Review Article Overview of Bearingless Induction...

Review ArticleOverview of Bearingless Induction Motors

Xiaodong Sun1 Long Chen1 and Zebin Yang2

1 Automotive Engineering Research Institute Jiangsu University Zhenjiang 212013 China2 School of Electrical and Information Engineering Jiangsu University Zhenjiang 212013 China

Correspondence should be addressed to Xiaodong Sun xdsunujseducn

Received 21 September 2013 Accepted 5 February 2014 Published 9 March 2014

Academic Editor Ivo Dolezel

Copyright copy 2014 Xiaodong Sun et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Bearingless induction motors combining functions of both torque generation and noncontact magnetic suspension together haveattracted more and more attention in the past decades due to their definite advantages of compactness simple structure lessmaintenance no wear particles high rotational speed and so forth This paper overviews the key technologies of the bearinglessinduction motors with emphasis on motor topologies mathematical models and control strategies Particularly in the controlissues the vector control independent control direct torque control nonlinear decoupling control sensorless control and so forthare investigated In addition several possible development trends of the bearingless induction motors are also discussed

1 Introduction

The idea of bearingless motors can be traced back to 1973whenHermannproposed probably the first radial activemag-netic bearing topology [1] in which two sets of windings areembedded in the stator so as to produce the driving momentand radial strength simultaneously In 1988 Swiss scholarBosch first proposed and used the ldquobearingles sic motorrdquoconcept [2] Since then there is a fast growing interest in bear-ingless motor and the concept has been reported in variouspublications on magnetic levitationThe importance of bear-inglessmotors is related to the integration of the drive controlof the electrical motor and the suspension control of its rotorin a compact volume Generally speaking the principal char-acteristic of bearinglessmotors is the existence of two kinds ofstator windings and one assists in the torque generation andthe other one for the rotor suspension Compared with thewell-known magnetic bearing driving topology of the elec-trical motor and independent magnetic bearings mounted inthe same axis the advantages of the bearingless motor arecompactness a simple structure and cost reduction

So far various types of motors have been put forwardas bearingless motors such as synchronous reluctance [3 4]and switched reluctance types [5 6] induction type [7 8]surface mounted permanent magnet (PM) [9 10] inset PM

[11] interior and buried PM types [12] Lorentz slotless type[13 14] consequent-pole type [15 16] and brushless DCtype [17 18] Among these types of bearingless motors thebearingless induction motor is being actively researched anddeveloped around the word since it possesses the followingadvantages

(1) Its rotor topology is relatively simple and robust

(2) It provides nearly constant rotational speed

(3) Its torque ripples and cogging torque are less

(4) The cost is low for open loop operation

Being continually fueled by new motor topologies andcontrol strategies bearingless induction motors are becom-ing more and more attractive and have been identified to beone of the most promising motors for the special industrialapplications

The purpose of this paper is to give an overview of thebearingless inductionmotorsThus the state-of-the-art tech-nology of bearingless induction motors including operationprinciples motor topologies mathematical models controlstrategies and latest development trends will be reviewedand discussed

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 570161 10 pageshttpdxdoiorg1011552014570161

2 Mathematical Problems in Engineering

Airgap 2-2Airgap 1-1

120572F120572iB120573iB120573

iM120573

iM120573

iM120573

iM120572iM120572

iM120572iM120572

iB120572

iB120572

iM120573

120573

Ψ2Ψ4

Figure 1 Principle of radial suspension forces generation

2 Principle of Radial SuspensionForce Generation

The basic winding configuration of a bearingless inductionmotor in the stationary perpendiculars 120572- and 120573-axes isshown in Figure 1 Two sets of windings are wound inthe same stator slots One is the 4-pole windings for theproduction of the torque The other is the 2-pole windingsfor the production of the radial suspension force so as tocontrol the rotor radial position in the airgapThese windingsare referred as the torque and suspension force windingsrespectively

The main 4-pole flux Ψ4is generated by torque winding

current 119894119872120572

Under no-load balanced conditions if a positiveradial suspension force along the 120572-axis is needed the sus-pension force winding current 119894

119861120572is fed as shown in Figure 1

The flux density in the airgap 1-1 is increased because bothΨ2

and Ψ4fluxes are in the same direction On the other hand

the flux density in the airgap 2-2 is decreased because Ψ2

and Ψ4are in the opposite direction A positive suspension

force 119865120572is produced in the 120572-axis direction only The reverse

current can produce the opposite radial suspension forceThe radial suspension force 119865

120573in the 120573-axis direction can be

produced using electrically perpendicular 2-pole suspensionforce winding current 119894

119861120573distribution

3 Motor Topologies

31 2 Degrees of Freedom (DOF) Bearingless Induction MotorAt present the bearingless induction motor topologies aremainly concentrated in the 2-DOF 3-phase squirrel cagetype bearingless induction motors which are usually used asprinciple prototypes in the laboratory However the standardsquirrel cage rotor will cause problem when it is used in abearingless inductionmotor to produce the radial suspensionforce As known a sudden change in the radial suspensionforce will lead to a sudden change of the stator flux of thesuspension force winding The rotor flux however does notchange suddenly because the voltage is induced into the

rotor circuit which generates the rotor currentTherefore theinteraction of stator and rotor circuits will engender a delay inthe flux of the suspension force winding which in turn delaysthe radial suspension force response

In order to conquer the problem associated with the con-ventional squirrel cage rotor Chiba and Fukao [19] proposeda novel bearingless inductionmotorwith an optimal designedrotor circuits The proposed bearingless induction motorwith 4-pole torque and 2-pole suspension force windings hasa 4-pole pole-specific rotor short circuit Four rotor bars areconnected by four end-ring segments (rather than completerings) so that a 4-pole circuit is constructed If a 4-polerotating magnetic field of the torque winding is applied thecirculating current is generated in the short circuitsHoweverthere is no current when a 2-pole rotating magnetic field ofthe suspension winding is applied because the EMFs inducedinto the circuits sum to zero Therefore there is no mutualinductance between the rotor and suspension force windingsand the radial suspension force is also not influenced by theinduced rotor current

In the 2-DOF bearingless induction motors the motorswith two sets of windings one for generating torque andanother for producing the radial suspension forces areprimarily researched Besides Ribeiro et al [20] proposedanother structure of the bearingless induction motor inwhich the 3-phase windings of a 4-pole off-shelf inductionmotor are splitting into two sets of 3-phase windings and itsmidpoint is grounded The corresponding configuration ofthe split-phase bearingless induction motor drive system isshown in Figure 2 in which there are six windings namelywindings 119886 119887 and 119888 and windings minus119886 minus119887 and minus119888 The radialsuspension force can be generated by using a phase currentdeviation parcel Δ119894 in a group of two windings in the samedirection For instance if a positive radial suspension forcealong the 119910-axis is needed the windings 119886 and minus119886 are fedas presented in Figure 2 In this condition the motor phasecurrents for the rotor levitation scheme can be expressed as119894119886+Δ119894 and 119894

119886minusΔ119894The asymmetry caused by the introduction

of Δ119894 produces a resultant force in the 119910-axis In comparisonto the traditional bearingless induction motor with thestructure of double windings the split-phase bearinglessinduction motor with the single set of winding has theadvantages of simple structure low power loss low cost andso forth However it requires a nonstandard control strategyto accomplish a suitable motor operation

As it is well known the multiphase motor with phasesnumber not less than 5 has the multiple orthogonal 119889-119902planes One 119889-119902 plane can be utilized for the torque con-trol and the other 119889-119902 planes can be used in a differentmanner Based on this theory Huang et al [21] introducedthe multiphase motor technology into the single windingbearingless inductionmotor and proposed a 5-phase bearing-less induction motor with multiphase windings which cangenerate two needed rotating magnetic fields by feeding twogroups of currents to the single set of multiphase windings byusing a multiphase converter The 5-phase windings have thesame structure and each of them is 72∘ displaced in angularspace around the motor stator In the proposed bearinglessinduction motor one 119889-119902 plane is used for the motor drive

Mathematical Problems in Engineering 3

3-p

hase

inve

rter

3-p

hase

inve

rter

ia + Δi

ia minus Δiminusa

minusbminusc

a

bc

ic ic

ib

ib

Figure 2 Configuration of the split-phase bearingless inductionmotor drive system [20]

control and the other 119889-119902 plane is utilized for the rotor levita-tion controlThe proposedmotor not only has the advantagesof a simpler structure and lowpower switch loss of bearinglessmotors with a single set of windings but also possessesadvantages of high power ratings with lower voltage limiteddevices of the multiphase motors In addition the proposedmotor also has the redundant features and it is most viablefor fault-tolerant operation

32 4-DOF Bearingless Induction Motor As stated earlierthe 2-DOF bearingless induction motors are primarily usedin the laboratory as the principle prototypes It is worthto mention that evaluating the performance of the rotorlevitation as well as electric motor characteristics is necessaryfor them to apply in the practical application In [22] Chibaet al proposed a 4-DOF bearingless induction motor and itsstructure diagram is shown in Figure 3 The 4-DOF bearing-less induction motor consists of two tandem 2-DOF bear-ingless induction motor units The units 1 and 2 regulatethe radial shaft positions of the left and right shaft endsrespectively In each unit two sets of 3-phase windings arearranged in the stator core One is for motor torque controland the other is for radial suspension force control And therotating magnetic field can guarantee the horizontal shaftposition stable passively In the experimental platform arotor resistance identification method was introduced andcorresponding controller strategy was designed Finally theexperimental studies were carried out and the results con-firmed that the proposed control strategy for rotor resistanceidentification is effective in compensating the adverse effectsof temperature increase for the stable operation of the 4-DOFbearingless induction motors

33 5-DOF Bearingless Induction Motor In Figure 3 the 4-DOF bearingless induction motor is split into two 2-DOFbearingless induction motors which together provide thetotal torque and 2-DOF radial suspension of the rotor inthe left and right shaft ends respectively In case of big axialsuspension forces or strict requirements to axial positioningan axial magnetic bearing needs to be added In [23]Santisteban et al proposed a 5-DOF bearingless inductionmotor consisting of two 2-DOF bearingless induction motorunits and an axialmagnetic bearing unit as shown in Figure 4Besides some advantages for example low friction and lowmaintenance the 5-DOF bearingless induction motor has

2-DOF bearinglessinduction motor unit 1


Figure 3 Structure diagram of 4-DOF bearingless inductionmotor

Axial magneticbearing



Figure 4 Structure diagram of 5-DOF bearingless induction motor(one structure) [23]

2-DOF bearinglessinduction motor unit

1

3-DOF axial-radialmagnetic bearing

Figure 5 Structure diagram of the 5-DOF bearingless inductionmotor (another structure) [24]

many disadvantages such as complex mechanical structureincreased shaft length limited critical rotor speed reducedshaft resonance frequencies need for special iron lamina-tions anddc choppers which increase systemcomplexity andcost In addition synchronization control between the two2-DOF bearingless induction motors is indispensable whichresults in the complicated decoupling control system

In viewof the insufficient of the 5-DOFbearingless induc-tion motor proposed in [23] an innovative 5-DOF bearing-less induction motor consisting of a 2-DOF bearinglessinduction motor and a 3-DOF axial-radial magnetic bearingis proposed in [24] as shown in Figure 5 Since the 3-DOFcombined axial-radial magnetic bearing with permanent


magnet bias excitation possesses the ability of integrating theaxial and radial suspension forces generation into one unitthe axial length of the rotor is reduced and the axial utiliza-tion rate is increased which further promote the criticalspeed and power density the of the 5-DOF bearingless induc-tion motor

4 Mathematical Model

The mathematical models including electromagnetic torqueand radial suspension force equations are the theoreticalfoundation of the bearingless inductionmotor Obtaining theaccurate mathematical expressions of the electromagnetismtorque and the radial suspension force is critical to realizethe stable suspension operation of the bearingless inductionmotor

41 Radial Suspension Force Model Basically the method ofcalculating the radial suspension force can be classified as twokinds of methods virtual displacement method [4 8 22 26]and Maxwell tensor method [27ndash29]

411 Virtual Displacement Method The inductance matrix[L] of two sets of the windings of the bearingless inductionmotor can be derived according to the equivalent magneticcircuit principle which are given by

[L] =

[

[

[

[

119871119872

0 minus119872119909 119872119910

0 119871119872

119872119910 119872119909

minus119872119909 119872119910 119871119861

0

119872119910 119872119909 0 119871119861

]

]

]

]

(1)

where 119871119872and 119871

119861are self-inductances of torque and suspen-

sion force windings respectively119872 is the mutual inductancecoefficient of torque and suspension force windings and 119909

and 119910 are the rotor radial displacement in the 119909- and 119910-directions respectively Subscripts 119872 and 119861 correspond totorque winding and suspension force winding respectively(the same hereafter) And the current matrix [i] of the torqueand suspension force windings can be written as

[i] = [119894119872119889119894119872119902

119894119861119889

119894119861119902]

119879

(2)

where 119894119872119889

and 119894119872119902

are current components of torque wind-ings in 119889-119902 coordinate respectively and 119894

119861119889and 119894119861119902

are cur-rent components of suspension force windings in 119889-119902 coor-dinate respectively And then the expression of the electro-magnetic energy is gotten according to the energy conversionrelationship which is written as

119882119898

=

1

2

[i]119879 [L] [i] (3)

Finally the model of the radial suspension force canbe obtained by the virtual displacement method which isexpressed as

[

119865119909

119865119910

] =

[

[

[

[

120597W119898

120597119909

120597W119898

120597119910

]

]

]

]

= 119872[

minus119894119872119889

119894119872119902

119894119872119902

119894119872119889

] [

119894119861119889

119894119861119902

] (4)

412 Maxwell Tensor Method The airgap magnetic fluxdensity of the bearingless induction motor is collectivelyproduced by the torque and suspension force windings andit can be written as

119861 (120593) = 119861119872cos (119901

119872120593 minus 120596119872119905 + 120583) + 119861

119861cos (119901

119861120593 minus 120596119861119905 + 120582)

(5)

where 120593 is the space position angle 120583 and 120582 are initial phaseangles of torque and suspension windings respectively and119861119872

and 119861119861are the amplitude of the airgap magnetic flux

density of torque and suspension windings respectively Forthe airgap flux density 119861 the Maxwell force element whichacts on a surface element 119889119860 of the rotor can be expressed as

119889119865 =

1198612

21205830

119889119860 (6)

where 1205830is the vacuum magnetic permeability and d119860 is the

infinitesimal surface element of the rotorBy integrating (6) when 119901

119861= 119901119872

+1 the Maxwell forcesin the 119909- and 119910-directions can be given as

119865119909= 119865119872cos (120582 minus 120583)

119865119910= 119865119872sin (120582 minus 120583)

(7)

where 119901119872

and 119901119861are the pole-pair numbers of torque and

suspension force winding respectively 119865119909and 119865

119910are the

Maxwell forces in 119909- and 119910-direction respectively 119865119872

=

11989711990312058711986111987211986111986121205830is the amplitude ofMaxwell force 119897 is the active

core length and 119903 is the rotor outer radiusThe airgap flux linkage of torque and suspension force

windings can be expressed as

Ψ119872

=

2119897119903119861119872119873119872

119901119872

Ψ119861=

2119897119903119861119861119873119872

119901119861

asymp 119871119898119861

119894119861

(8)

where 119871119898119861

is the mutual inductance of the suspension forcewindings and 119873

119872and 119873

119861are number of turns of the torque

and suspension force windings respectivelyBased on the vector multiplication operation (7) can be

expressed in the 119889-119902 rotating coordinate as

119865119909= 119896119872

(119894119861119889

Ψ119872119889

+ 119894119861119902

Ψ119872119902

)

119865119910= 119896119872

(119894119861119902

Ψ119872119889

minus 119894119861119889

Ψ119872119902

)

(9)

where 119865119872

= 120587119901119872119901119861119871119898119861

21198971199031205830119873119872119873119861 Ψ119872119889

and Ψ119872119902

arethe airgap flux linkages components of torque windings in119889-119902 coordinates respectively and Ψ

119861119889and Ψ

119861119902are the airgap

flux linkages components of suspension forcewindings in119889-119902coordinates respectively

In the process of practical operation the eccentricity ofthe stator and rotor is inescapable which will lead to complexanalysis and computation of the radial suspension force Inorder to improve the control precision of the radial suspen-sion force an accurate radial suspension force expression


considering the rotor positioning eccentricity was established[30] which is suitable for real-time computation in rotorsuspension control application In addition the computationaccuracy of the proposed radial suspension force modelwas verified by the Finite Element (FE) analysis And thena novel radial suspension force feedback control methodfor the bearingless induction motor was proposed on thebasis of the aforementioned radial suspension force modeland corresponding simulation studies were carried out Theresearch results indicated that the proposed radial suspensionforce model as well as the corresponding control strategycould improve the radial positioning control accuracy of therotor markedly and enhance the overall static and dynamicbehaviors of stable suspension operation obviously for thebearingless induction motor

42 Electromagnetic Torque Equation In comparison to themagnetic field produced by torque windings the magneticfield produced by suspension force windings is so small thatit can be ignored So the airgap flux linkages equation of thetorque windings can be expressed as

Ψ119872119889

= 119871119898119872

(119894119872119889

+ 119894119872119903119889

)

Ψ119872119902

= 119871119898119872

(119894119872119902

+ 119894119872119903119902

)

(10)

where 119894119872119903119889

and 119894119872119903119902

are rotor current components of torquewindings in119889-119902 coordinate respectively And the electromag-netic torque equation can be written as

119879119890= 119901119872

(119894119872119902

Ψ119872119889

minus 119894119872119889

Ψ119872119902

) (11)

5 Control Strategies

51 Vector Control The vector control (VC) strategy includesairgap flux oriented control and rotor flux oriented controland in this section the rotor flux oriented control for thebearingless induction motor is presented as an example

When the rotor flux oriented control method is adoptedthe rotor flux vector of torque windings is aligned with d-axis which means that the rotor flux linkages components oftorque windings can be given as Ψ

119872119889119903= Ψ119872119903

and Ψ119872119902119903

=

0 Then the torque winding currents 119894119872119889

and 119894119872119902

the slipangular speed 120596

119904 and the electromagnetic torque 119879

119890can be

expressed as

119894119872119889

=

119871119872119903

119901119872

+ 1

119877119872119903

119871119898119872

Ψ119872119903

119894119872119902

=

119879119890119871119872119903

119901119872119871119898119872

Ψ119872119903

120596119904=

119877119872119903

119871119898119872

119871119872119903

Ψ119872119903

119894119872119902

119879119890= 119901119872

119871119898119872

119871119872119903

119894119872119902

Ψ119872119903

(12)

where 119871119872119903

and 119877119872119903

are the rotor inductance and resistanceof torque windings respectivelyΨ

119872119889119903andΨ

119872119902119903are rotor flux

linkages components of torque windings respectively and119871119898119872

is the mutual inductance of torque windingsFrom (9) we can see that the radial suspension forces

are related to the airgap flux linkages of the torque windingsTherefore only after the airgap flux linkages are obtained theycan be used to calculate the radial suspension forces In viewof the relationship between airgap flux and rotor flux linkagesthe rotor flux linkages and stator currents of torque windingsare used to identify the airgap flux linkages which can beexpressed as

Ψ119872119889

=

119871119898119872

119871119872119903

(Ψ119872119889119903

+ 119871119872119903119897

119894119872119889

)

Ψ119872119902

=

119871119898119872

119871119872119903

119871119872119903119897

119894119872119902

(13)

where 119871119872119903119897

is the rotor leakage inductance of the torquewindings After the airgap is obtained the suspension forcewinding currents can be determined in accordance with (9)By solving (9) we obtain

[

119894119861119889

119894119861119902

] =

1

119896

[

cos 120588 minus sin 120588

sin 120588 cos 120588 ] [

119865119909

119865119910

] (14)

where 119896 = 119870119872radic

Ψ2

119872119889+ Ψ2

119872119902and 120588 = arctan(Ψ

119872119902Ψ119872119889

) Thecontrol block diagram of the rotor flux oriented control isshown in Figure 6

52 Independent Control Radial suspension force and torqueare the control objectives that determine the machine perfor-mance of levitation and rotation in a bearingless inductionmotor However from (9) it can be seen that the informationin regards to the airgap flux linkages of the torque windingsis crucial for the radial suspension force control As for theVC there is the time delay of the information transmissionbetween torque control and radial suspension force controlsystems which leads to the restriction between the controlschemes of torque and suspension force windings and fur-ther affects the whole control performance of bearinglessinductionmotor drives To effectively avoid the disadvantagethe independent control (IC) strategy for the bearinglessinduction motor was proposed [25] and the correspondingcontrol block diagram is shown in Figure 7 The airgap fluxlinkage of the torque windings can be identified by usingthe conventional voltage-current model which can realizethe torque and radial suspension force separately controlledby different variables and hence simplifying the controlalgorithm of the torque winding

53 Direct Torque Control Direct torque control (DTC) is apowerful and attractive control strategy with a simple struc-ture fast behavior and tolerance to the variation of motorparameters which offers direct and effective control of statorflux and torque by optimally selecting the inverter switchstates in each sampling period The DTC method provides asystematic solution for improving the operating characteris-tics of themotor aswell as the voltage source inverter In orderto overcome the limitations such as complexity unsteady


xxlowast

ylowasty+

+

+

++

minus

minus

minus

Flowastx

Flowasty

ilowastBd

ilowastBq(14) VRminus1

VRminus1

ilowastBa

ilowastBb

ilowastBc

iBaiBb

iBcMotor

Gapsensor

Rotaryencoder

120596r

120596r

120596lowastr

120596lowasts

PI

PID

PID

120595lowastMr

Tlowaste

(12)

(13)120588lowast

120595lowastMd 120595lowast

Mq

ilowastMd

ilowastMq

ilowastMa

ilowastMb

ilowastMc

iMa

iMb

iMc

23

23 CRPWM

CRPWM

Speed detector

Value absolutingFlux linkage generatorIntegrator

VRminus1 Inverse park transformation23 Inverse clark transformation

ilowastB120572

ilowastB120573

ilowastM120572

ilowastM120573

120579r120579lowasts

120579lowast2

120579lowast1

Figure 6 Control block diagram of the rotor flux oriented control

Observationof torquewinding

flux linage

Generalfrequencyconverter

xlowast

ylowast

y

x

+

+

minus

minus

Flowastx

Flowasty

ilowastBa

ilowastBb

ilowastBc

iBa

iBb

iBc

MotorPID

PID23

32

CRPWM

ilowastB120572

ilowastB120573

120595lowastM120572

120595lowastM120573

uM120572

uM120573

iM120572

iM120573

iMa

iMb

iMc

uMa

uMb

uMc

iMa iMb

algorithmIC

Figure 7 Control block diagram of the IC [25]

torque and nonlinearity in the VC algorithm Wang et alproposed a space vector pulse width modulation (SVPWM-) based DTC method for the bearingless induction motordrives [31] The small signal model of Maxwell force wasadopted to analyze the influence of the current ripple oftorque windings on radial suspension force The outputs ofthe torque PI and flux PI modulators namely flux phaseangle and amplitude increments provided proper voltagevectors via the inverter in such a way that these two variableswere forced to be predefined trajectories In addition a regu-lator for phase angle increment was also adopted to solve thedisturbance problems in torque and flux loops The experi-mental results have validated that the proposed algorithmhasa better performance in reducing disturbances of current andtorque and hence improving the suspension performance ofthe bearingless induction motor

54 Nonlinear Decoupling Control Thebearingless inductionmotor is a multivariable nonlinear and strong coupledsystem which makes the control of the whole system morecomplex To realize the bearingless induction motor suspen-sion operation steadily and reliably it is necessary to achievethe nonlinear decoupling control (NDC) between torque andradial suspension forces independently As for the decouplingcontrol of the bearingless induction motor the traditionalapproach is the VC method Its control performance isacceptable when the rotor always suspends at the center of theairgap Moreover the VC method is essentially a steady-statedecoupling control which can only achieve the decouplingcontrol between radial suspension forces and electromagnetictorque but cannot realize the dynamic decoupling control ofthem Therefore the dynamic response performance is notsatisfactory


5 D

OF

bear

ingl

ess i

nduc

tion

mot

or

PD

PI

PI

PD

PD

PD

PD

xlowastl

ylowastl

zlowast

xlowastr

ylowastr

120596lowast

120595lowastr

xl

yl

z

xr

yr

120596

120595r

l

yl

z

xr

yr

120595r

Sminus1

Sminus1

Sminus1Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

ANN inverse

Stat

ic A

NN

ilx

ily

i998400z

id1s

iq1s

id2s

iq2s

+

+

+

+

+

+

+

minus

minus

minus

minus

minus

minus

minus

x

Figure 8 Control block diagram of the ANNI method [24]

In [32] the inverse system method is proposed by Zhuet al for the nonlinear decoupling control of the bearinglessinduction motor By applying the inverse method the bear-ingless inductionmotor system is decoupled into two 2-orderlinear displacement subsystems a 1-order linear speed sub-system and a 1-order linear magnetic linkage subsystemBased on this the linear control techniques were applied todesign the close-loop regulators of these pseudo-linear sys-tems However the decoupling and the linearization of mul-tivariate nonlinear system with the inverse system methoddemand a precise mathematical model of the controlledobject Since there are some uncertain nonlinear factors inthe practical operation such as load disturbance rotor eccen-tricity and rotor parameter variation a high-precision fast-response control is not easy to be achieved by the inversesystem approach

As it is well-known the static artificial neural network(ANN) such as radial basis function network and multilayerneural network has the ability to learn and self-adaptapproximate any arbitrary nonlinear mapping and have theeffective control to complex and uncertain system Takingthe advantage of approximating ability of the static ANNa kind of continuous dynamic ANN structure was formedin [24] by introducing integrators to a static ANN andthen the ANN inverse (ANNI) method was proposed forthe nonlinear decoupling control of the 5-DOF bearinglessinductionmotorsThe static ANN is adopted to approach theinversion of the bearingless induction motor and the inte-grators are used to characterize its dynamic characteristicsThe corresponding control diagram of the ANNI method isshown in Figure 8

55 Sensorless Control Similar to the conventional inductionmotors the rotor position information which is traditionallymeasured by a physical sensor is mandatory for the properoperation of the bearingless inductionmotor In addition themechanical displacement sensors are also indispensable for

the stable suspension operation In order to avoid some dif-ficulties resulting from the traditional sensor control methodand effectively reduce the cost and short a shaft length thesensorless control (SC) of bearingless induction motor wasimplemented [33] The proposed SC method is based onthe detection of currents induced by mutual inductanceswhich vary as a function of the rotor radial displacements Bysuperimposing a high-frequency carrier voltage on the torquewindings the induced carrier-frequency current componentis obvious from the suspension force winding current More-over a simple current estimator is designed to eliminate thecarrier-frequency component originated from the transientvoltage of the suspension force windings

56 Comparison of Control Strategies The main advantagesmajor disadvantages and typical techniques of the aforemen-tioned control strategies are compared and the correspond-ing conclusions are summed up as shown in Table 1 As forthe NDC the ANNI control is used for exemplification as anexample

6 Development Trends

In this section several emerging development trends of thebearingless induction motor are identified and discussed

61 Prototype Structure Generally to make the bearinglessinduction motor drives satisfy the requirements of engi-neering application it is necessary to achieve the suspen-sion control of the radial 4-DOF and axial single-DOFcontrol of the rotor The aforementioned two kinds of the5-DOF bearingless induction motors must be configuredwith magnetic bearings which increases the axial length ofthe rotor and the reactive power losses of the system andrestricts the enhancement of the critical speed and the systemefficiencyTherefore an intensive study on designing novel 5-DOF bearingless induction motor prototype structure with a


Table 1 Comparison of control strategies

Advantages Disadvantages Techniques

VCRealizing easily no specialrequirements for hardwareand software

Causing coupling betweentwo sets of the windings

Generating the currentcontrol signals using thefeedback and coordinatetransformation

ICAchieving IC of radialsuspension force and henceimproving the flexibility oftorque control scheme

Requiring additionalmagnetic flux observer

Obtaining the torquewinding flux linagedependently

DTCFast torque response lessparameter dependence noneed for current control

Causing errors due tovariation of statorresistance and drift in fluxlinkage estimation

Generating the voltagevectors using independenttorque and fluxcomputations

NDCFlexible control algorithmsadapting nonlinear theoriesand parameter variations

Requiring sophisticatedhardware and intensivecomputation orexperiential knowledge

Taking advantage of neuralnetwork or other nonlineartheory

SC

Removing the mechanicalsensors and hencereducing the system costand size readily merginginto other controls

Requiring sophisticatedhardware and intensivecomputation

Estimating the position anddisplacement based on themotor mutual inductance

simple motor topology low power losses and high efficiencyis of great practical significance

62 Advanced Control As for the control strategies of thesuspension force windings the most common method isthe radial displacement negative feedback modulation-basedcontrol strategy which requires the complicated forcecur-rent transformation and coordinate transformations As aresult the algorithm is more complex which seriously influ-ence the dynamic response and anti-interference ability ofthe bearingless inductionmotorsTherefore it is necessary todevelop the new control strategy for the suspension controlof the rotor Among these control algorithms the directradial suspension force control which can be inspired bythe DTC method will be the next research hot spot of theradial suspension force control for the bearingless inductionmotors

63 Sensor Integration and Sensorless Technologies Currentspeed displacement and temperature sensors which are thevery important part of the drive system for bearingless induc-tion motors play an important role for the table suspensionoperation of the whole system However these sensors arealso the potential fault hidden troubles since after long-timeuse they cause problems and then lead to the misoperationand malfunction of the whole control system In this casethe sensorless technologies may be the preferred solutionAlthough some sensorless technologies have been proposedseparately for the position or displacement detection by inter-national and domestic academics and experts the positionand displacement sensorless operation of bearingless induc-tion motor was still investigated separately which cannotrealize the integrated self-sensing of the rotor position and

displacement Therefore to do some research to implementthe integrated sensorless suspension operation the functionintegration of the prototype and sensors has importantpractical significance and theoretical value

64 Reliability Technology Reliability is one of themost criti-cal requirements in some special applications such as turbo-molecular pumps canned pumps and centrifugal machineswhere a continuous operation must be ensured Under thepremise of satisfying each performance index of the bearing-less inductionmotors the study on developing the redundantor conservative design techniques and the fault-tolerant con-trol strategies so as to reduce or avoid the unnecessary lossescaused by the failures has very important practical meaningand is also an important issue for the researchers in this field

7 Conclusion

In this paper the concepts key technologies developmentsand potential trends of bearingless induction motors havebeen reviewed with particularly emphasis on the opera-tion principles motor topologies mathematical models andcontrol strategies Some selected control strategies are alsocompared In addition there are many issues which stillneed to be investigated such as the novel motor topologiesadvanced control algorithms and sensor integration andsensorless technologies as well as reliability technology forspecific applications

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper


Acknowledgment

This work was supported by the National Natural Sci-ence Foundation of China under Project nos 51305170 and61104016 the National Science Foundation of Jiangsu Pro-vince of China under Project no BK20130515 the ChinaPostdoctoral Science Foundation which funded the projectunder Project no 2012M521012 and the Startup Foundationfor Advanced Professional Talents of Jiangsu Universityunder Project no 12JDG057

References

[1] P K Hermann ldquoA radial active magnetic bearingrdquo LondonPatent Patent 1973

[2] R Bosch ldquoDevelopment of a bearingless motorrdquo in Proceedingsof the International Conference of Electric Machines (ICEM rsquo88)pp 373ndash375 Pisa Italy September 1988

[3] A Chiba M Hanazawa T Fukao and M Azizur RahmanldquoEffects of magnetic saturation on radial force of bearinglesssynchronous reluctance motorsrdquo IEEE Transactions on IndustryApplications vol 32 no 2 pp 354ndash362 1996

[4] W Bu S Huang S Wan and W Liu ldquoGeneral analytical mod-els of inductance matrices of four-pole bearingless motors withtwo-pole controlling windingsrdquo IEEE Transactions on Magnet-ics vol 45 no 9 pp 3316ndash3321 2009

[5] L Chen and W Hofmann ldquoSpeed regulation technique of onebearingless 86 switched reluctance motor with simpler singlewinding structurerdquo IEEE Transactions on Industrial Electronicsvol 59 no 6 pp 2592ndash2600 2012

[6] H Wang Y Wang X Liu and J-W Ahn ldquoDesign of novelbearingless switched reluctance motorrdquo IET Electric PowerApplications vol 6 no 2 pp 73ndash81 2012

[7] M Henzel K Falkowski and M Zokowski ldquoThe analysis ofthe control system for the bearingless induction electric motorrdquoJournal of Vibroengineering vol 14 no 1 pp 16ndash21 2012

[8] A Chiba and J A Santisteban ldquoA PWMharmonics eliminationmethod in simultaneous estimation of magnetic field and dis-placements in bearingless inductionmotorsrdquo IEEETransactionson Industry Applications vol 48 no 1 pp 124ndash131 2012

[9] X-D Sun H-Q Zhu and W Pan ldquoDecoupling control ofbearingless permanent magnet-type synchronous motor usingartificial neural networks-based inverse system methodrdquo Inter-national Journal of Modelling Identification and Control vol 8no 2 pp 114ndash121 2009

[10] M Ooshima A Chiba T Fukao and M Azizur RahmanldquoDesign and analysis of permanent magnet-type bearinglessmotorsrdquo IEEE Transactions on Industrial Electronics vol 43 no2 pp 292ndash299 1996

[11] K Inagaki A Chiba M A Rahman and T Fukao ldquoPerfor-mance characteristics of inset-type permanentmagnet bearing-less motor drivesrdquo in Proceedings of the IEEE Power EngineeringSociety Winter Meeting pp 202ndash207 Singapore January 2000

[12] Y Okada S Miyamoto and T Ohishi ldquoLevitation and torquecontrol of internal permanent magnet type bearingless motorrdquoIEEE Transactions on Control Systems Technology vol 4 no 5pp 565ndash571 1996

[13] Z Ren L S Stephens and A V Radun ldquoImprovements onwinding flux models for a slotless self-bearing motorrdquo IEEETransactions on Magnetics vol 42 no 7 pp 1838ndash1848 2006

[14] Z Ren and L S Stephens ldquoForce characteristics and gain deter-mination for a slotless self-bearing motorrdquo IEEE Transactionson Magnetics vol 42 no 7 pp 1849ndash1860 2006

[15] J Asama R Kawata T Tamura T Oiwa and A Chiba ldquoReduc-tion of force interference and performance improvement of aconsequent-pole bearingless motorrdquo Precision Engineering vol36 no 1 pp 10ndash18 2012

[16] J Asama M Amada N Tanabe et al ldquoEvaluation of a bearing-less PMmotor with wide magnetic gapsrdquo IEEE Transactions onEnergy Conversion vol 25 no 4 pp 957ndash964 2010

[17] M Ooshima and C Takeuchi ldquoMagnetic suspension perfor-mance of a bearingless brushless DC motor for small liquidpumpsrdquo IEEE Transactions on Industry Applications vol 47 no1 pp 72ndash78 2011

[18] H Grabner W Amrhein S Silber and W Gruber ldquoNonlin-ear feedback control of a bearingless brushless DC motorrdquoIEEEASME Transactions onMechatronics vol 15 no 1 pp 40ndash47 2010

[19] A Chiba and T Fukao ldquoOptimal design of rotor circuits ininduction type bearingless motorsrdquo IEEE Transactions on Mag-netics vol 34 no 4 pp 2108ndash2110 1998

[20] R L A Ribeiro F E F Castro A O Salazar and A L MaitellildquoA suitable current control strategy for split-phase bearinglessthree-phase inductionmachinerdquo in Proceedings of the 36th IEEEPower Electronics Specialists Conference pp 701ndash706 RecifeBrazil June 2005

[21] J Huang M Kang and J-Q Yang ldquoAnalysis of a new 5-phasebearingless induction motorrdquo Journal of Zhejiang University Avol 8 no 8 pp 1311ndash1319 2007

[22] A Chiba D Akamatsu T Fukao and M A Rahman ldquoAnimproved rotor resistance identification method for magneticfield regulation in bearingless induction motor drivesrdquo IEEETransactions on Industrial Electronics vol 55 no 2 pp 852ndash8602008

[23] J Santisteban O Salazar R Stephan and W Dunford ldquoAbearingless machinemdashan alternative approachrdquo in Proceedingsof the 5th International Symposium onMagnetic Bearings (ISMBrsquo96) pp 345ndash349 Kanazawa Japan August 1996

[24] X Sun and H Zhu ldquoArtificial neural networks inverse controlof 5 degrees of freedom bearingless induction motorrdquo Interna-tional Journal of Modelling Identification and Control vol 15no 3 pp 156ndash163 2012

[25] Z-Q Deng X-L Wang B Li L-G He and Y-G Yan ldquoStudyon independent control of the levitation subsystem of bear-ingless induction motorsrdquo Proceedings of the Chinese Society ofElectrical Engineering vol 23 no 9 pp 107ndash111 2003

[26] Z Yang X Sun M Wang and H Zhu ldquoDecoupling controlof bearingless induction motors based on least squares supportvector machine inverserdquo Journal of Computational andTheoret-ical Nanoscience vol 11 no 5 pp 1403ndash1409 2014

[27] U A U Amirulddin G M Asher P Sewell and K J BradleyldquoDynamic field modelling of torque and radial forces in vec-tor-controlled inductionmachines with bearing reliefrdquo IEE Pro-ceedings Electric Power Applications vol 152 pp 894ndash904 2005

[28] U A U Amirulddin G M Asher P Sewell and K J BradleyldquoDynamic field modelling of torque and radial forces in vec-tor-controlled inductionmachines with bearing reliefrdquo IEE Pro-ceedings-Electric PowerApplications vol 152 pp 894ndash904 2005

[29] A Laiho A Sinervo J Orivuori K Tammi A Arkkio andK Zenger ldquoAttenuation of harmonic rotor vibration in a cagerotor induction machine by a self-bearing force actuatorrdquo IEEETransactions on Magnetics vol 45 no 12 pp 5388ndash5398 2009


[30] Y He and H Nian ldquoAnalytical model and feedback control ofthe levitation force for an induction-type bearingless motorrdquoin Proceedings of the the 5th International Conference on PowerElectronics and Drive Systems pp 242ndash246 2003

[31] YWang Z-Q Deng and X-LWang ldquoDirect torque control ofbearingless induction motorrdquo Proceedings of the Chinese Societyof Electrical Engineering vol 28 no 21 pp 80ndash84 2008

[32] H-Q Zhu Y Zhou T-B Li andX-X Liu ldquoDecoupling controlof 5 degrees of freedom bearingless induction motors using 120572-th order inverse system methodrdquo Acta Automatica Sinica vol33 no 3 pp 273ndash278 2007

[33] T Tera Y Yamauchi A Chiba T Fukao and M A RahmanldquoPerformances of bearingless and sensorless induction motordrive based on mutual inductances and rotor displacementsestimationrdquo IEEE Transactions on Industrial Electronics vol 53no 1 pp 187ndash194 2006

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Airgap 2-2Airgap 1-1

120572F120572iB120573iB120573

iM120573

iM120573

iM120573

iM120572iM120572

iM120572iM120572

iB120572

iB120572

iM120573

120573

Ψ2Ψ4

Figure 1 Principle of radial suspension forces generation

2 Principle of Radial SuspensionForce Generation

The basic winding configuration of a bearingless inductionmotor in the stationary perpendiculars 120572- and 120573-axes isshown in Figure 1 Two sets of windings are wound inthe same stator slots One is the 4-pole windings for theproduction of the torque The other is the 2-pole windingsfor the production of the radial suspension force so as tocontrol the rotor radial position in the airgapThese windingsare referred as the torque and suspension force windingsrespectively

The main 4-pole flux Ψ4is generated by torque winding

current 119894119872120572

Under no-load balanced conditions if a positiveradial suspension force along the 120572-axis is needed the sus-pension force winding current 119894

119861120572is fed as shown in Figure 1

The flux density in the airgap 1-1 is increased because bothΨ2

and Ψ4fluxes are in the same direction On the other hand

the flux density in the airgap 2-2 is decreased because Ψ2

and Ψ4are in the opposite direction A positive suspension

force 119865120572is produced in the 120572-axis direction only The reverse

current can produce the opposite radial suspension forceThe radial suspension force 119865

120573in the 120573-axis direction can be

produced using electrically perpendicular 2-pole suspensionforce winding current 119894

119861120573distribution

3 Motor Topologies

31 2 Degrees of Freedom (DOF) Bearingless Induction MotorAt present the bearingless induction motor topologies aremainly concentrated in the 2-DOF 3-phase squirrel cagetype bearingless induction motors which are usually used asprinciple prototypes in the laboratory However the standardsquirrel cage rotor will cause problem when it is used in abearingless inductionmotor to produce the radial suspensionforce As known a sudden change in the radial suspensionforce will lead to a sudden change of the stator flux of thesuspension force winding The rotor flux however does notchange suddenly because the voltage is induced into the

rotor circuit which generates the rotor currentTherefore theinteraction of stator and rotor circuits will engender a delay inthe flux of the suspension force winding which in turn delaysthe radial suspension force response

In order to conquer the problem associated with the con-ventional squirrel cage rotor Chiba and Fukao [19] proposeda novel bearingless inductionmotorwith an optimal designedrotor circuits The proposed bearingless induction motorwith 4-pole torque and 2-pole suspension force windings hasa 4-pole pole-specific rotor short circuit Four rotor bars areconnected by four end-ring segments (rather than completerings) so that a 4-pole circuit is constructed If a 4-polerotating magnetic field of the torque winding is applied thecirculating current is generated in the short circuitsHoweverthere is no current when a 2-pole rotating magnetic field ofthe suspension winding is applied because the EMFs inducedinto the circuits sum to zero Therefore there is no mutualinductance between the rotor and suspension force windingsand the radial suspension force is also not influenced by theinduced rotor current

In the 2-DOF bearingless induction motors the motorswith two sets of windings one for generating torque andanother for producing the radial suspension forces areprimarily researched Besides Ribeiro et al [20] proposedanother structure of the bearingless induction motor inwhich the 3-phase windings of a 4-pole off-shelf inductionmotor are splitting into two sets of 3-phase windings and itsmidpoint is grounded The corresponding configuration ofthe split-phase bearingless induction motor drive system isshown in Figure 2 in which there are six windings namelywindings 119886 119887 and 119888 and windings minus119886 minus119887 and minus119888 The radialsuspension force can be generated by using a phase currentdeviation parcel Δ119894 in a group of two windings in the samedirection For instance if a positive radial suspension forcealong the 119910-axis is needed the windings 119886 and minus119886 are fedas presented in Figure 2 In this condition the motor phasecurrents for the rotor levitation scheme can be expressed as119894119886+Δ119894 and 119894

119886minusΔ119894The asymmetry caused by the introduction

of Δ119894 produces a resultant force in the 119910-axis In comparisonto the traditional bearingless induction motor with thestructure of double windings the split-phase bearinglessinduction motor with the single set of winding has theadvantages of simple structure low power loss low cost andso forth However it requires a nonstandard control strategyto accomplish a suitable motor operation

As it is well known the multiphase motor with phasesnumber not less than 5 has the multiple orthogonal 119889-119902planes One 119889-119902 plane can be utilized for the torque con-trol and the other 119889-119902 planes can be used in a differentmanner Based on this theory Huang et al [21] introducedthe multiphase motor technology into the single windingbearingless inductionmotor and proposed a 5-phase bearing-less induction motor with multiphase windings which cangenerate two needed rotating magnetic fields by feeding twogroups of currents to the single set of multiphase windings byusing a multiphase converter The 5-phase windings have thesame structure and each of them is 72∘ displaced in angularspace around the motor stator In the proposed bearinglessinduction motor one 119889-119902 plane is used for the motor drive


3-p

hase

inve

rter

3-p

hase

inve

rter

ia + Δi

ia minus Δiminusa

minusbminusc

a

bc

ic ic

ib

ib













1











[L] =

[

[

[

[

119871119872

0 minus119872119909 119872119910

0 119871119872

119872119910 119872119909

minus119872119909 119872119910 119871119861

0

119872119910 119872119909 0 119871119861

]

]

]

]

(1)

where 119871119872and 119871




[i] = [119894119872119889119894119872119902

119894119861119889

119894119861119902]

119879

(2)

where 119894119872119889

and 119894119872119902


119861119889and 119894119861119902


119882119898

=

1

2

[i]119879 [L] [i] (3)


[

119865119909

119865119910

] =

[

[

[

[

120597W119898

120597119909

120597W119898

120597119910

]

]

]

]

= 119872[

minus119894119872119889

119894119872119902

119894119872119902

119894119872119889

] [

119894119861119889

119894119861119902

] (4)


119861 (120593) = 119861119872cos (119901

119872120593 minus 120596119872119905 + 120583) + 119861

119861cos (119901

119861120593 minus 120596119861119905 + 120582)

(5)




119889119865 =

1198612

21205830

119889119860 (6)



119861= 119901119872


119865119909= 119865119872cos (120582 minus 120583)

119865119910= 119865119872sin (120582 minus 120583)

(7)

where 119901119872



119910are the


=




Ψ119872

=

2119897119903119861119872119873119872

119901119872

Ψ119861=

2119897119903119861119861119873119872

119901119861

asymp 119871119898119861

119894119861

(8)

where 119871119898119861


119872and 119873




119865119909= 119896119872

(119894119861119889

Ψ119872119889

+ 119894119861119902

Ψ119872119902

)

119865119910= 119896119872

(119894119861119902

Ψ119872119889

minus 119894119861119889

Ψ119872119902

)

(9)

where 119865119872

= 120587119901119872119901119861119871119898119861

21198971199031205830119873119872119873119861 Ψ119872119889

and Ψ119872119902


119861119889and Ψ







Ψ119872119889

= 119871119898119872

(119894119872119889

+ 119894119872119903119889

)

Ψ119872119902

= 119871119898119872

(119894119872119902

+ 119894119872119903119902

)

(10)

where 119894119872119903119889

and 119894119872119903119902


119879119890= 119901119872

(119894119872119902

Ψ119872119889

minus 119894119872119889

Ψ119872119902

) (11)




119872119889119903= Ψ119872119903

and Ψ119872119902119903

=


and 119894119872119902



119890can be

expressed as

119894119872119889

=

119871119872119903

119901119872

+ 1

119877119872119903

119871119898119872

Ψ119872119903

119894119872119902

=

119879119890119871119872119903

119901119872119871119898119872

Ψ119872119903

120596119904=

119877119872119903

119871119898119872

119871119872119903

Ψ119872119903

119894119872119902

119879119890= 119901119872

119871119898119872

119871119872119903

119894119872119902

Ψ119872119903

(12)

where 119871119872119903

and 119877119872119903


119872119889119903andΨ

119872119902119903are rotor flux




Ψ119872119889

=

119871119898119872

119871119872119903

(Ψ119872119889119903

+ 119871119872119903119897

119894119872119889

)

Ψ119872119902

=

119871119898119872

119871119872119903

119871119872119903119897

119894119872119902

(13)

where 119871119872119903119897


[

119894119861119889

119894119861119902

] =

1

119896

[


sin 120588 cos 120588 ] [

119865119909

119865119910

] (14)

where 119896 = 119870119872radic

Ψ2

119872119889+ Ψ2

119872119902and 120588 = arctan(Ψ

119872119902Ψ119872119889





xxlowast

ylowasty+

+

+

++

minus

minus

minus

Flowastx

Flowasty

ilowastBd


VRminus1

ilowastBa

ilowastBb

ilowastBc

iBaiBb

iBcMotor

Gapsensor

Rotaryencoder

120596r

120596r

120596lowastr

120596lowasts

PI

PID

PID

120595lowastMr

Tlowaste

(12)

(13)120588lowast


Mq

ilowastMd

ilowastMq

ilowastMa

ilowastMb

ilowastMc

iMa

iMb

iMc

23

23 CRPWM

CRPWM

Speed detector



ilowastB120572

ilowastB120573

ilowastM120572

ilowastM120573


120579lowast2

120579lowast1



flux linage


xlowast

ylowast

y

x

+

+

minus

minus

Flowastx

Flowasty

ilowastBa

ilowastBb

ilowastBc

iBa

iBb

iBc

MotorPID

PID23

32

CRPWM

ilowastB120572

ilowastB120573

120595lowastM120572

120595lowastM120573

uM120572

uM120573

iM120572

iM120573

iMa

iMb

iMc

uMa

uMb

uMc

iMa iMb

algorithmIC





5 D

OF

bear

ingl

ess i

nduc

tion

mot

or

PD

PI

PI

PD

PD

PD

PD

xlowastl

ylowastl

zlowast

xlowastr

ylowastr

120596lowast

120595lowastr

xl

yl

z

xr

yr

120596

120595r

l

yl

z

xr

yr

120595r

Sminus1

Sminus1

Sminus1Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

ANN inverse

Stat

ic A

NN

ilx

ily

i998400z

id1s

iq1s

id2s

iq2s

+

+

+

+

+

+

+

minus

minus

minus

minus

minus

minus

minus

x

























SC









7 Conclusion





Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










3-p

hase

inve

rter

3-p

hase

inve

rter

ia + Δi

ia minus Δiminusa

minusbminusc

a

bc

ic ic

ib

ib













1











[L] =

[

[

[

[

119871119872

0 minus119872119909 119872119910

0 119871119872

119872119910 119872119909

minus119872119909 119872119910 119871119861

0

119872119910 119872119909 0 119871119861

]

]

]

]

(1)

where 119871119872and 119871




[i] = [119894119872119889119894119872119902

119894119861119889

119894119861119902]

119879

(2)

where 119894119872119889

and 119894119872119902


119861119889and 119894119861119902


119882119898

=

1

2

[i]119879 [L] [i] (3)


[

119865119909

119865119910

] =

[

[

[

[

120597W119898

120597119909

120597W119898

120597119910

]

]

]

]

= 119872[

minus119894119872119889

119894119872119902

119894119872119902

119894119872119889

] [

119894119861119889

119894119861119902

] (4)


119861 (120593) = 119861119872cos (119901

119872120593 minus 120596119872119905 + 120583) + 119861

119861cos (119901

119861120593 minus 120596119861119905 + 120582)

(5)




119889119865 =

1198612

21205830

119889119860 (6)



119861= 119901119872


119865119909= 119865119872cos (120582 minus 120583)

119865119910= 119865119872sin (120582 minus 120583)

(7)

where 119901119872



119910are the


=




Ψ119872

=

2119897119903119861119872119873119872

119901119872

Ψ119861=

2119897119903119861119861119873119872

119901119861

asymp 119871119898119861

119894119861

(8)

where 119871119898119861


119872and 119873




119865119909= 119896119872

(119894119861119889

Ψ119872119889

+ 119894119861119902

Ψ119872119902

)

119865119910= 119896119872

(119894119861119902

Ψ119872119889

minus 119894119861119889

Ψ119872119902

)

(9)

where 119865119872

= 120587119901119872119901119861119871119898119861

21198971199031205830119873119872119873119861 Ψ119872119889

and Ψ119872119902


119861119889and Ψ







Ψ119872119889

= 119871119898119872

(119894119872119889

+ 119894119872119903119889

)

Ψ119872119902

= 119871119898119872

(119894119872119902

+ 119894119872119903119902

)

(10)

where 119894119872119903119889

and 119894119872119903119902


119879119890= 119901119872

(119894119872119902

Ψ119872119889

minus 119894119872119889

Ψ119872119902

) (11)




119872119889119903= Ψ119872119903

and Ψ119872119902119903

=


and 119894119872119902



119890can be

expressed as

119894119872119889

=

119871119872119903

119901119872

+ 1

119877119872119903

119871119898119872

Ψ119872119903

119894119872119902

=

119879119890119871119872119903

119901119872119871119898119872

Ψ119872119903

120596119904=

119877119872119903

119871119898119872

119871119872119903

Ψ119872119903

119894119872119902

119879119890= 119901119872

119871119898119872

119871119872119903

119894119872119902

Ψ119872119903

(12)

where 119871119872119903

and 119877119872119903


119872119889119903andΨ

119872119902119903are rotor flux




Ψ119872119889

=

119871119898119872

119871119872119903

(Ψ119872119889119903

+ 119871119872119903119897

119894119872119889

)

Ψ119872119902

=

119871119898119872

119871119872119903

119871119872119903119897

119894119872119902

(13)

where 119871119872119903119897


[

119894119861119889

119894119861119902

] =

1

119896

[


sin 120588 cos 120588 ] [

119865119909

119865119910

] (14)

where 119896 = 119870119872radic

Ψ2

119872119889+ Ψ2

119872119902and 120588 = arctan(Ψ

119872119902Ψ119872119889





xxlowast

ylowasty+

+

+

++

minus

minus

minus

Flowastx

Flowasty

ilowastBd


VRminus1

ilowastBa

ilowastBb

ilowastBc

iBaiBb

iBcMotor

Gapsensor

Rotaryencoder

120596r

120596r

120596lowastr

120596lowasts

PI

PID

PID

120595lowastMr

Tlowaste

(12)

(13)120588lowast


Mq

ilowastMd

ilowastMq

ilowastMa

ilowastMb

ilowastMc

iMa

iMb

iMc

23

23 CRPWM

CRPWM

Speed detector



ilowastB120572

ilowastB120573

ilowastM120572

ilowastM120573


120579lowast2

120579lowast1



flux linage


xlowast

ylowast

y

x

+

+

minus

minus

Flowastx

Flowasty

ilowastBa

ilowastBb

ilowastBc

iBa

iBb

iBc

MotorPID

PID23

32

CRPWM

ilowastB120572

ilowastB120573

120595lowastM120572

120595lowastM120573

uM120572

uM120573

iM120572

iM120573

iMa

iMb

iMc

uMa

uMb

uMc

iMa iMb

algorithmIC





5 D

OF

bear

ingl

ess i

nduc

tion

mot

or

PD

PI

PI

PD

PD

PD

PD

xlowastl

ylowastl

zlowast

xlowastr

ylowastr

120596lowast

120595lowastr

xl

yl

z

xr

yr

120596

120595r

l

yl

z

xr

yr

120595r

Sminus1

Sminus1

Sminus1Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

ANN inverse

Stat

ic A

NN

ilx

ily

i998400z

id1s

iq1s

id2s

iq2s

+

+

+

+

+

+

+

minus

minus

minus

minus

minus

minus

minus

x

























SC









7 Conclusion





Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra















[L] =

[

[

[

[

119871119872

0 minus119872119909 119872119910

0 119871119872

119872119910 119872119909

minus119872119909 119872119910 119871119861

0

119872119910 119872119909 0 119871119861

]

]

]

]

(1)

where 119871119872and 119871




[i] = [119894119872119889119894119872119902

119894119861119889

119894119861119902]

119879

(2)

where 119894119872119889

and 119894119872119902


119861119889and 119894119861119902


119882119898

=

1

2

[i]119879 [L] [i] (3)


[

119865119909

119865119910

] =

[

[

[

[

120597W119898

120597119909

120597W119898

120597119910

]

]

]

]

= 119872[

minus119894119872119889

119894119872119902

119894119872119902

119894119872119889

] [

119894119861119889

119894119861119902

] (4)


119861 (120593) = 119861119872cos (119901

119872120593 minus 120596119872119905 + 120583) + 119861

119861cos (119901

119861120593 minus 120596119861119905 + 120582)

(5)




119889119865 =

1198612

21205830

119889119860 (6)



119861= 119901119872


119865119909= 119865119872cos (120582 minus 120583)

119865119910= 119865119872sin (120582 minus 120583)

(7)

where 119901119872



119910are the


=




Ψ119872

=

2119897119903119861119872119873119872

119901119872

Ψ119861=

2119897119903119861119861119873119872

119901119861

asymp 119871119898119861

119894119861

(8)

where 119871119898119861


119872and 119873




119865119909= 119896119872

(119894119861119889

Ψ119872119889

+ 119894119861119902

Ψ119872119902

)

119865119910= 119896119872

(119894119861119902

Ψ119872119889

minus 119894119861119889

Ψ119872119902

)

(9)

where 119865119872

= 120587119901119872119901119861119871119898119861

21198971199031205830119873119872119873119861 Ψ119872119889

and Ψ119872119902


119861119889and Ψ







Ψ119872119889

= 119871119898119872

(119894119872119889

+ 119894119872119903119889

)

Ψ119872119902

= 119871119898119872

(119894119872119902

+ 119894119872119903119902

)

(10)

where 119894119872119903119889

and 119894119872119903119902


119879119890= 119901119872

(119894119872119902

Ψ119872119889

minus 119894119872119889

Ψ119872119902

) (11)




119872119889119903= Ψ119872119903

and Ψ119872119902119903

=


and 119894119872119902



119890can be

expressed as

119894119872119889

=

119871119872119903

119901119872

+ 1

119877119872119903

119871119898119872

Ψ119872119903

119894119872119902

=

119879119890119871119872119903

119901119872119871119898119872

Ψ119872119903

120596119904=

119877119872119903

119871119898119872

119871119872119903

Ψ119872119903

119894119872119902

119879119890= 119901119872

119871119898119872

119871119872119903

119894119872119902

Ψ119872119903

(12)

where 119871119872119903

and 119877119872119903


119872119889119903andΨ

119872119902119903are rotor flux




Ψ119872119889

=

119871119898119872

119871119872119903

(Ψ119872119889119903

+ 119871119872119903119897

119894119872119889

)

Ψ119872119902

=

119871119898119872

119871119872119903

119871119872119903119897

119894119872119902

(13)

where 119871119872119903119897


[

119894119861119889

119894119861119902

] =

1

119896

[


sin 120588 cos 120588 ] [

119865119909

119865119910

] (14)

where 119896 = 119870119872radic

Ψ2

119872119889+ Ψ2

119872119902and 120588 = arctan(Ψ

119872119902Ψ119872119889





xxlowast

ylowasty+

+

+

++

minus

minus

minus

Flowastx

Flowasty

ilowastBd


VRminus1

ilowastBa

ilowastBb

ilowastBc

iBaiBb

iBcMotor

Gapsensor

Rotaryencoder

120596r

120596r

120596lowastr

120596lowasts

PI

PID

PID

120595lowastMr

Tlowaste

(12)

(13)120588lowast


Mq

ilowastMd

ilowastMq

ilowastMa

ilowastMb

ilowastMc

iMa

iMb

iMc

23

23 CRPWM

CRPWM

Speed detector



ilowastB120572

ilowastB120573

ilowastM120572

ilowastM120573


120579lowast2

120579lowast1



flux linage


xlowast

ylowast

y

x

+

+

minus

minus

Flowastx

Flowasty

ilowastBa

ilowastBb

ilowastBc

iBa

iBb

iBc

MotorPID

PID23

32

CRPWM

ilowastB120572

ilowastB120573

120595lowastM120572

120595lowastM120573

uM120572

uM120573

iM120572

iM120573

iMa

iMb

iMc

uMa

uMb

uMc

iMa iMb

algorithmIC





5 D

OF

bear

ingl

ess i

nduc

tion

mot

or

PD

PI

PI

PD

PD

PD

PD

xlowastl

ylowastl

zlowast

xlowastr

ylowastr

120596lowast

120595lowastr

xl

yl

z

xr

yr

120596

120595r

l

yl

z

xr

yr

120595r

Sminus1

Sminus1

Sminus1Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

ANN inverse

Stat

ic A

NN

ilx

ily

i998400z

id1s

iq1s

id2s

iq2s

+

+

+

+

+

+

+

minus

minus

minus

minus

minus

minus

minus

x

























SC









7 Conclusion





Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












Ψ119872119889

= 119871119898119872

(119894119872119889

+ 119894119872119903119889

)

Ψ119872119902

= 119871119898119872

(119894119872119902

+ 119894119872119903119902

)

(10)

where 119894119872119903119889

and 119894119872119903119902


119879119890= 119901119872

(119894119872119902

Ψ119872119889

minus 119894119872119889

Ψ119872119902

) (11)




119872119889119903= Ψ119872119903

and Ψ119872119902119903

=


and 119894119872119902



119890can be

expressed as

119894119872119889

=

119871119872119903

119901119872

+ 1

119877119872119903

119871119898119872

Ψ119872119903

119894119872119902

=

119879119890119871119872119903

119901119872119871119898119872

Ψ119872119903

120596119904=

119877119872119903

119871119898119872

119871119872119903

Ψ119872119903

119894119872119902

119879119890= 119901119872

119871119898119872

119871119872119903

119894119872119902

Ψ119872119903

(12)

where 119871119872119903

and 119877119872119903


119872119889119903andΨ

119872119902119903are rotor flux




Ψ119872119889

=

119871119898119872

119871119872119903

(Ψ119872119889119903

+ 119871119872119903119897

119894119872119889

)

Ψ119872119902

=

119871119898119872

119871119872119903

119871119872119903119897

119894119872119902

(13)

where 119871119872119903119897


[

119894119861119889

119894119861119902

] =

1

119896

[


sin 120588 cos 120588 ] [

119865119909

119865119910

] (14)

where 119896 = 119870119872radic

Ψ2

119872119889+ Ψ2

119872119902and 120588 = arctan(Ψ

119872119902Ψ119872119889





xxlowast

ylowasty+

+

+

++

minus

minus

minus

Flowastx

Flowasty

ilowastBd


VRminus1

ilowastBa

ilowastBb

ilowastBc

iBaiBb

iBcMotor

Gapsensor

Rotaryencoder

120596r

120596r

120596lowastr

120596lowasts

PI

PID

PID

120595lowastMr

Tlowaste

(12)

(13)120588lowast


Mq

ilowastMd

ilowastMq

ilowastMa

ilowastMb

ilowastMc

iMa

iMb

iMc

23

23 CRPWM

CRPWM

Speed detector



ilowastB120572

ilowastB120573

ilowastM120572

ilowastM120573


120579lowast2

120579lowast1



flux linage


xlowast

ylowast

y

x

+

+

minus

minus

Flowastx

Flowasty

ilowastBa

ilowastBb

ilowastBc

iBa

iBb

iBc

MotorPID

PID23

32

CRPWM

ilowastB120572

ilowastB120573

120595lowastM120572

120595lowastM120573

uM120572

uM120573

iM120572

iM120573

iMa

iMb

iMc

uMa

uMb

uMc

iMa iMb

algorithmIC





5 D

OF

bear

ingl

ess i

nduc

tion

mot

or

PD

PI

PI

PD

PD

PD

PD

xlowastl

ylowastl

zlowast

xlowastr

ylowastr

120596lowast

120595lowastr

xl

yl

z

xr

yr

120596

120595r

l

yl

z

xr

yr

120595r

Sminus1

Sminus1

Sminus1Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

ANN inverse

Stat

ic A

NN

ilx

ily

i998400z

id1s

iq1s

id2s

iq2s

+

+

+

+

+

+

+

minus

minus

minus

minus

minus

minus

minus

x

























SC









7 Conclusion





Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










xxlowast

ylowasty+

+

+

++

minus

minus

minus

Flowastx

Flowasty

ilowastBd


VRminus1

ilowastBa

ilowastBb

ilowastBc

iBaiBb

iBcMotor

Gapsensor

Rotaryencoder

120596r

120596r

120596lowastr

120596lowasts

PI

PID

PID

120595lowastMr

Tlowaste

(12)

(13)120588lowast


Mq

ilowastMd

ilowastMq

ilowastMa

ilowastMb

ilowastMc

iMa

iMb

iMc

23

23 CRPWM

CRPWM

Speed detector



ilowastB120572

ilowastB120573

ilowastM120572

ilowastM120573


120579lowast2

120579lowast1



flux linage


xlowast

ylowast

y

x

+

+

minus

minus

Flowastx

Flowasty

ilowastBa

ilowastBb

ilowastBc

iBa

iBb

iBc

MotorPID

PID23

32

CRPWM

ilowastB120572

ilowastB120573

120595lowastM120572

120595lowastM120573

uM120572

uM120573

iM120572

iM120573

iMa

iMb

iMc

uMa

uMb

uMc

iMa iMb

algorithmIC





5 D

OF

bear

ingl

ess i

nduc

tion

mot

or

PD

PI

PI

PD

PD

PD

PD

xlowastl

ylowastl

zlowast

xlowastr

ylowastr

120596lowast

120595lowastr

xl

yl

z

xr

yr

120596

120595r

l

yl

z

xr

yr

120595r

Sminus1

Sminus1

Sminus1Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

ANN inverse

Stat

ic A

NN

ilx

ily

i998400z

id1s

iq1s

id2s

iq2s

+

+

+

+

+

+

+

minus

minus

minus

minus

minus

minus

minus

x

























SC









7 Conclusion





Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










5 D

OF

bear

ingl

ess i

nduc

tion

mot

or

PD

PI

PI

PD

PD

PD

PD

xlowastl

ylowastl

zlowast

xlowastr

ylowastr

120596lowast

120595lowastr

xl

yl

z

xr

yr

120596

120595r

l

yl

z

xr

yr

120595r

Sminus1

Sminus1

Sminus1Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

Sminus1

ANN inverse

Stat

ic A

NN

ilx

ily

i998400z

id1s

iq1s

id2s

iq2s

+

+

+

+

+

+

+

minus

minus

minus

minus

minus

minus

minus

x

























SC









7 Conclusion





Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
























SC









7 Conclusion





Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Acknowledgment


References










































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









Review Article Overview of Bearingless Induction...

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Transcript of Review Article Overview of Bearingless Induction...