Design, Analysis and Control of a Semi-active Magnetic Bearing System

for Rotating Machine Applications

T.-J. Yeh

Department of Power Mechanical Engineering, National Tsing-Hua University, Hsinchu, Taiwan, R.O.C.

Keywords:

Magnetic Bearing, Permanent Magnet, LTR Control.

Abstract:

In this paper, a semi-active magnetic bearing system which incorporates both the active and passive magnetic

bearings is proposed for rotating machine applications. Particularly, the design, analysis, and control issues of

the semi-active system are investigated by using an axial fan as the platform. In the proposed system, while

the rotor is levitated axially by the active bearing, its radial and tilting stabilities are guaranteed by the passive

bearings. By carefully designing the radial and tilting stiffnesses of the passive bearings and the controller

of the active bearing, the system can be successfully operated to the rated speed of 4000rpm. Because the

semi-active magnetic system is frictionless and consumes insigniﬁcant power in levitation, its total power

consumption is 14.7% less than the conventional fan in which mechanical ball bearings are used.

1 INTRODUCTION

The use of magnetic bearings in industrial applica-

tions has attracted increasing attention in recent years.

The major advantage offered by magnetic bearings is

that there is no physical contact between the bearing

and the levitated object, so friction is eliminated and

lubrication is not needed. In general, magnetic bear-

ings can be classiﬁed into two types: the active type

and the passive type. Active magnetic bearings are

made of electromagnets whose coil currents are con-

trolled based on the sensor measurements(T.-J. Yeh

and Wu, 2001)(Yeh et al., 2001). Active magnetic

bearings allow the system designers to ﬂexibly ad-

just the bearing stiffness and damping, and inject ap-

propriate signals to cancel the undesired vibrations.

Nevertheless, due to the necessary control hardware

including sensors, control electronics/digital signal

processor, and power ampliﬁers, the use of active

magnetic bearings substantially increases system cost

and complexity. On the other hand, passive mag-

netic bearings are simply made of permanent mag-

nets and rely on either the attractive or repulsive mag-

netic force to achievelevitation (J. Delamare and Yon-

net, 1995)(H. Okuda and Ito, 1984)(Yonnet, 1981).

Passive magnetic bearings do not require any control

hardware as the active bearings do, so they are inex-

pensive and structurally simple. However, by Earn-

shaw’s theorem, total stability is not possible for sys-

tems containing only passive magnetic bearings. In

these systems, the object to be levitated always has

to be constrained mechanically in certain degrees of

freedom. As a result, physical contact is established

and frictional loss is induced.

Considering the pros and cons in magnetic bear-

ings, if one wants to keep the system complexity to

minimum and yet achieve total levitation, the most

economical solution will be a system combining the

favorable features from both types of the bearings,

or so-called the semi-active magnetic bearing system.

Semi-active systems have been reported by several re-

searchers. For example, in (J. Delamare and Rulli,

1994) an angularly stable radial bearing is incorpo-

rated with an active magnetic bearing in the axial di-

rection to levitate a rotor. However, due to the low

stiffness in the passive bearing, total levitation is not

possible for the whole range of speed that the rotor

has to start its rotation with ball bearings until the ﬁrst

critical speed of 750rpm is passed. In (J.F. Antaki

and Groom, 2000)(J.F. Antaki and Groom, 2001), the

authors devised a magnetically levitated blood pump

as the artiﬁcial heart. In this system, the rotor is sus-

pended by two permanent magnet radial bearings and

an active magnetic thrust bearing which is actuated

by two voice coils. With the help of the blood as

the damping source, the system is capable of spin-

ning between 4000rpm and 8000rpm. In this paper,

the development of a semi-active magnetic bearing

system for rotating machine applications is demon-

strated by using a commercially available 127mm ×

503

Yeh T..

Design, Analysis and Control of a Semi-active Magnetic Bearing System for Rotating Machine Applications.

DOI: 10.5220/0005528205030510

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 503-510

ISBN: 978-989-758-122-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

127mm ×38mm axial fan as the platform. The axial

fan, whose photograph is shown in Figure 1, is driven

by a brushless DC motor and uses axial air ﬂow to

provide cooling for computer peripherals. Given the

limited space for mounting the magnetic bearings, the

requirement to spin to the rated speed of 4000rpm

without using any mechanical bearings, as well as

lack of ﬂuid damping because the fan is operated in

the air, the development requires systematic proce-

dures in design, analysis, and control. The rest of

the paper is organized as follows: System conﬁgura-

tion and dynamic analysis of the semi-activemagnetic

bearing system are introduced in section 2. Section

3 discusses how the passive bearings are designed to

achieve the desired radial and tilting stiffnesses. In

section 4, the physical model of the active magnetic

bearing is ﬁrst presented. Then system identiﬁca-

tion and controller design are performed to stabilize

the bearing dynamics. Section 5 presents experimen-

tal veriﬁcations of the system performance. Finally,

conclusions are given in section 6.

Figure 1: Photo of the axial fan.

2 SYSTEM CONFIGURATION

AND DYNAMIC ANALYSIS

Figure 2 shows the schematic of the semi-active mag-

netic bearing system. There are one active magnetic

bearing and two passive magnetic bearings. The

active bearing consists of an annular electromagnet

and a thrust disk which contains a circular permanent

magnet with the same diameter as the inner pole face

of the electromagnet. This active bearing is used to

provide frictionless support to the rotor in the axial

direction. Since feedback is always needed for the ac-

tive bearing, a ﬁber-optic sensor, which measures ro-

tor’s axial position, is mounted on a structural mem-

ber whose both ends are in turn attached rigidly to the

top of the fan housing.

Passive bearing I is composed of two permanent

magnet rings with one on the top of the rotor and

the other attached to the same structural member on

which the senor is mounted. The two magnets are

polarized axially and are aligned with the rotor’s axis.

Because the magnets are placed in attractive manner,

an upward magnetic force is applied to the rotor. Pas-

sive bearing II consists of two concentric stacks of

permanent magnet rings respectively attached to the

rotor and the housing. The permanent magnet rings

are polarized axially and are stacked in a repelling

manner for squeezing more magnetic ﬂuxes towards

the air gap between the stacks. The polarities of

the two stacks are arranged so that they repel against

each other. Moreover, because the magnetic poles of

the outer stack are not aligned with those of the in-

ner stack, passive bearing II applies an downard force

to the rotor. These two sets of passive bearings to-

gether serve two purposes. One is to provide tilting

and radial stiffnesses so that when the rotor tilts or

translates radially, a restoring torque or force can be

produced. The other is to provide a suitable upward

axial bias force for the active bearing to counteract.

Such a counteraction allows the active bearing, which

generates downward force only, to have full control of

rotor’s axial motion so as to generate axial stiffness.

Figure 2: Conﬁguration of the semi-active magnetic bearing

system.

Figure 3: Deﬁnitions of variables for dynamic analysis.

The dynamic analysis follows the deﬁnitions of

variablesin Figure 3. For simpliﬁcation, it is assumed

that the controller of the active magnetic bearing ren-

ders the rotor with high axial stiffness that the center

point of the thrust disk, or the point O in Figure 3, can

be treated as a ﬁxed point in the free space. By do-

ing so, the rotor becomes an axially symmetric body

spinning about a ﬁxed point. The rotor dynamics is

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thus given by:

x+ k

x = meΩ

sinΩt (1)

y+ k

y = meΩ

cosΩt (2)

+ ΩI

+ (k

−mgL)θ

= meΩ

LsinΩt(3)

−ΩI

+ (k

−mgL)θ

= meΩ

LcosΩt(4)

where m is the mass of the rotor, I

is the trans-

verse moment of inertia about the ﬁxed point, I

the axial moment of inertia, Ω is the rotor speed, x, y

and θ

, θ

are respectively the rotor’s radial displace-

ments and tilting angles, k

and k

are the radial and

the tilting stiffnesses provided by the magnetic bear-

ings, L is the distance from rotor’s center of gravity

to the ﬁxed point O, and e is the rotor unbalance. It

should be noted that while the ﬁrst two equations are

from the translational dynamics, the last two are due

to the gyroscopic effect. Moreover, the right side

of the equations are caused by the unbalance forces

(torques) which are proportionalto meΩ

and are syn-

chronized with Ω.

By considering the resonance in the rotor dynam-

ics, one can compute the minimum bearing stiffnesses

needed for the rotor to successfully spin to the rated

speed of 4000rpm. Taking the the radial stiffness k

for example, in order to avoid resonance during accel-

eration of the rotor, it is desired to place the resonant

frequency above the rated speed. For m = 0.2kg and

the given rated speed, it can be shown from (1) or (2)

that k

has to be larger than 35,092

. The rotor in

consideration has a mass unbalance speciﬁcation of

85µm. If keeping the amplitude of vibration within

0.25mm(which equals half of the bearing gap) at the

rated speed is desired, then the lower bound for k

raised to 47, 000

. To determine the tilting stiffness,

by taking Laplace transform on (3) and (4), it can be

found that if k

> mgL, the rotor is stable with two

resonant frequencies:

n1,n2



−mgL)+ Ω



Ω

+ 4I

−mgL)Ω

(5)

Figure 4 shows how ω

, ω

(in the unit of rpm)

vary with for I

= 1.4×10

−4

kg·m

, I

= 3×10

−4

kg·

, L = 0.022m, and k

= 1, 8, 18.02

N·m

rad

. Ap-

parently, while ω

increases with Ω, ω

decreases

with Ω. When either one of the resonant frequencies

equals the rotation speed, resonance occurs. Ideally,

to avoid the resonance as Ω varies from zero rpm to

the rated speed, the two resonant curves should not

intersect with the ω

= Ω line in Figure 4. It can be

computed that to achieve such a condition k

has to

be greater than 55

N·m

rad

Figure 4: Resonant speed v.s. rotation speed for different.

3 DESIGN AND ANALYSIS OF

PASSIVE MAGNETIC

BEARINGS

Although the lower bounds for the radial and tilting

stiffnesses can be computed via the dynamic analy-

sis, it is still desired to make the stiffnesses as high as

possible for minimizing rotor’s vibration during spin-

ning. However, as implied by Earnshaw’s theorem,

the stable radial and tilting stiffnesses simultaneously

induce instability in the axial direction and indeed the

instability increases with the stable stiffnesses. In siz-

ing the passive bearings, other than pursuing high ra-

dial and tilting stiffness, the axial instability also has

to be kept low so that the active bearing is able to

compensate.

Figure 5: Schematics of Passive Bearing I.

Figure 6: Schematics of Passive bearing II.

In this research, a ﬁnite-element package(ans, )

is employed to analyze the relevant bearing proper-

Design,AnalysisandControlofaSemi-activeMagneticBearingSystemforRotatingMachineApplications

505

ties including stiffnesses and instabilities so that a

better compromise among the design parameters can

be achieved. The magnetic material used here is

NdFeB with the remanence magnetic ﬂux density of

1.23Telsa. The schematics of two passive bearings

obtained after several design iterations are shown re-

spectively in Figure 5 and Figure 6. Particularly, in

passive bearing II, while the outer stack consists of

three magnetic rings, the inner stack consists of four

magnetic rings, and the magnetic poles of the outer

stack are dislocated from those of the inner stack by

0.2mm in the downward manner.

Table 1: Properties of the Passive Bearings.

Passive

Bearing I

Passive

Bearing II

Radial Stiffness 8,000

38,000

Tilting Stiffness 16.62

N·m

rad

1.4

N·m

rad

Axial Instability 26,300

74,400

Axial bias force 49.44N −21.2N

The radial stiffness, tilting stiffness, axial stabil-

ity and the upward force respectively provided by the

two passive bearings are listed in Table 1. According

to this table, the tilting stiffness is mainly contributed

by passive bearing I and the radial stiffness is mainly

contributed by passive bearing II. In order to keep

the axial instability to minimum, we deliberately limit

the radial stiffness of passive bearing II, which is the

main source of axial instability, to 38, 000

by hav-

ing unequal numbers of magnetic rings for the inner

and outer stack

. The total radial stiffness in this case

is only 46,000

, which is still 1, 000

less than the

lower bound computed in previous section. As will

be shown later, the additional radial stiffness needed

will be provided by the active bearing. From the ta-

ble it can also be found that the total tilting stiffness is

only 18.02

N·m

rad

, which means that the rotor will expe-

rience a resonance at 2,200rpm. Due to the limited

space for placing the magnets and the unavailability

of magnets of extreme strength, it is difﬁcultto further

increase the tilting stiffness to avoid the resonance.

In the following investigation, this tilting stiffness is

adopted, so as the rotor accelerates towards the rated

speed, it will experience resonance shortly. Since the

unbalance force is small at low speeds, as long as the

The ﬁnite element simulations indicate that if the inner and

outer stacks of passive bearing II both have three rings,

then the radial stiffness is only 33.450

. If the number

of rings for both stacks are increased to four, the radial

stiffness becomes 44,510

but the axial instability also

becomes excessive. As a comprimise, unequal number of

rings are adopted respectively for the outer (3) and inner

(4) stack.

rotor accelerates fast enough, it will not collide with

the stator and such resonance will be acceptable. Fi-

nally, the dislocation between the concentric stacks

of bearing II induces a downward axial bias force of

21.2N to the rotor. This downward force is used to

cancel part of the upward force from bearing I. By

doing so, the total upward force that the active bearing

has to counteract is not excessive and thus its power

consumption at steady state is reduced.

4 MODELING, IDENTIFICATION,

AND CONTROL OF THE

ACTIVE MAGNETIC BEARING

In the active magnetic bearing, if the magnetic ﬂux

leakage, fringing ﬂux, and the magnetic reluctance in

the iron core are ignored, one can derive the following

magnetic force equation:

−A

[µ

Ni+ B

l/µ

]

2µ

(z+ l/µ

)

(1+ A

)

(6)

where F

is the downward magnetic force generated,

is the air permeability, µ

and B

are respectively

the relative permeability and the remanence magnetic

ﬂux density of the permanent magnet, z is the air gap,

is the air permeability, i is the coil current, N is

the number of coil turns, l is the thickness of the per-

manent magnet, A

and A

are respectively the areas

of the inner(circular) and outer(annular) pole faces.

Table 2 lists the numerical values of the relevant pa-

rameters for the active magnetic bearing. Comparing

the magnetic force computed by (6) with the ﬁnite-

element simulations, it can be found that the theo-

retical equation tends to overestimate the magnetic

force because it ignores the magnetic ﬂux leakage and

fringing ﬂux associated with the permanent magnet.

To make a more accurate force prediction, one can in-

troduce a correction factor η in which ηl replaces l in

(6) as the equivalent thickness of the permanent mag-

net. By choosing η to be 0.946, Figure 7 shows that

the theoretical equation matches the ﬁnite element re-

sults better with maximum error less than 3%.

4.1 Linear Model and Identiﬁcation

To facilitate the subsequent linear control design, the

nonlinear force equation (6) with the correction factor

is linearized around i = 0, and z = z

, where z

is the

nominal air gap. The linearization results in

≈ −k

δi+ k

δz−F

(7)

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506

Figure 7: Comparisions of the force equations with the

ﬁnite-element results.

Table 2: The numerical values of the relevent parameters

for the active magnetic bearing.

3.14×10

−4

)

7.06×10

−4

)

4π ×10

−7

N 300 (turn)

0.55 (T)

l 2×10

−3

(m)

1.06

where k

ηl/µ

+ηl/µ

)

(1+A

)

is the current gain,

ηl/µ

]

(1+A

)(z

+ηl/µ

)

is the unstable stiffness,

ηl/µ

)

2µ

+ηl/µ

)

(1+A

)

is the downward bias

force provided by the permanent magnet, δi and δz

denote the perturbations in current and axial displace-

ment respectively. If z

is selected to be 0.2mm, then

≈ 21.385N. This bias force, when combined with

the rotor’s weight, cancel most of the upward force

from the passive bearings. Therefore, if the ac-

tive bearing is stabilized at this nominal air gap, the

steady-state power required for levitation is insigniﬁ-

cant.

It should be noted that although the active bearing

is open-loop unstable in the axial direction, it is sta-

ble in the radial and tilting directions. Finite element

simulations reveal that the associated radial and tilt-

ing stiffnesses are respectively 1,000

and 0.01

N·m

rad

Although the tilting stiffness is minuscule compared

to those offered by the passive bearings, as mentioned

in the previous section that such a radial stiffness is

just enough to limit rotor’s amplitude of vibration

to within half of the airgap as the rotor accelerates

towards the rated speed. Assume that the passive

bearings’ downward force balances with the rotor’s

weight and permanent’s bias force, the linearized dy-

namic equation for the axial motion can be derive as

= (k

+ k

)z−k

i (8)

Figure 8: Frequency responses of the active magnetic bear-

ing.

where k

is the total axial instability contributed by

the two passive bearings. Notice that in this equa-

tion the perturbation symbol δ associated with i and z

has been removed for simplicity. By substituting the

respective numerical values into (8) and then taking

Laplace transform, the system transfer function G(s)

can be computed as

G(s) =

z(s)

i(s)

−11.9

0.2s

−114,000

(9)

System identiﬁcation is performed on the active

bearing to experimentally identify the transfer func-

tion. The identiﬁcation is based on frequency re-

sponse tests. Because the system is open-loop unsta-

ble, the identiﬁcation is performed in closed loop by

using a PID controller to stabilize the system. Dur-

ing the identiﬁcation test, a sinusoidal signal, whose

frequency ranges from 10Hz to 10kHz, is injected as

a disturbance and the frequency response is obtained

by comparing the amplitudes and phases of the coil

current and the rotor position.

In Figure 8, the experimental frequency response

is shown. This frequency response is also curve-

ﬁtted by a transfer function which retains the form

of the theoretical input-output behavior in (9) except

that one extra pole and zero are added. The transfer

function, given by

G(s) =

z(s)

i(s)

−10(

5027

+ 1)

(0.21s

−100,000)(

942

+ 1)

(10)

is also plotted in Figure 8. The second order part of

this transfer function, which has phase of zero for all

frequencies, only differs slightly from the theoretical

model, and the extra pole and zero added are used to

account for the additional phase lag for ω > 10Hz. It

should be noted that the experimental frequency re-

sponse matches the curve-ﬁtted transfer function ex-

cept for the ﬁrst structural frequency at about 200Hz

and other structural modes occurring at ω > 500Hz.

Therefore, the transfer function in (10) will be used

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507

as the nominal model and its discrepancy from the ex-

perimental frequency response will be treated as the

modeling error in the following controller design.

4.2 LTR Controller Design

The PID controller designed for identiﬁcation, al-

though is simple and stabilizing, has limited perfor-

mance due to its restricted control structure and trial-

and-error nature. Experimentally, the axial stiff-

ness provided by the PID controller is too compli-

ant for the rotor to spin. In this section, we use the

loop-transfer-recovery(LTR) design to systematically

devise a high-performance controller to increase the

stiffness of the active bearing.

In order for the control system to be stiff enough

to reject disturbances at low frequencies, an integrator

is augmented to G(s) and then the LTR design is con-

ducted on the state-space representation of the aug-

mented system. LTR is a linear quadratic Gaussian

(LQG) optimal control based method. The design

procedure requires one to solve two algebraic Riccati

equations: one corresponds to the Linear Quadratic

Regulator problem, and the other to the Kalman Fil-

ter problem. As shown in (Athans, 1986), by im-

plementing the cheap control LQR problem in LQG,

the system’s loop transfer function can be recovered

to a Kalman ﬁlter loop transfer function which mim-

ics a pure integrator with a bandwidth equal to

√

where µ is a ﬁctitious output noise intensity. This in-

dicates that the LTR design allows one to designate

the closed-loop system bandwidth by the choice of µ.

Ideally the closed-loop bandwidth should be set as

high as possible so that the system can achieve better

disturbance rejection. However, the higher the band-

width, the less likely the control system can maintain

the robust stability against the modeling error. To se-

lect the appropriate bandwidth, we employ the small-

gain result (K. Zhou and Glover, 1996) which, when

applied to the current case, states that given a nominal

model G with additive modeling error ∆G, a stabiliz-

ing controller K can provide robust stability if

|∆G( jω)| <



(1+ K(jω)G( jω))

−1

K(jω)



. (11)

Figure 9 plots



(1+ K( jω)G( jω))

−1

K(jω)



corre-

sponding to several different designated bandwidths

as well as |∆G( jω)|which denotes the modeling error

between G and the experimental frequency response

in Figure 8. It is clear that when ω

is raised to 60Hz,

the two functions in (11) intersect with each other at

the ﬁrst structural frequency. Thus in the ﬁnal LTR

design ω

= 50Hz is adopted and the controller is

given by

LQG

(s) = −

8.23×10

+ 1.358×10

s(s

+ 9224s

+ 4.157×10

+5.635 ×10

s+ 1.602×10

+1.147 ×10

s+ 1.621×10

)

(12)

Figure 9: Examination of robust stability criterion in the

frequency domain.

5 EXPERIMENTS AND

PERFORMANCE EVALUATION

Figure 10 shows the photo of the semi-active

magnetically-levitatedaxial fan for experimental vali-

dation. To initiate the levitation, the LTR controller is

demanded to track a 2nd-order critically damped tra-

jectory so that the rotor can eventually settles at the

nominal gap. The displacement response in Figure 11

indicates the controller can inhibit the transiency to

within 0.3sec. According to the current response in

Figure 12, to achieve so the maximum coil current is

less than 2.5A. Moreover, the steady-state current is

less than 0.1A, which implies that the active bearing

consumes almost zero power for levitation. It should

be noted that this steady-state current can be further

reduced by slightly modifying the designated nomi-

nal air gap.

Figure 10: Photo of the semi-active magnetically levitated

axial fan.

When the rotor is levitated axially by the active

bearing, its radial and tilt stabilities are also auto-

matically guaranteed by the passive bearings. Af-

ter the rotor settles to the nominal gap at steady state,

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Figure 11: Transcient response of the axial displacement.

Figure 12: Transcient response of the coil current in the

active magnetic bearing.

the brushless DC motor is activated to spin the ro-

tor. The spinning test indicates that the rotor can

spin successfully to 4000rpm. Figure 13 shows the

disturbance rejection responses of the active bearing

for 0rpm, 2000rpm, and 4000rpm. The experimen-

tal setup for identifying these responses is the same

as what used in system identiﬁcation except that the

input is changed to the disturbance signal. This ﬁg-

ure indicates that the LTR controller renders the active

bearing fairly consistent disturbance-rejection perfor-

mance as the rotor speed varies. Particularly, the

static axial stiffness is greater than 10

, which ver-

iﬁes the high stiffness assumption in section 2. The

amplitudes of axial vibration and radial vibration

for

different spinning speeds are respectively shown in

Figure’s 14 and 15. It is clear that the bearings can

limit the rotor’s vibration to within one tenth and half

of the bearing gap respectively in axial and radial di-

rections. Moreover, according to Figure 15 the ra-

dial vibration is most signiﬁcant between 2000rpm

and 3000rpm. This veriﬁes the previous calculation

on the gyroscopic resonant frequency associated with

the designated tilting stiffness 18.02

N·m

rad

The radial vibration of the semi-active magneti-

cally levitated fan is also compared with two other

systems. One is the original fan in which mechani-

cal ball bearings are used to support the rotor, and the

other is the passive magnetic bearing system whose

The radial vibration is measured experimentally using a

laser displacement sensor.

Figure 13: Disturbance rejection responses of the active

magnetic bearing.

Figure 14: Steady state response of the axial displacement.

Figure 15: Steady state response of the radial displacement.

structure is similar to the current one except that the

active bearing is replaced by a mechanical thrust bear-

ing. The results of comparison are shown in Fig-

ure 16. Due to the gyroscopic resonance, the semi-

active system exhibits highest amplitude of vibration

between 1000rpm and 3000rpm. After 3000rpm, the

semi-active system’s vibration becomes smaller than

the passive one but still larger than the original fan.

In general, the vibration of the original fan is the low-

est among the three systems for Ω > 1000rpm. The

powerconsumption of these three systems are also ex-

perimentally compared and the results are plotted in

Design,AnalysisandControlofaSemi-activeMagneticBearingSystemforRotatingMachineApplications

509

Figure 17. It should be noted that while the power

in the semi-active system is consumed by the DC mo-

tor and the active bearing, the power for the other two

systems is solely consumed by the motor. As shown

in this ﬁgure, because the semi-active system is to-

tally frictionless and consumes almost zero-power in

levitation, it exhibits the lowest power consumption

among the three systems. Particularly, at the rated

speed the semi-active system consumes 14.7% less

than the original fan and 12% less than the passive

bearing system.

Figure 16: Comparision of the radial displacement for three

systems

Figure 17: Comparison of power for the three systems

6 CONCLUSIONS

In this paper, a semi-active magnetic bearing system

which incorporates both the active and passive mag-

netic bearings is proposed to support the rotor of an

axial fan. By carefully designing the radial stiffness

and tilting stiffness of the passivebearing and the con-

troller of the active bearing, the system can be suc-

cessfully operated to the rated speed with less power

consumption than the original fan. Currently, two

research efforts are conducted to further improve the

proposed system. One is to use inexpensive, small

hall-effect sensors to replace the expensive, bulky

ﬁber-optic sensor for positioning sensing. The other

is to modify the design of passive bearing I so that

it can be integraged with passive bearing II and be

placed internally. By doing so, the structural member

which mounts the magnetic ring and the senor can be

removed and the size, weight as well as the cost of the

semi-active system can be reduced.

ACKNOWLEDGEMENTS

The author gratefully acknowledges the support pro-

vided by Ministry of Science and Technology of Tai-

wan.

REFERENCES

Ansoft corporation, maxwell 3d, pittsburgh, pa, 2003.

Athans, M. (1986). A tutorial on the lqg/ltr method. In

Proc. American Control Conference, Seattle, WA.

H. Okuda, T. Abukawa, K. A. and Ito, M. (1984). Char-

acteristics of ring permanent magnet bearing. IEEE

Transactions on Magnetics, MAG-20(5).

J. Delamare, E. R. and Yonnet, J.-P. (1995). Classiﬁcation

and synthesis of permanent magnet bearing conﬁgu-

rations. IEEE transactions on Magentics, 31(6).

J. Delamare, J.-P. Y. and Rulli, E. (1994). A compact mag-

netic suspension with only one axis control. IEEE

transactions on Magentics, 30(6).

J.F. Antaki, B. Paden, G. B. and Groom, N. (2000). Mag-

netically suspended miniature ﬂuid pump and method

of designing the same.

J.F. Antaki, B. Paden, G. B. and Groom, N. (2001). Blood

pump having a magnetically suspended rotor.

K. Zhou, J. D. and Glover, K. (1996). Robust and optimal

control. Prentice Hall.

T.-J. Yeh, Y.-J. C. and Wu, W.-C. (2001). Robust con-

trol of multi-axis magnetic bearing systems. Interna-

tional Journal of Robust and Nonlinear Control, pages

1375–1395.

Yeh, T.-J., Chung, Y.-J., and Wu, W.-C. (2001). Sliding

control of magnetic bearing systems. ASME Journal

of Dynamic Systems, Measurement, 123(3):353–362.

Yonnet, J.-P. (1981). Permanent magnet bearings and cou-

plings. IEEE transactions on Magentics, 17(1).

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