1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME
200
FUZZY CONTROL OF A VERTICAL SHAFT SINGLE AXIS
CONTROLLED REPULSIVE-TYPE MAGNETIC BEARING
TAPAN SANTRA1
, Dr. D. ROY2
, A.B. CHOUDHURY3
1
Department of Electrical Engineering, Kalyani Government Engineering College, Kalyani,
Nadia, Pin.-741235, W.B, India
2
Department of Electrical Engineering, Bengal Engineering & Science University, Shibpur,
Howrah-711103, W.B, India
3
Department of Electrical Engineering, Bengal Engineering & Science University, Shibpur,
Howrah-711103, W.B, India
ABSTRACT
In present century green technology is getting importance. This technology offers low
loss, low noise, low pollution and low hazards. Magnetic bearing is one of the best examples
of this technology. Among different type of magnetic bearings single axis controlled
repulsive type magnetic bearing (SACRMB) is best fitted regarding performance and cost.
This paper introduces a vertical shaft SACRMB, consists of permanent magnets for radial
stability and electromagnets for levitation & axial stability. SACRMB has tremendous
opportunities to become a common choice for house hold to industrial applications. A device
becomes popular due to its simple construction, reliability & simple control system which do
not depend upon system parameters. A person knows nothing about control system, when
becomes able for understanding & maintenance of the control of SACRMB then only the
mass production is possible. Here is the importance of fuzzy controller which is
nonparametric and very simple in nature. In this paper the design & performance of fuzzy
controller has been introduced for the axial control of the SACRMB. The radial control is
done by passive permanent magnet. It is found that the radial & axial vibrations are under
tolerable limit and SACRMB works extremely well.
Keywords: SACRMB, fuzzy control, magnetic forces, stability, vibration.
INTERNATIONAL JOURNAL OF ADVANCED RESEARCH IN
ENGINEERING AND TECHNOLOGY (IJARET)
ISSN 0976 - 6480 (Print)
ISSN 0976 - 6499 (Online)
Volume 4, Issue 4, May – June 2013, pp. 200-207
© IAEME: www.iaeme.com/ijaret.asp
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2. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
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I. INTRODUCTION
The existing mechanical bearing has some disadvantages like high noise, requirement
of lubrication, maintenance, high energy loss & frequent occurrence of hazards. So there is
always a demand for a bearing which will be free from these disadvantages, will be simple,
economic, standalone & reliable. To achieve all these requirements, magnetic bearing is one
of the best solutions [1]. Most of the commercially available magnetic bearing is active or
passive [2, 3, 4, 5 & 7] in nature. For pure passive magnetic bearing (MB) stability is one
problem and for active MB, reliability and cost is another problem, due to its complex control
system, high number of electromagnets requirement and associated circuit. In this
background scenario, people has embarked on developing of single axis controlled repulsive
type magnetic bearing [6] which provides the advantages like simple construction, high
reliability and low cost. In this configuration the radial stability is achieved by repulsive force
between stator permanent magnet (connected with fixed frame) and rotor permanent magnet
(connected with shaft) as shown in Fig.1. Axial stability is achieved by the attraction force
between a flywheel (connected with shaft) and electromagnets. Among different types of
configuration, the vertical shaft configuration of SACRMB has been represented in our
research. In this paper the constructional design has been done by ANSYS software and
control design has been carried out by MATLAB.
Fig. 1 Construction of SACRMB Fig. 2 Different forces acting on SACRMB
Till date the people concentrate on PID controller for the tuning of SACRMB, which
is not easy to tune and logically cumbersome to implement. This is a great hurdle for mass
production of SACRMB. So for mass production of SACRMB, the primary requirement is a
very simple control system so that anybody can maintain or develop the control mechanism,
who knows very little bit of control theory. So we are embarked on designing a fuzzy logic

3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME
202
based controller which do not depends on the bearing parameters. The fuzzy rule based
controller has been designed and simulated. The vibration characteristics along three different
axes have been simulated which looks extremely well and under tolerable limit.
II. CONSTRUCTION OF SACRMB
A single-axis controlled repulsive-type magnetic bearing is a device which
supports the rotor system by magnetic levitation and allows it to rotate freely with
less vibration and low loss. Here two things are important; number one the rotor
system should be levitated and number two the vibration of the rotor system should
be less as much as possible at steady running condition as well as in different
transient conditions like sudden change in load, on & off of the machine etc. In this
paper vertical shaft configuration of SACRMB has been discussed. The levitation
force can be achieved by the attractive force between electromagnet & flywheel and
the radial stability can be achieved due to repulsive force between stator & rotor
permanent magnet [Fig.1].To reduce the effect of radial disturbance, higher radial stiffness
is desired which can be achieved by proper configuration of stator & rotor permanent magnet
and by selecting proper magnet material. In this work NdFeB permanent magnet has been
selected as magnetic material. The axial X-axis vibration can be controlled by the
attraction force between electro magnet and flywheel. A controller will sense the X-
axis vibration or displacement by a gap sensor (capacitive or eddy current type) and
control the current through the coil of electro magnet [Fig. 2].
III. MODELLING OF SACRMB
The rotor is assumed to be rigid body. The origin G of the stator fixed frame of
reference and O is the mass center of the rotor. (xe, ye, ze) is the location of O with respect to
the fixed frame of reference. The forces acting on the rotor are shown in the Fig. 2. The force
and moment balance around ܺ௥ ܻ௥ & ܼ௥ and force of electromagnets are given by following
equations.
Force balance equations
‫ܨ‬௫ ൌ ݉‫ݔ‬ሷ௘=݂ଵ ൅ ݂ଶ ൅ ݂ଷ ൅ ݂ସ ൅ ݂௟௫ ൅ ݂௨௫ െ ݉݃….Equation.1
‫ܨ‬௬ ൌ ݉‫ݕ‬ሷ௘=݂௟௬ ൅ ݂௨௬ ……Equation. 2
‫ܨ‬௭ ൌ ݉‫ݖ‬ሷ௘=݂௟௭ ൅ ݂௨௭ …..Equation. 3
Moment balance equation
‫ܯ‬ ൌ ‫ܬ‬௬ߠሷ ൅ ‫ܬ݌‬௫߰ሶ ൌ ݂௟௭‫ܮ‬଴ଵ െ ݂௨௭‫ܮ‬଴ଶ െ ݂ଵ݈ ൅ ݂ଶ݈ ……Equation. 4
ܰ ൌ ‫ܬ‬௫߰ሷ െ ‫ܬ݌‬௫ߠሶ ൌ ݂௟௬‫ܮ‬଴ଵ െ ݂௨௬‫ܮ‬଴ଶ െ ݂ଶ݈ ൅ ݂ସ݈ ……Equation. 5
Equations for electromagnet
݂௝
′
ൌ 2‫ܨ‬௝ሺ
௜ೕ
′
ூೕ
െ
௚ೕ
ௐ
ሻ ……Equation. 6
dij/dt = (R/L) ij+ (1/L) v………Equation.7 where ݆ ൌ 1, … … 4

4. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May
Here m is the mass of rotor.
to 4, i.e four number of electromagnet
between stator & rotor permanent magnet along axial direction (X
magnetic bearing respectively.f
permanent magnet along radial direction (Y
respectively. flz & fuz are the repulsive force between stator & rotor permanent magnet along
radial direction (Z-axis) at lower & upper magnetic bearing respectiv
inertia of rotor around X & Y axis respectively.
shaft centre. L01 & L02 are the distance of lower & upper permanent magnetic bearing from
mass centre o. R & L are the resistance & inductanc
V is the supplied voltage to the electromagnet.
rotor along X-axis, Y-axis, Z-axis ,angular rotation around Y & Z axis
Fig. 3 Axial force Vs axial
displacement (Y-axis)
Fig. 5 Radial force Vs radial
displacement (Z-axis)
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
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Here m is the mass of rotor. fi are forces between electro magnets & flywheel, for i=1
to 4, i.e four number of electromagnets have been used. flx & fux are the repulsive force
between stator & rotor permanent magnet along axial direction (X-axis) at lower & upper
fly & fuy are the repulsive force between stato
permanent magnet along radial direction (Y-axis) at lower & upper magnetic bearing
are the repulsive force between stator & rotor permanent magnet along
axis) at lower & upper magnetic bearing respectively. Jx
inertia of rotor around X & Y axis respectively. l is the distance of each electromagnet from
are the distance of lower & upper permanent magnetic bearing from
mass centre o. R & L are the resistance & inductance of the electromagnet coil respectively.
V is the supplied voltage to the electromagnet. xe, ye, ze, θ & ψ are the displacement of the
axis ,angular rotation around Y & Z axis respectively.
Vs axial Fig. 4 Radial force Vs
axis) displacement (X-axis)
radial Fig. 6 Dimension of permanent magnet
in SACRMB
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
June (2013), © IAEME
are forces between electro magnets & flywheel, for i=1
are the repulsive force
axis) at lower & upper
are the repulsive force between stator & rotor
axis) at lower & upper magnetic bearing
are the repulsive force between stator & rotor permanent magnet along
& Jy are the
is the distance of each electromagnet from
are the distance of lower & upper permanent magnetic bearing from
e of the electromagnet coil respectively.
are the displacement of the
respectively.
radial
axis)
Dimension of permanent magnet

5. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
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204
F, I, & W are the electromagnetic force, coil current & gap between electromagnet &
flywheel at steady operating condition respectively. g, i are the instantaneous gap between
flywheel and electromagnet & coil current respectively. Now the forces flx & fux, fly & fuy, flz &
fuz are to be formulated as a function of displacement along X- axis, Y-axis & Z-axis
respectively (equation...8). For that purpose the rotor has been shifted along three different
axis and the corresponding forces has been derived by ANSYS software. The result has been
displayed in Fig. 3, Fig. 4 & Fig. 5 respectively.
.
flx or fux =Sx(x-A)+FA, fly & fuy=-Sy(y-B)+FB, & flz fuz =-Sz(z-C)+FC….Equation.8
Where (A, B, C) is the steady operating point of the rotor. Sx, Sy & Sz are the
measured slope of the force Vs displacement characteristics from Fig. 3, Fig. 4 & Fig. 5
respectively. FA, FB & FC are the steady force at operating point or force offset. The 14
number variables xe, ye, ze, dxe/dt, dye/dt, dze/dt, , θ , dθ/dt , ψ, dψ/dt,i1,i2,i3&i4 are taken as
state variables. So from equation 1 to 7 the following state space model can be achieved.
ୢ
ୢ୲
ൣXሶ൧ ൌ AഥሾXሿ ൅ BഥሾUሿ Y ൌ CതሾXሿ………equation. 9
IV. PARAMETER OF SACRMB
The proposed bearing system has two axially magnetized stator and rotor permanent
magnets (Fig. 1) which passively supports along radial direction (Z & Y axis) due to the
repulsive force between stator & rotor magnet. The tentative dimension of these magnets for
a 2 kg rotor system is shown in Fig. 6. This device also consists of four number
electromagnets which provide the levitation force as well as actively controls the rotor in the
axial direction (X-axis) by the attractive force between electromagnet & flywheel. So here the
detailed specification of stator & rotor permanent magnet, rotor system & electromagnet has
been given.
Permanent Magnet Specification: physical dimension: As shown in Fig. 6. Type: NdFe35
.Steady axial force (X axis) = 3.98 N, Steady radial force (Y & Z axis) = 0.747395N & -
0.51385 N Stiffness along three axis Sx= 77120 N/m, Sy=-72500N/m and Sz=-76900 N/m
respectively.
Rotor: Mass=2 Kg, Inertia with respect to X & Y Axis 0.0161 kg-m2
& 0.0383 kg-m2
respectively, length of shaft=0.210m, radius of flywheel= 0.060 m
Electromagnet: Coil resistance=2.93 ohm, Coil inductance=0.0485 H, Steady Current=1.33
A & Steady Attractive Force=3.91 N
Gap sensor: scaled output= 1V/mm
V. FUZZY CONTROLLER DESIGN
After modelling of the SACRMB as per equation. 9 , all the paratemeter values
can be placed in A, B & C matrix. Then the model has been simulated for axial & radial
vibration with a unit step input. Axial vibration is unbounded in nature [Fig. 7]. This
means the open loop system is unstable along axial (X-axis) direction.

6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May
Fig. 7 Axial vibration without
controller
From Fig. 8 & Fig. 9 it is observed that there is very negligible radial vibration
because of the passive vibration control by stator & rotor permanent magnet. So the
system is inherently radially stable but axial
make the system axially(x-axis) stable. This control scheme is given in Fig. 10 . In this
respect it is observed that PID controller may be used but the tuning of this controller is
found to be cumbersome. So the
its non parametric nature which is very much usefull for mass production of SACRMB.
To design the fuzzy controller first the input & output membership functions has been
developed. In SACRMB the errror ( set change in axial position
position by gap sensor) & deviation of this error are taken as the input of the controller
and the corresponding membership functions (MF) is shown in Fig. 11 & Fig. 12. The
range of allowable error is -3 mm to +3 mm & deviation in error is
Accordingly the input MF has been developed such as nz (negative zero), sp (small
positive), mp (medium positive), vp ( very positive), sn (small negative), mn (medium
negative) & vn (very negative). The output of the controller is the control force, that is
current through electromagnet coil & the corresponding membership functions are shown
in Fig. 13 such as z (zero),
increment), sd (small decrement), md (medium decrement) & ld (large decrement). The
range of the control force is -4.5 A to +4 .5 A. The rule base for the fuzzy ontroller is
show in Table. 1 & corresponding
Fig. 10
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
6499(Online) Volume 4, Issue 4, May – June (2013), © IAEME
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Fig. 8 Z-axis radial vibration Fig. 9 Y
controller vibration
& Fig. 9 it is observed that there is very negligible radial vibration
because of the passive vibration control by stator & rotor permanent magnet. So the
system is inherently radially stable but axially unstable. So a controller is required to
axis) stable. This control scheme is given in Fig. 10 . In this
respect it is observed that PID controller may be used but the tuning of this controller is
found to be cumbersome. So the idea of fuzzy logic controller has been introduced due to
its non parametric nature which is very much usefull for mass production of SACRMB.
To design the fuzzy controller first the input & output membership functions has been
rror ( set change in axial position – sensed change in axial
position by gap sensor) & deviation of this error are taken as the input of the controller
and the corresponding membership functions (MF) is shown in Fig. 11 & Fig. 12. The
3 mm to +3 mm & deviation in error is -6 mm to +6 mm.
MF has been developed such as nz (negative zero), sp (small
positive), mp (medium positive), vp ( very positive), sn (small negative), mn (medium
tive). The output of the controller is the control force, that is
current through electromagnet coil & the corresponding membership functions are shown
in Fig. 13 such as z (zero), si(small increment), mi (medium increment), li (large
decrement), md (medium decrement) & ld (large decrement). The
4.5 A to +4 .5 A. The rule base for the fuzzy ontroller is
show in Table. 1 & corresponding circuit is given in Fig. 14.
Fig. 10 Control scheme for SACRMB
International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
June (2013), © IAEME
Y-axis radial
vibration
& Fig. 9 it is observed that there is very negligible radial vibration
because of the passive vibration control by stator & rotor permanent magnet. So the
ly unstable. So a controller is required to
axis) stable. This control scheme is given in Fig. 10 . In this
respect it is observed that PID controller may be used but the tuning of this controller is
idea of fuzzy logic controller has been introduced due to
its non parametric nature which is very much usefull for mass production of SACRMB.
To design the fuzzy controller first the input & output membership functions has been
sensed change in axial
position by gap sensor) & deviation of this error are taken as the input of the controller
and the corresponding membership functions (MF) is shown in Fig. 11 & Fig. 12. The
6 mm to +6 mm.
MF has been developed such as nz (negative zero), sp (small
positive), mp (medium positive), vp ( very positive), sn (small negative), mn (medium
tive). The output of the controller is the control force, that is
current through electromagnet coil & the corresponding membership functions are shown
si(small increment), mi (medium increment), li (large
decrement), md (medium decrement) & ld (large decrement). The
4.5 A to +4 .5 A. The rule base for the fuzzy ontroller is

7. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN
0976 – 6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 4, May
Fig. 11 input MF ‘Erroe
Fig. 13
Fig. 14 Fuzzy logic controller
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Erroe’ Fig. 12 Input MF ‘Deviation error
Fig. 13 Output MF ’current’
Table 1. Rulle Base
Fuzzy logic controller Fig. 15 Axial vibration with Fuzzy controller
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Deviation error’
Axial vibration with Fuzzy controller

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Fig. 15 represents the axial vibration characteristic of SACRMB with a fuzzy
controller. It is observed that at first some vibration is there but within 3 sec the vibration
deceases to almost zero. The maximum peak of vibration is 0.45 mm which is acceptable.
The fuzzy controller work exceptionally well.
VI. CONCLUSION
In this paper modelling & controller design of a vertical shaft single axis controlled
repulsive type magnetic bearing has been represented. For its advantageous position over
existing mechanical bearing, SACRMB will replace all the existing bearing within next few
years. For this mass production is necessary, which is possible only when a simple, low cost
construction & control system of SACRMB is adopted. For this purpose it is advantageous to
use a nonparametric controller (fuzzy controller) which is simple and logically easy to
implement. In this paper by using a fuzzy controller excellent axial stability of SACRMB has
been achieved.
REFERENCES
[1] J. P. Yonnet, “Passive magnetic bearing with permanent magnets”, IEEE Trans. Magn
.1978,14, (5), pp. 803-805
[2] Lembke. T, “Design for magnetic induction bearing”, in Chalmers Univesity of
Technology, Göteborg, 1990
[3] Xu Feipeng, Li Tiecai, Liu Yajing,”A study on passive magnetic bearing with Halbach
magnetized array", Electrical Machines and Systems, 2008. ICEMS 2008, pp. 417 -
420, Volume: Issue: 17-20 Oct. 2008
[4] Falkowski K., Henzel M.: “High Efficiency Radial Passive Magnetic Bearing”, SOLID
STATE PHENOMENA, Vol. 164, pp. 360-365, 2010
[5] SAMANTA, P. HIRANI, H. “MAGNETIC BEARING CONFIGURATIONS: THEORETICAL AND
EXPERIMENTAL STUDIES”, MAGNETICS, IEEE TRANSACTIONS ON, ON PAGE(S) 2038 - 2042
VOLUME: 44 ISSUE: 2, FEB. 2008
[6] S. C. mukhopadhyay, T. Ohji, M. Iwahara, S. Yamada and F. Matsumura, "influence of
permanent magnet configuration on the stability of repulsive type magnetic bearing",
proceeding of japanese national conference on linear drive, ld - 96 - 105, pp. 57-66, 1996
[7] Abdul Rashid Husain, Mohamad Noh Ahmad, and Abdul Halim Mohd. Yatim
“asymptotic stabilization of an active magnetic bearing system using lmi-based sliding
mode control”, world academy of science, engineering and technology, p. 37, 20
[8] Neeraj Tiwari, D. Bhagwan Das and Prabal Pratap Singh, “Design, Development and
Hardware Realization of X-Beebased Single Axis Solar Tracking System”, International
Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 3, 2012, pp. 8
- 20, ISSN Print : 0976-6545, ISSN Online: 0976-6553.
[9] Amit Shrivastava and Dr. S. Wadhwani, “Application of Time-Domain Features with
Neural Network for Bearing Fault Detection”, International Journal of Electrical
Engineering & Technology (IJEET), Volume 3, Issue 2, 2012, pp. 151 - 155,
ISSN Print : 0976-6545, ISSN Online: 0976-6553.