075
Fig. 10. Turn ratio “a” versus phase lead angle of . inductance is larger than that of the rotor. Therefore, it can be
considered that stator leakage inductance is larger than rotor
delayed when “ ” is set to a value larger than 1.0. Since the turn leakage inductance in this experimental bearingless machine.
ratio “ ” is larger than 1.0, is shifted toward . The expression for slip frequency of the universal field-
The simulation results shown in Fig. 11 illustrate the variation oriented controller from [11] and Fig. 8 can be written as
of the phase lead angle of the air-gap flux vector as a function
of rotor resistance value. The rotor resistance is expressed in
per-unit value based on actual value of the machine. (21)
It is seen that the phase angle of is advanced by the in-
crease of rotor resistance due to temperature rise of the wind-
ings. Thus, the fact of can be explained. The turn ratio When the rotor resistance is relatively increased by more
“ ” is set to a value larger than 1.0 in order to delay the phase than the reference value, then the denominator of (21) becomes
angle of which is advanced by 2.4 degree with the increase smaller, and is increased. Hence, the phase angle of is
of rotor resistance. However, there may be other causes like sat- advanced.
uration and leakage inductance variations for this phase shift. On the other hand, the rotor leakage inductance is relatively
In a conventional induction motor it is assumed that stator set to a value larger than the actual value, because the reference
leakage inductance and the rotor leakage inductance are equal value of the stator leakage is equal to that of the rotor leakage
in value. However, in all practical bearingless induction motors, inductance. Then, the is increased, the denominator of equa-
these stator and rotor leakage inductances are not necessarily tion (21) is decreased, and is increased. Consequently, the
equal in values. At least, the sum of the stator leakage induc- phase angle of will also be advanced.
tance and rotor leakage inductance has a set of fixed value, only
distribution of leakage components can be changed. The effect VI. CONCLUSION
of distribution of the leakage inductance is simulated in Fig. 12.
At overloaded conditions, the magnetic suspension of the
The leakage factor is defined as
bearingless induction motor becomes unstable. A new con-
(19) troller with air-gap-flux vector control has been proposed. It has
(20) been experimentally validated that stable magnetic suspension
where indicates stator leakage inductance, and indicates can be realized with the proposed controller, even in overload
rotor leakage inductance. conditions. It is noted that the phase angle of the flux reference
It is found from Fig. 12 that the phase angle of is delayed vector is delayed in stationary load conditions. It is found by
when is smaller than 0.5; that means that the stator leakage simulation that this phase shift of the flux reference vector is
inductance is smaller than that of rotor. The phase angle of caused by changes of rotor resistance value and the distribution
is advanced when is larger than 0.5, that is, the stator leakage of machine leakage inductance.
1076 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 36, NO. 4, JULY/AUGUST 2000