a bearingless induction motor direct torque control and

Research ArticleA Bearingless Induction Motor Direct TorqueControl and Suspension Force Control Based onSliding Mode Variable Structure

Zebin Yang1 Lin Chen1 Xiaodong Sun2 Weiming Sun1 and Dan Zhang1

1School of Electrical and Information Engineering Jiangsu University Zhenjiang 212013 China2Automotive Engineering Research Institute Jiangsu University Zhenjiang 212013 China

Correspondence should be addressed to Xiaodong Sun xdsunujseducn

Received 31 March 2017 Accepted 14 June 2017 Published 1 August 2017

Academic Editor Jun M Wang

Copyright copy 2017 Zebin Yang 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

Aiming at the problems of the large torque ripple and unstable suspension performance in traditional direct torque control (DTC)for a bearingless induction motor (BIM) a new method of DTC is proposed based on sliding mode variable structure (SMVS)The sliding mode switching surface of the torque and flux linkage controller are constructed by torque error and flux error andthe exponential reaching law is used to design the SMVS direct torque controller On the basis of the radial suspension forcemathematical model of the BIM a radial suspension force closed-loop control method is proposed by utilizing the inverse systemtheory and SMVS The simulation models of traditional DTC and the new DTC method based on SMVS of the BIM are set up inthe MATLABSimulink toolbox On this basis the experiments are carried out Simulation and experiment results showed that thestable suspension operation of the BIM can be achieved with small torque ripple and flux ripple Besides the dynamic responseand suspension performance of the motor are improved by the proposed method

1 Introduction

Bearingless motors inherited the characteristics of the tra-ditional magnetic bearing motors such as being withoutlubrication having no wear and having nomechanical noiseCompared with the traditional magnetic bearing motor thespace utilization rate electromagnetic efficiency and otheraspects have been improved It is of great significance tothe development of the field of the biochemical medicineand industrial field such as the heart blood pump theturbo molecular pump and the high speed flywheel energystorage system [1 2] The levitation windings of bearinglessmotors breaking the balance of the original state of the airgap magnetic field changing the distribution of the air gapmagnetic field and producing the Maxwell force which havean effect on the rotor were to realize the stable suspensionMany scholars at home and abroad have studied the bear-ingless permanent magnet motor However the bearinglessinduction motor (BIM) has the advantages of low loss lowcost simple structure and withstanding high temperature

and it is easy to realize the open-loop speed control bythe voltage source inverter which people are increasinglyconcerned with [3]

The BIM is a strongly coupled nonlinear system In orderto realize the decoupling between the radial suspension forceand the torque the rotor flux oriented vector control isintroduced into the BIM in [4] However the use of therotor flux instead of the air gap flux in this method hasbad influence on the rotor stable suspension Reference [5]overcame the limitation of rotor flux orientation introducedthe air gap flux oriented of the BIM and deduced thesuspension force expression of the air gap flux orientedcontrol but the control algorithm is much more complicatedandhighly nonlinear and the torque responsewill be instablewhich makes the application of this method limited

Direct torque control (DTC) is another way of AC speedregulation after field oriented vector control The method issimple and does not need the complex vector transform andcurrent control which improves the dynamic response ofthe system From the retrieved papers there are not many

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 2409179 11 pageshttpsdoiorg10115520172409179

2 Mathematical Problems in Engineering

literatures researching on the DTC of bearingless motor TheDTC is introduced into the bearingless permanent magnetsynchronous motor and the bearingless permanent magnetslice motor in [6 7] The DTC is applied to the BIM in [8 9]and theDTCbased on space vector pulsewidthmodulation isproposed The experimental results showed that the methodcan realize the stable suspension of the motor Howeverthe traditional DTC has the problems of high torque rippleand nonfixed switching frequency Because the stator fluxestimation directly affects the performance of DTC a largenumber of papers have been studied on the stator fluxestimation [10ndash12] Some papers committed to improvingthe structure of the controller [13ndash16] but these controllershave increased the complexity of the system which make thecontrol system of the BIM more complicated and influencethe motor stable suspension operation

In order to reduce the torque ripple and improve theperformance of the traditional DTC of the BIM slidingmodevariable structure (SMVS) control is introduced to the DTCsystem Two hysteresis controllers in the traditional DTC arereplaced by the slidingmode controllerThe switching table isno longer used to select the space voltage vector instead thevoltage vectors of the two-phase static coordinate system areoutput by the sliding mode controller which is constructedaccording to the torque error and flux linkage error Thechoice of inverter switching value based on space voltagepulse width modulation (SVPWM) reduces the torque ripplefundamentally

The BIM control system includes torque control andsuspension force control For the part of suspension forcecontrol the traditional method is by detecting the radialdisplacement of the rotor and the given value of suspensionforce is obtained by the PID modulation which can realizethe closed-loop control of the suspension force [17] Themethod is relevant to air gap flux identification and itsdynamic response and the anti-interference performance arenot good To overcome this problem the SMVS suspensionforce control method based on inverse system is proposedOn the basis of the radial suspension force mathematicalmodel of the BIM the reversibility of the inverse system isanalyzed the SMVS control is introduced into the inversesystem and realized suspension force control The BIM DTCand suspension force control system based on SMVS are builtin MATLABSimulink toolboxThe dynamic performance ofthe torque response and the rotor suspension performanceare compared and analyzed for two cases that are basedon traditional DTC and SMVS-DTC respectively On thisbasis the experiments were carried out Simulation andexperiment results showed that the torque ripple has greatlyreduced and the performance of the rotor suspension isimproved

2 Sliding Mode Variable Structure DirectTorque Control of the BIM

21 Principle of SMVS SMVS control is a special kind ofnonlinear control method which is a kind of control strategyof variable structure control system The difference betweenthis control strategy and the traditional control strategy is

that the control is not continuous It is a kind of switchingcharacteristic that makes the system structure change withtimeThe control strategy makes the system pass through theprescribed state locus back and forth in high frequency andsmall amplitude Because the state locus can be designed andnot related to the system parameters and outside disturbanceit has a strong robustness [18]

Sliding mode variable structure control has three basicproblems firstly the sliding mode should exist secondlythe reach-ability condition should be satisfied finally thestability of the sliding mode should be analyzed [19ndash21]

22 Design of SMVS-DTC Controller SMVS controller isused to replace the traditional hysteresis comparators Thetorque winding reference voltage vector should be calculatedby torque error andflux error and thus the controller includesflux controller and torque controller

Themathematicalmodel of the BIM in the two-phase sta-tionary 120572-120573 coordinate system and with the torque windingstator current and stator flux as state variables is as follows

119889119889119905 1198941119904120572 = minus 1120590(11987711199041198711119904 +

11987711199031198711119903)1198941119904120572 minus 1205961199031198941119904120573

+ 1198771119903120590119871111990411987111199031205951119904120572 +12059611990312059011987111199041205951119904120573 +

11205901198711119904 1199061119904120572119889119889119905 1198941119904120573 = minus 1

120590(11987711199041198711119904 +11987711199031198711119903)

1198941119904120573 + 1205961199031198941119904120572

+ 1198771119903120590119871111990411987111199031205951119904120573 minus12059611990312059011987111199041205951119904120572 +

11205901198711119904 11990611199041205731198891198891199051205951119904120572 = 1199061119904120572 minus 119877111990411989411199041205721198891198891199051205951119904120573 = 1199061119904120573 minus 11987711199041198941119904120573

(1)

where 120590 = 1 minus 1198712111989811987111199041198711119903 1198941119904120572 and 1198941119904120573 respectively rep-resent two components of the torque winding stator currentand rotor current in coordinate system1205951119903120572 and1205951119903120573 respec-tively represent two components of the torque winding statorflux and rotor flux in coordinate system 1198711119904 and 1198711119903 are statorand rotor self-inductance of torque winding 1198771119904 and 1198771119903 arestator and rotor resistance of torque winding 1198711119898 is mutualinductance between stator and rotor of torque winding1199061119904120572 and 1199061119904120573 respectively represent two components of thetorque winding stator voltage and rotor voltage in coordinatesystem 120596119903 is the rotor angular velocity

The electromagnetic torque equation of the BIM is asfollows

119879119890 = 321198751 (12059511199041205721198941119904120573 minus 12059511199041205731198941119904120572) (2)

where 1198751 is the number of the pole-pairs of torque winding

Mathematical Problems in Engineering 3

The voltage-current model is used to estimate the statorflux of the torque winding in the two-phase stationarycoordinate system (120572-120573)

1205951119904120572 = int (1199061119904120572 minus 11987711199041198941119904120572) 1198891199051205951119904120573 = int (1199061119904120573 minus 11987711199041198941119904120573) 119889119905

(3)

In order to track the desired trajectory of the torque andflux the sliding mode switching surface is selected as follows

1198781 = 119879lowast119890 minus 1198791198901198782 = 1205952lowast1119904 minus 12059521119904119878 = [1198781 1198782]119879

(4)

where 119879lowast119890 and 1205952lowast1119904 are the given values of torque and thesquare of flux 119879119890 and 12059521119904 are the calculated values of torqueand the square of flux

To make the system have a good dynamic performancethe reaching law is selected as the exponential reaching law

119878 = minus120576 sgn 119878 minus 119870119878 (5)

where 120576 and 119870 are positive constants When the value of 120576is very small and the value of 119870 is great the speed of thereaching law away from the switching surface is fast and nearthe switching surface is slow This can effectively reduce thechattering and shorten the transition time [22]

Calculating the derivation of 1198781 and 11987821198781 = minus32sdot 1198751 [ 1120590 (11987711199041198711119904 + 11987711199031198711119903) (12059511199041205731198941119904120572 minus 12059511199041205721198941119904120573)+ 120596119903 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) minus 120596119903120590119871111990412059521119904+ (1198941119904120573 minus 12059511199041205731205901198711119904)1199061119904120572 minus (1198941119904120572 minus

12059511199041205731205901198711119904)1199061119904120573] = 1198621+ 1198631119906

(6)

where 12059521119904 = 12059521119904120572 + 120595211199041205731198782 = minus212059511199041205721199061119904120572 minus 212059511199041205731199061119904120573

+ 2119877119904 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) = 1198622 + 1198632119906(7)

in which C1 D1 C2 D2 and u are as follows

1198621 = minus321198751[[[[

1120590(11987711199041198711119904 +

11987711199031198711119903)(12059511199041205731198941119904120572 minus 12059511199041205721198941119904120573)

+ 120596119903 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) minus 120596119903120590119871111990412059521119904]]]]

1198631 = [minus321198751 (1198941119904120573 minus12059511199041205731205901198711119904)

321198751 (1198941119904120572 minus 12059511199041205721205901198711119904)] 1198622 = 2119877119904 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) 1198632 = [minus21205951119904120572 minus21205951119904120573] 119906 = [1199061119904120572 1199061119904120573]119879

(8)

Combining (5) and (6) one can obtain

119878 = [ 11987811198782] = [11986211198622] + [

11986311198632][11990611199041205721199061119904120573] (9)

Substituting (4) into (7) one can obtain the controllerformula

119906 = minus119863minus1 [1198621 + 1205761sgn (1198781) + 119870111987811198622 + 1205762sgn (1198782) + 11987021198782] (10)

and119863minus1 = [ 1198891 11988921198893 1198894 ] where1198891= minus2120595111990412057331199011 (12059511199041205731198941119904120573 + 12059511199041205721198941119904120572) minus 31199011 (12059521119904120573 + 12059521119904120572) 1205901198711119904

1198892= minus151199011 (1198941119904120572 minus 12059511199041205721205901198711119904)31199011 (12059511199041205731198941119904120573 + 12059511199041205721198941119904120572) minus 31199011 (12059521119904120573 + 12059521119904120572) 1205901198711119904

1198893= 2120595111990412057231199011 (12059511199041205731198941119904120573 + 12059511199041205721198941119904120572) minus 31199011 (12059521119904120573 + 12059521119904120572) 1205901198711119904


(11)

23 Analyses of the Reach-Ability Condition of the SlidingMode If the sliding mode exists the moving point beyondthe switching surface will reach the switching surface in finite


time and the sliding mode motion is stable The followingreach-ability condition is satisfied

lim119878rarr0+

119878 lt 0lim119878rarr0minus

119878 gt 0 (12)

The global reach-condition is 119878 119878 lt 0 From the exponen-tial reaching law it can be obtained that

119878 119878 = 119878 (minus120576 sgn 119878 minus 119870119878) = minus120576 |119878| minus 1198701198782 (13)

Because 120576 and119870 are positive constant 119878 119878 lt 0 The slidingmode satisfies the reach-ability condition

24 Analyses of the Stability of SMVS-DTC Controller Select-ing Lyapunov function119881 = 1198781198781198792 the derivation of it can becalculated

= [1198781 1198782] [minus1205761sgn 1198781 minus 11987011198781minus1205762sgn 1198782 minus 11987021198782]= minus1198781 (1205761sgn 1198781 + 11987011198781) minus 1198782 (1205762sgn 1198782 + 11987021198782)= minus1205761 100381610038161003816100381611987811003816100381610038161003816 minus 119870111987821 minus 1205762 100381610038161003816100381611987821003816100381610038161003816 minus 119870211987822

(14)

in which 1205761 1198701 1205762 and 1198702 are positive constant so it can beobtained that

= minus1205761 100381610038161003816100381611987811003816100381610038161003816 minus 119870111987821 minus 1205762 100381610038161003816100381611987821003816100381610038161003816 minus 119870211987822 lt 0 (15)

It can be concluded that this SMVS-DTC controller satis-fies the stability conditions

3 SMVS Suspension Force Control of the BIM

31 Radial Suspension Force Mathematical Model of the BIMAccording to the relationship between the suspension forceand the suspension winding stator current of the BIM in thetwo-phase stationary coordinate system (120572-120573) [23]

119865119909 = 119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) 119865119910 = 119870119898 (11989421199041205731205951120572 minus 11989421199041205721205951120573)

(16)

where 119870119898 = 12058711987511198752119871211989818120583011989711990311988211198822 1198751 and 1198752 are thenumbers of pole-pairs of torque winding and suspensionwinding respectively 1205951120572 and 1205951120573 are the component of airgap flux in120572-120573 axis respectively119865119909 and119865119910 are the suspensionforce of radial 119909 and 119910 1198712119898 is the mutual inductance betweenstator and rotor of suspension winding 1205830 is the permeabilityof vacuum 119897 is the effective length of the rotor 119903 is the outsidediameter of rotor 1198821 and 1198822 are the torque winding turnsand suspension winding turns

When the rotor deviates from the center of the motorstator it will cause the motor flux distribution Then theMaxwell force is not zero and the direction of its action andthe direction of the rotor eccentricity are consistent pointing

to the direction of minimum air gap it is called unbalancedmagnetic force and is showed as

119865119904119909 = 119896119904119909119865119904119910 = 119896119904119910 (17)

where 119896119904 = 119896(12058711990311989711986121212058301198920) and 119865119904119909 and 119865119904119910 are the unbal-ancedmagnetic force in the direction of 119909 and 119910 respectively119909 and 119910 are the displacement in the direction of 119909 and 119910respectively and 1198920 is the air gap length

The motion equations of the rotor are expressed as

119898 = 119865119909 minus 119865119904119909119898 119910 = 119865119910 minus 119865119904119910 minus 119898119892 (18)

where 119898 is the mass of the rotor and 119892 is the gravityacceleration By (16)ndash(18) it can be obtained that

= [119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) minus 119896119904119909]119898

119910 = [119870119898 (11989421199041205731205951120572 minus 11989421199041205721205951120573) minus 119896119904119910 minus 119898119892]119898 (19)

32 SMVS Radial Suspension Force Control of the BIM Basedon Inverse System The basic principle of inverse systemmethod is to compensate the controlled object as a systemwith a linear transfer relationship by using the inverse systemof the controlled object then to synthesize the systemaccording to the linear system theory and to realize thedecoupling in nonlinear systems [24 25]

Theorem 1 For a system of 119901 dimensional input 119906(119905) = (11990611199062 119906119901)119879 and for 119902 dimensional output 119910(119905) = (1199101 1199102 119910119902)119879 with a set of initial states 119909(1199050) = 1199090 and it can beexpressed as the following state equation

= 119891 (119909 119906) 119910 = ℎ (119909 119906)

119909 (1199050) = 1199090(20)

The necessary and sufficient condition for the systemto be reversible in the neighborhood of (1199090 1199060) has vectorrelative order 120572 = (1205721 1205722 120572119902)119879 in this neighborhood

Select the state variables in (19)

119883 = [1199091 1199092 1199093 1199094]119879 = [119909 119910 119910]119879 (21)

The input variable is

119880 = [1199061 1199062]119879 = [1198942119904120572 1198942119904120573]119879 (22)

The output variable is

119884 = [1199101 1199102]119879 = [119909 119910]119879 (23)


The state equation of the composite controlled object isobtained by (19) and(21)

1 = 11990932 = 11990943 = 119870119898119898 (11990611205951120572 + 11990621205951120573) minus 11989611990411989811990914 = 119870119898119898 (11990621205951120572 minus 11990611205951120573) minus 1198961199041198981199092 minus 119892

(24)

Taking the derivative of the output function until eachcomponent in 119884119902 = (11991011205721 119910119902120572119902) include input 119906 explicit

1199101 = 11990931199101 = 119870119898119898 (11990611205951120572 + 11990621205951120573) minus 11989611990411989811990911199102 = 11990941199102 = 119870119898119898 (11990621205951120572 minus 11990611205951120573) minus 1198961199041198981199092 minus 119892

(25)

The Jacobi matrix of the input 119906 can be expressed as

119860 = [[[[[

120597 11991011205971199061120597 11991011205971199062

120597 11991021205971199061120597 11991021205971199062

]]]]]= 119870119898119898 [ 1205951120572 1205951120573minus1205951120573 1205951120572] (26)

Because Det119860 = 119870119898(12059511205722 + 12059511205732)119898 = 0 according toTheorem 1 the relative order of the system is 120572 = (1205721 1198862)119879 =(2 2)119879 1205721 + 1198862 = 4 = 119899 so the system is reversible

Assuming = [ 1199101 1199102]119879 = [1206011 1206012]119879 (25) can be calcu-lated as

1199061 = 119898119870119898 (12059521120572 + 12059521120573) (12059511205721206011 minus 12059511205731206012 +

11989611990411989811990911205951120572

minus 11989611990411989811990921205951120573 minus 1198921205951120573) 1199062 = 119898

119870119898 (12059521120572 + 12059521120573) (12059511205731206011 + 12059511205721206012 +11989611990411989811990911205951120573

+ 11989611990411989811990921205951120572 + 1198921205951120572)

(27)

In order to realize closed-loop displacement controland improve the performance of anti-interference SMVSis introduced into the inverse system The sliding modeswitching surface of the sliding mode controller is defined asfollows

1198783 = 1198881 (119909lowast minus 119909) + lowast minus

1198784 = 1198882 (119910lowast minus 119910) + 119910lowast minus 119910(28)

where 119909lowast and 119910lowast are the given displacement of 119909 and 119910direction 119909 and 119910 are the measured displacement and 1198881 and1198882 are constants

Exponential reaching law is adopted in this paper and theexpression is as follows

1198783 = minus1205763sgn (1198783) minus 119870311987831198784 = minus1205764sgn (1198784) minus 11987041198784 (29)

According to (14)-(15) the sliding mode controller isstable It can be obtained by (28)-(29) that

= 1206011 = 1198881 (lowast minus ) + lowast + 1205763sgn (1198783) + 11987031198783119910 = 1206011 = 1198881 ( 119910lowast minus 119910) + 119910lowast + 1205764sgn (1198784) + 11987041198784 (30)

Torque winding and suspension winding of the BIM arecoupled by air gap flux of torquewinding and torquewindingcan be obtained by torque winding stator flux subtractingstator leakage inductance

1205951120572 = 1205951119904120572 minus 119871111990411989711989411199041205721205951120573 = 1205951119904120573 minus 11987111199041198971198941119904120573 (31)

It can be known from (3) that the stator flux identificationin the DTC has the pure integral part The initial valueof integration the accumulated error and other factorswill make the flux identification inaccurate Therefore thetraditional suspension force control method cannot meet therequirements of the stable suspension of the BIM Becauseof the introduction of SMVS to the suspension force controlthe robustness of the controller is improved the dependenceof the accuracy of stator flux estimation is reduced and theperformance of stator stable suspension is improved

Through the separate control of torque and suspensionforce the SMVS-DTC system of the BIM can be constructedand the structure diagram of the system is showed as Figure 1

The control block diagram of the BIM includes two partstorque winding control part and suspension winding controlpart In torque winding control part the voltage and currentof the stator are obtained by the coordinate transformationand then the estimated value of the stator flux is calculated bythe stator flux calculation blockThe given value of the torqueis obtained by the speed regulator and the estimation value oftorque is calculated by torque calculation block The torqueerror signal is obtained by given value and the estimationvalue of torque and then the voltage control signal of inverteris obtained by SMVS-DTC block In suspension windingcontrol part through the SMVS block the component oflevitation force can be calculated by position error signalThe air gap flux is calculated by the stator flux of torquewinding through the inverse system block the stator currentof suspension winding can be calculated by the componentof levitation force and the air gap flux so as to realize radialstable suspension of the rotor


Speed regulator

Stator fluxcalculation

Torque calculation

SMVS-DTC

Inverter

x2s3s

CRPWM

Air gap fluxcalculation

y

BIM

SMVS Inversesystem

i1s120572

i1s120573

i1s120572

i1s120572

i1s120573

i1s120573

i1s120572i1s120573

u1s120572

u1s120573

u1s120572

u1s120573

R1s

minus

minus

+

+

minus+

minus+

1205951s

120595lowast1s

120596r

120596r

1205951s120572

1205951s120572

1205951s120573

1205951s120573

xlowast

ylowast

1206011

1206012

1205951120572 1205951120573

ilowast2s120572

ilowast2s120573

Te

Tlowaste

u1sa

u1sb

u1sc

120596lowastr

i2sa

i2sb

i2sc

ilowast2sa

ilowast2sb

ilowast2sc

Figure 1 The structure diagram of the BIM SMVS-DTC system

Table 1 Parameters of the BIM

Motor parameters Torque winding Suspension winding119875 (W) 1500 500119899 (rmin) 6000 6000Rs (Ω) 201 103Rr (Ω) 1148 0075Lm (H) 015856 0009321198711119904119897 (H) 000454 0002671198711119903119897 (H) 000922 000542J (kgsdotm2) 000769 000769119898 (kg) 285 285p 1 2

4 Simulation and Experimental Study ofthe BIM SMVS-DTC and Suspension ForceControl System

41 Results and Analysis of Simulation In order to verify thefeasibility of the control method the simulation model ofthe BIM SMVS-DTC and suspension force control systemis established The simulation results of SMVS-DTC controlmethod proposed and the traditional DTC control methodare compared and analyzed The simulation parameters arein Table 1

The simulation parameters are as follows 1205761 = 1205762 = 0031198701 = 1198702 = 1500 1205763 = 1205764 = 001 and 1198703 = 1198704 = 3000The given speed is 6000 rmin and the simulation timeis 06 seconds The load torque is added to 2Nsdotm at 119905 =03 s To verify the superiority of the proposed methodSMVS-DTC with SMVS suspension force control method

and the traditional DTC with traditional suspension forcecontrol method are compared and analyzed by simulationThe simulation results are in Figures 2 3 and 4

The stator flux trajectory torque response and speedresponse are showed in Figures 2 3 and 4 respectively Itcan be seen from Figure 2(a) that the amplitude of stator fluxoscillations is large and the dynamic response is not good bytraditional DTC method From Figure 2(b) we can see thatthe amplitude of stator flux oscillations is smaller by SMVS-DTC method Compared with Figures 3(a) and 3(b) we cansee that the torque ripple of SMVS-DTC is reduced greatlythan traditional DTC And the dynamic performance of themotor is also improved when the motor is started When 119905= 03 s the load torque is added The transition time of theproposed method is reduced It can be found in Figure 3(b)that there is chattering at steady state due to the sliding modevariable structure control and it can not be avoided but thechattering is small which does not affect the stable operationof the motor From Figure 4 it can be found that the speedrise time has been reduced and the dynamic response hasbeen improvedwhen using SMVS-DTCmethod compared totraditional DTCmethod In addition when the load is addedthe speed fluctuation is obviously reducedwhen using SMVS-DTC method

The simulation results of the rotor motion trajectoryand rotor radial displacement by traditional suspension forcecontrol method and the proposed method are showed inFigures 5 and 6 respectively We can see that the proposedmethod can effectively reduce the radial displacement ofthe rotor and the displacement fluctuation time which canrealize stable suspension operation of the BIM In order toverify the performance of antidisturbance of the suspensionforce control method the given radial displacement was set


minus05 0 05 1minus1

1205951s (Wb)

minus1

minus05

0

05

1

1205951s

(Wb)

(a) DTC

minus1

minus05

0

05

1

1205951s

(Wb)

1205951s (Wb)minus11 05 0 minus05

(b) SMVS-DTC

Figure 2 Trajectory of stator flux

minus505

10152025

Te

(Nlowast

m)

01 02 03 04 05 060t (s)

(a) DTC

01 02 03 04 05 060t (s)

minus5

0

5

10

15

20

Te

(Nlowast

m)

(b) SMVS-DTC

Figure 3 Torque response

DTCSMVS-DTC

01 02 03 04 05 06t (s)

0100020003000400050006000

n(r

min

)

Figure 4 Speed response

to 005mm when 119905 = 03 and the simulation waveforms areshown in Figure 7

As can be seen from the figure the radial displacementfluctuation is only 0015mm when the given displacementsuddenly changed and the fluctuation time is less than 005seconds so it has good performance of robustness

42 Results and Analysis of Experiment In order to verify theeffect of the proposed method experimental research on theprototype of the BIM has been carried out We analyzed andcompared thismethodwith the traditional DTCmethodTheTI companyrsquos 32-bit fixed point DSP chip F2812 is used asthe control chip of the control system The EVA and EVB onthis chip can produce six complementary PWM waveformstherefore the torque winding and suspension winding ofthe BIM can be independently controlled The experimentalparameters are similar to the simulation parameters androtor speed is set to 2000 rmin started with no-load andthen the load torque of 2Nsdotm is added to the motor Thetorque responses of these two kinds of DTC methods arecompared with the experimental results The experimentalblock diagram of the control system is shown in Figure 8 andthe experimental results are shown in Figures 9 and 10

The experimental block diagram of the control systemincludes two parts torque winding control part and suspen-sion winding control part In torque winding control partthe speed signal is obtained by the photoelectric encoderand the DSP (Digital Signal Processor) as the control chip


0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC

0005 0015001 002minus001minus0015 minus0005minus002 0X (mm)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC

Figure 5 Rotor trajectory

01 02 03 04 05 060t (s)

minus006minus0045minus003minus0015

00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC

minus0025minus002minus0015minus001minus0005

00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC

Figure 6 Rotor radial displacement

MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)


of the control system to achieve the SMVS-DTC controlThe sample of busbar current and voltage was achieved bythe current and voltage sensor The PWM signal outputby DSP was put into IPM (Intelligent Power Module) Insuspension winding control part the radial displacementsignal of the suspension winding is obtained by the position

sensor and this signal was put into DSP to realize the closed-loop control of radial displacement The power drive part ofthe suspension winding is the same as the torque winding

Figure 9 is the displacement response of the rotor withSMVS suspension force control method based on inversesystem Figure 10 is the speed and torque response of tradi-tional DTC and SMVS-DTC methods Figure 9 shows thatthe rotor displacement in 119909 and 119910 direction is small with thesuspension force control method and it can realize themotorstable suspension operation We can see from Figure 10(a)that the torque ripple is relatively large when the motoroperates with no load and with load and the torque rippleis large and the dynamic performance is not good when theload is suddenly added at the same time the rotor speed issignificantly fluctuated In addition the BIM is vibratedwhenthe motor starts accompanied by a sharp noise It can beknown fromFigures 10(a) and 10(b) that the torque ripple canbe reduced effectively by the proposed method the torquetransition process is faster and the speed is not fluctuatedobviously when the load is suddenly added The operationnoise of experimental prototype is reduced and the startingprocess is stable with no violent vibration


PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor

Position detection circuit of x

Position loop Position sensor

Suspension control

Torque winding

BIM

Suspensionwinding

Photoelectric encoder

SMVS-DTC

IPMIsolation drive

Position detection circuit of y

Figure 8 The experiment block diagram of the control system

Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion

Aimed at the problems of the large torque ripple and unstablesuspension performance in traditional DTC and suspensionforce control of the BIM the traditional method is improvedin this paper and the DTC and suspension force controlmethod based on SMVS are proposed The performance oftorque control and suspension force control of the BIM isbetter with the proposed method From the simulation andexperiment results of the control system of the BIM based

on the traditional DTC and SMVS-DTC we can draw thefollowing conclusions

(1) The torque ripple can be reduced effectively andthe dynamic performance and the anti-interferenceability are improved by SMVS-DTC method

(2) The SMVS suspension force control method not onlyreduced the rotor radial displacement fluctuation andfluctuation time but also realized the motor stablesuspension operation


Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC

Figure 10 Speed and torque response

Conflicts of Interest

The authors declare no conflicts of interest

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China under Projects 51305170 and 51475214the Natural Science Foundation of Jiangsu Province of Chinaunder Projects BK20141301 and BK20170071 the China Post-doctoral Science Foundation under Projects 2016M601726and 2015T80508 the Six Categories Talent Peak of JiangsuProvince under Projects 2015-XNYQC-003 and 2014-ZBZZ-017 Zhenjiang Key Research and Development Project underProject GY2016003 the ldquo333 projectrdquo of Jiangsu Provinceunder Project BRA2017441 and the Priority Academic Pro-gram Development of Jiangsu Higher Education Institutions(PAPD)

References

[1] X Sun L Chen and Z Yang ldquoOverview of bearinglesspermanent-magnet synchronousmotorsrdquo IEEETransactions onIndustrial Electronics vol 60 no 12 pp 5528ndash5538 2013

[2] X Sun L Chen H Jiang Z Yang J Chen and W ZhangldquoHigh-performance control for a bearingless permanent-magnet synchronous motor using neural network inversescheme plus internal model controllersrdquo IEEE Transactions onIndustrial Electronics vol 63 no 6 pp 3479ndash3488 2016

[3] Z Yang L Wan X Sun L Chen and Z Chen ldquoSliding ModeControl for Bearingless Induction Motor Based on a NovelLoad Torque Observerrdquo Journal of Sensors vol 2016 Article ID8567429 2016

[4] Z Wang and X Liu ldquoAn improved rotor flux oriented controlsystem of bearingless induction motorsrdquo in Proceedings of theChinese Control and Decision Conference (CCDC rsquo10) pp 2733ndash2737 May 2010

[5] X Wang Z Deng and Y Yan ldquoThe nonlinear decouplingcontrol of the bearingless inductionmotors based on the air-gapflux orientationrdquo Transactions of China Electrotechnical Societyvol 6 p 4 2002

[6] Y X Sun C S Xu and H Q Zhu ldquoAThree-Level DTC SystemBased on Virtual Space Vector Modulation for BearinglessPermanent Magnet Synchronous Motorrdquo Applied Mechanicsand Materials vol 703 pp 356ndash359 2014

[7] H Zhu and Y Gu ldquoDirect torque control and direct suspensionforce control of bearingless permanent magnetic slice motorrdquoPaiguan Jixie Gongcheng XuebaoJournal of Drainage and Irri-gation Machinery Engineering vol 6 p 16 2015

[8] Y Wang Z Deng and X Wang ldquoDirect torque control ofbearingless induction motorrdquo in Proceedings of the CSEE vol28 pp 80ndash84 2008

[9] X LiuHChen and J Zhou ldquoSVM-DTCSystem for bearinglessinduction motor based on discrete time deadbeatrdquo Bearing vol3 2012

[10] Y Liao X Feng and Z Wang ldquoInductionMotor Direct TorqueControl Based on Stator Flux SlidingMode Observer and SpaceVector Pulse Width Modulationrdquo in Proceedings of the CSEEvol 18 p 12 2012

[11] Y Liu L M Shi and L Zhao ldquoDirect torque control of asyn-chronous motor based on hybrid flux observerrdquo Transactions ofChina Electrotechnical Sosiety vol 30 no 10 pp 157ndash163 2015

[12] B Wang Y Wang W Guo and Z Wang ldquoDeadbeat directtorque control of permanent magnet synchronous motor basedon reduced order stator flux observerrdquo Diangong Jishu Xue-baoTransactions of China Electrotechnical Society vol 29 no3 pp 160ndash171 2014

[13] X Sun L Chen Z Yang and H Zhu ldquoSpeed-sensorless vectorcontrol of a bearingless induction motor with artificial neuralnetwork inverse speed observerrdquo IEEEASME Transactions onMechatronics vol 18 no 4 pp 1357ndash1366 2013

[14] Y Xu Y Lei L Ma and D Sha ldquoA novel direct torquecontrol of permanent magnet synchronous motors based onbackstepping controlrdquo Diangong Jishu XuebaoTransactions ofChina Electrotechnical Society vol 30 no 10 pp 83ndash89 2015

[15] S Lv L Shuai M Hui and Q Dong ldquoDirect torque controlfor permanent magnet synchronous motor with optimal dutycycle controlrdquo Diangong Jishu XuebaoTransactions of ChinaElectrotechnical Society vol 30 pp 35ndash42 2015

[16] J Huang Q Xu X Shi L Cui and Z Xiang ldquoDirect torquecontrol of PMSM based on fractional order sliding modevariable structure and space vector pulse width modulationrdquo in


Proceedings of the 33rd Chinese Control Conference (CCC rsquo14)pp 8097ndash8101 July 2014

[17] H Li and H Zhu ldquoBearingless motorrsquos radial suspensionforce control based on virtual winding current analysisrdquo inProceedings of the 17th International Conference on ElectricalMachines and Systems (ICEMS rsquo14) pp 2141ndash2146October 2014

[18] Y Shtessel C Edwards L Fridman andA Levant SlidingModeControl and Observation Birkhauser Springer New York NYUSA 2014

[19] C Lascu and F Blaabjerg ldquoSuper-twisting sliding mode directtorque contol of induction machine drivesrdquo in Proceedings ofthe Energy Conversion Congress and Exposition (ECCE rsquo14) pp5116ndash5122 2014

[20] B-Z Guo and F-F Jin ldquoSliding mode and active disturbancerejection control to stabilization of one-dimensional anti-stablewave equations subject to disturbance in boundary inputrdquoInstitute of Electrical and Electronics Engineers Transactions onAutomatic Control vol 58 no 5 pp 1269ndash1274 2013

[21] J-J Liu and J-M Wang ldquoBoundary stabilization of a cascadeof ODE-wave systems subject to boundary control matcheddisturbancerdquo International Journal of Robust and NonlinearControl vol 27 no 2 pp 252ndash280 2017

[22] A Wang X Jia and S Dong ldquoA new exponential reaching lawof sliding mode control to improve performance of permanentmagnet synchronous motorrdquo IEEE Transactions on Magneticsvol 49 no 5 pp 2409ndash2412 2013

[23] Z Yang D Dong H Gao X Sun R Fan and H Zhu ldquoRotormass eccentricity vibration compensation control in bearinglessinduction motorrdquo Advances in Mechanical Engineering vol 7no 1 Article ID 168428 2015

[24] X Sun B Su L Chen Z Yang X Xu and Z Shi ldquoPrecisecontrol of a four degree-of-freedom permanent magnet biasedactive magnetic bearing system in a magnetically suspendeddirect-driven spindle using neural network inverse schemerdquoMechanical Systems and Signal Processing vol 88 pp 36ndash482017

[25] X Sun Z Shi L Chen and Z Yang ldquoInternal model control fora bearingless permanent magnet synchronous motor based oninverse system methodrdquo IEEE Transactions on Energy Conver-sion vol 31 no 4 pp 1539ndash1548 2016

Submit your manuscripts athttpswwwhindawicom

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

Journal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


literatures researching on the DTC of bearingless motor TheDTC is introduced into the bearingless permanent magnetsynchronous motor and the bearingless permanent magnetslice motor in [6 7] The DTC is applied to the BIM in [8 9]and theDTCbased on space vector pulsewidthmodulation isproposed The experimental results showed that the methodcan realize the stable suspension of the motor Howeverthe traditional DTC has the problems of high torque rippleand nonfixed switching frequency Because the stator fluxestimation directly affects the performance of DTC a largenumber of papers have been studied on the stator fluxestimation [10ndash12] Some papers committed to improvingthe structure of the controller [13ndash16] but these controllershave increased the complexity of the system which make thecontrol system of the BIM more complicated and influencethe motor stable suspension operation

In order to reduce the torque ripple and improve theperformance of the traditional DTC of the BIM slidingmodevariable structure (SMVS) control is introduced to the DTCsystem Two hysteresis controllers in the traditional DTC arereplaced by the slidingmode controllerThe switching table isno longer used to select the space voltage vector instead thevoltage vectors of the two-phase static coordinate system areoutput by the sliding mode controller which is constructedaccording to the torque error and flux linkage error Thechoice of inverter switching value based on space voltagepulse width modulation (SVPWM) reduces the torque ripplefundamentally

The BIM control system includes torque control andsuspension force control For the part of suspension forcecontrol the traditional method is by detecting the radialdisplacement of the rotor and the given value of suspensionforce is obtained by the PID modulation which can realizethe closed-loop control of the suspension force [17] Themethod is relevant to air gap flux identification and itsdynamic response and the anti-interference performance arenot good To overcome this problem the SMVS suspensionforce control method based on inverse system is proposedOn the basis of the radial suspension force mathematicalmodel of the BIM the reversibility of the inverse system isanalyzed the SMVS control is introduced into the inversesystem and realized suspension force control The BIM DTCand suspension force control system based on SMVS are builtin MATLABSimulink toolboxThe dynamic performance ofthe torque response and the rotor suspension performanceare compared and analyzed for two cases that are basedon traditional DTC and SMVS-DTC respectively On thisbasis the experiments were carried out Simulation andexperiment results showed that the torque ripple has greatlyreduced and the performance of the rotor suspension isimproved

2 Sliding Mode Variable Structure DirectTorque Control of the BIM

21 Principle of SMVS SMVS control is a special kind ofnonlinear control method which is a kind of control strategyof variable structure control system The difference betweenthis control strategy and the traditional control strategy is

that the control is not continuous It is a kind of switchingcharacteristic that makes the system structure change withtimeThe control strategy makes the system pass through theprescribed state locus back and forth in high frequency andsmall amplitude Because the state locus can be designed andnot related to the system parameters and outside disturbanceit has a strong robustness [18]

Sliding mode variable structure control has three basicproblems firstly the sliding mode should exist secondlythe reach-ability condition should be satisfied finally thestability of the sliding mode should be analyzed [19ndash21]

22 Design of SMVS-DTC Controller SMVS controller isused to replace the traditional hysteresis comparators Thetorque winding reference voltage vector should be calculatedby torque error andflux error and thus the controller includesflux controller and torque controller

Themathematicalmodel of the BIM in the two-phase sta-tionary 120572-120573 coordinate system and with the torque windingstator current and stator flux as state variables is as follows

119889119889119905 1198941119904120572 = minus 1120590(11987711199041198711119904 +

11987711199031198711119903)1198941119904120572 minus 1205961199031198941119904120573

+ 1198771119903120590119871111990411987111199031205951119904120572 +12059611990312059011987111199041205951119904120573 +

11205901198711119904 1199061119904120572119889119889119905 1198941119904120573 = minus 1

120590(11987711199041198711119904 +11987711199031198711119903)

1198941119904120573 + 1205961199031198941119904120572

+ 1198771119903120590119871111990411987111199031205951119904120573 minus12059611990312059011987111199041205951119904120572 +

11205901198711119904 11990611199041205731198891198891199051205951119904120572 = 1199061119904120572 minus 119877111990411989411199041205721198891198891199051205951119904120573 = 1199061119904120573 minus 11987711199041198941119904120573

(1)

where 120590 = 1 minus 1198712111989811987111199041198711119903 1198941119904120572 and 1198941119904120573 respectively rep-resent two components of the torque winding stator currentand rotor current in coordinate system1205951119903120572 and1205951119903120573 respec-tively represent two components of the torque winding statorflux and rotor flux in coordinate system 1198711119904 and 1198711119903 are statorand rotor self-inductance of torque winding 1198771119904 and 1198771119903 arestator and rotor resistance of torque winding 1198711119898 is mutualinductance between stator and rotor of torque winding1199061119904120572 and 1199061119904120573 respectively represent two components of thetorque winding stator voltage and rotor voltage in coordinatesystem 120596119903 is the rotor angular velocity

The electromagnetic torque equation of the BIM is asfollows

119879119890 = 321198751 (12059511199041205721198941119904120573 minus 12059511199041205731198941119904120572) (2)

where 1198751 is the number of the pole-pairs of torque winding




(3)



(4)



119878 = minus120576 sgn 119878 minus 119870119878 (5)



12059511199041205731205901198711119904)1199061119904120573] = 1198621+ 1198631119906

(6)


+ 2119877119904 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) = 1198622 + 1198632119906(7)


1198621 = minus321198751[[[[

1120590(11987711199041198711119904 +

11987711199031198711119903)(12059511199041205731198941119904120572 minus 12059511199041205721198941119904120573)

+ 120596119903 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) minus 120596119903120590119871111990412059521119904]]]]

1198631 = [minus321198751 (1198941119904120573 minus12059511199041205731205901198711119904)


(8)


119878 = [ 11987811198782] = [11986211198622] + [

11986311198632][11990611199041205721199061119904120573] (9)





1198893= 2120595111990412057231199011 (12059511199041205731198941119904120573 + 12059511199041205721198941119904120572) minus 31199011 (12059521119904120573 + 12059521119904120572) 1205901198711119904


(11)




lim119878rarr0+


119878 gt 0 (12)






(14)






119865119909 = 119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) 119865119910 = 119870119898 (11989421199041205731205951120572 minus 11989421199041205721205951120573)

(16)




119865119904119909 = 119896119904119909119865119904119910 = 119896119904119910 (17)





= [119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) minus 119896119904119909]119898




= 119891 (119909 119906) 119910 = ℎ (119909 119906)

119909 (1199050) = 1199090(20)



119883 = [1199091 1199092 1199093 1199094]119879 = [119909 119910 119910]119879 (21)


119880 = [1199061 1199062]119879 = [1198942119904120572 1198942119904120573]119879 (22)


119884 = [1199101 1199102]119879 = [119909 119910]119879 (23)




(24)



(25)


119860 = [[[[[

120597 11991011205971199061120597 11991011205971199062

120597 11991021205971199061120597 11991021205971199062

]]]]]= 119870119898119898 [ 1205951120572 1205951120573minus1205951120573 1205951120572] (26)



1199061 = 119898119870119898 (12059521120572 + 12059521120573) (12059511205721206011 minus 12059511205731206012 +

11989611990411989811990911205951120572

minus 11989611990411989811990921205951120573 minus 1198921205951120573) 1199062 = 119898

119870119898 (12059521120572 + 12059521120573) (12059511205731206011 + 12059511205721206012 +11989611990411989811990911205951120573

+ 11989611990411989811990921205951120572 + 1198921205951120572)

(27)










1205951120572 = 1205951119904120572 minus 119871111990411989711989411199041205721205951120573 = 1205951119904120573 minus 11987111199041198971198941119904120573 (31)





Speed regulator


Torque calculation

SMVS-DTC

Inverter

x2s3s

CRPWM


y

BIM

SMVS Inversesystem

i1s120572

i1s120573

i1s120572

i1s120572

i1s120573

i1s120573

i1s120572i1s120573

u1s120572

u1s120573

u1s120572

u1s120573

R1s

minus

minus

+

+

minus+

minus+

1205951s

120595lowast1s

120596r

120596r

1205951s120572

1205951s120572

1205951s120573

1205951s120573

xlowast

ylowast

1206011

1206012

1205951120572 1205951120573

ilowast2s120572

ilowast2s120573

Te

Tlowaste

u1sa

u1sb

u1sc

120596lowastr

i2sa

i2sb

i2sc

ilowast2sa

ilowast2sb

ilowast2sc












1205951s (Wb)

minus1

minus05

0

05

1

1205951s

(Wb)

(a) DTC

minus1

minus05

0

05

1

1205951s

(Wb)

1205951s (Wb)minus11 05 0 minus05

(b) SMVS-DTC


minus505

10152025

Te

(Nlowast

m)

01 02 03 04 05 060t (s)

(a) DTC

01 02 03 04 05 060t (s)

minus5

0

5

10

15

20

Te

(Nlowast

m)

(b) SMVS-DTC


DTCSMVS-DTC

01 02 03 04 05 06t (s)

0100020003000400050006000

n(r

min

)







0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC


minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC


01 02 03 04 05 060t (s)


00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC


00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC


MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)






PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







(3)



(4)



119878 = minus120576 sgn 119878 minus 119870119878 (5)



12059511199041205731205901198711119904)1199061119904120573] = 1198621+ 1198631119906

(6)


+ 2119877119904 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) = 1198622 + 1198632119906(7)


1198621 = minus321198751[[[[

1120590(11987711199041198711119904 +

11987711199031198711119903)(12059511199041205731198941119904120572 minus 12059511199041205721198941119904120573)

+ 120596119903 (12059511199041205721198941119904120572 + 12059511199041205731198941119904120573) minus 120596119903120590119871111990412059521119904]]]]

1198631 = [minus321198751 (1198941119904120573 minus12059511199041205731205901198711119904)


(8)


119878 = [ 11987811198782] = [11986211198622] + [

11986311198632][11990611199041205721199061119904120573] (9)





1198893= 2120595111990412057231199011 (12059511199041205731198941119904120573 + 12059511199041205721198941119904120572) minus 31199011 (12059521119904120573 + 12059521119904120572) 1205901198711119904


(11)




lim119878rarr0+


119878 gt 0 (12)






(14)






119865119909 = 119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) 119865119910 = 119870119898 (11989421199041205731205951120572 minus 11989421199041205721205951120573)

(16)




119865119904119909 = 119896119904119909119865119904119910 = 119896119904119910 (17)





= [119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) minus 119896119904119909]119898




= 119891 (119909 119906) 119910 = ℎ (119909 119906)

119909 (1199050) = 1199090(20)



119883 = [1199091 1199092 1199093 1199094]119879 = [119909 119910 119910]119879 (21)


119880 = [1199061 1199062]119879 = [1198942119904120572 1198942119904120573]119879 (22)


119884 = [1199101 1199102]119879 = [119909 119910]119879 (23)




(24)



(25)


119860 = [[[[[

120597 11991011205971199061120597 11991011205971199062

120597 11991021205971199061120597 11991021205971199062

]]]]]= 119870119898119898 [ 1205951120572 1205951120573minus1205951120573 1205951120572] (26)



1199061 = 119898119870119898 (12059521120572 + 12059521120573) (12059511205721206011 minus 12059511205731206012 +

11989611990411989811990911205951120572

minus 11989611990411989811990921205951120573 minus 1198921205951120573) 1199062 = 119898

119870119898 (12059521120572 + 12059521120573) (12059511205731206011 + 12059511205721206012 +11989611990411989811990911205951120573

+ 11989611990411989811990921205951120572 + 1198921205951120572)

(27)










1205951120572 = 1205951119904120572 minus 119871111990411989711989411199041205721205951120573 = 1205951119904120573 minus 11987111199041198971198941119904120573 (31)





Speed regulator


Torque calculation

SMVS-DTC

Inverter

x2s3s

CRPWM


y

BIM

SMVS Inversesystem

i1s120572

i1s120573

i1s120572

i1s120572

i1s120573

i1s120573

i1s120572i1s120573

u1s120572

u1s120573

u1s120572

u1s120573

R1s

minus

minus

+

+

minus+

minus+

1205951s

120595lowast1s

120596r

120596r

1205951s120572

1205951s120572

1205951s120573

1205951s120573

xlowast

ylowast

1206011

1206012

1205951120572 1205951120573

ilowast2s120572

ilowast2s120573

Te

Tlowaste

u1sa

u1sb

u1sc

120596lowastr

i2sa

i2sb

i2sc

ilowast2sa

ilowast2sb

ilowast2sc












1205951s (Wb)

minus1

minus05

0

05

1

1205951s

(Wb)

(a) DTC

minus1

minus05

0

05

1

1205951s

(Wb)

1205951s (Wb)minus11 05 0 minus05

(b) SMVS-DTC


minus505

10152025

Te

(Nlowast

m)

01 02 03 04 05 060t (s)

(a) DTC

01 02 03 04 05 060t (s)

minus5

0

5

10

15

20

Te

(Nlowast

m)

(b) SMVS-DTC


DTCSMVS-DTC

01 02 03 04 05 06t (s)

0100020003000400050006000

n(r

min

)







0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC


minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC


01 02 03 04 05 060t (s)


00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC


00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC


MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)






PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






lim119878rarr0+


119878 gt 0 (12)






(14)






119865119909 = 119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) 119865119910 = 119870119898 (11989421199041205731205951120572 minus 11989421199041205721205951120573)

(16)




119865119904119909 = 119896119904119909119865119904119910 = 119896119904119910 (17)





= [119870119898 (11989421199041205721205951120572 + 11989421199041205731205951120573) minus 119896119904119909]119898




= 119891 (119909 119906) 119910 = ℎ (119909 119906)

119909 (1199050) = 1199090(20)



119883 = [1199091 1199092 1199093 1199094]119879 = [119909 119910 119910]119879 (21)


119880 = [1199061 1199062]119879 = [1198942119904120572 1198942119904120573]119879 (22)


119884 = [1199101 1199102]119879 = [119909 119910]119879 (23)




(24)



(25)


119860 = [[[[[

120597 11991011205971199061120597 11991011205971199062

120597 11991021205971199061120597 11991021205971199062

]]]]]= 119870119898119898 [ 1205951120572 1205951120573minus1205951120573 1205951120572] (26)



1199061 = 119898119870119898 (12059521120572 + 12059521120573) (12059511205721206011 minus 12059511205731206012 +

11989611990411989811990911205951120572

minus 11989611990411989811990921205951120573 minus 1198921205951120573) 1199062 = 119898

119870119898 (12059521120572 + 12059521120573) (12059511205731206011 + 12059511205721206012 +11989611990411989811990911205951120573

+ 11989611990411989811990921205951120572 + 1198921205951120572)

(27)










1205951120572 = 1205951119904120572 minus 119871111990411989711989411199041205721205951120573 = 1205951119904120573 minus 11987111199041198971198941119904120573 (31)





Speed regulator


Torque calculation

SMVS-DTC

Inverter

x2s3s

CRPWM


y

BIM

SMVS Inversesystem

i1s120572

i1s120573

i1s120572

i1s120572

i1s120573

i1s120573

i1s120572i1s120573

u1s120572

u1s120573

u1s120572

u1s120573

R1s

minus

minus

+

+

minus+

minus+

1205951s

120595lowast1s

120596r

120596r

1205951s120572

1205951s120572

1205951s120573

1205951s120573

xlowast

ylowast

1206011

1206012

1205951120572 1205951120573

ilowast2s120572

ilowast2s120573

Te

Tlowaste

u1sa

u1sb

u1sc

120596lowastr

i2sa

i2sb

i2sc

ilowast2sa

ilowast2sb

ilowast2sc












1205951s (Wb)

minus1

minus05

0

05

1

1205951s

(Wb)

(a) DTC

minus1

minus05

0

05

1

1205951s

(Wb)

1205951s (Wb)minus11 05 0 minus05

(b) SMVS-DTC


minus505

10152025

Te

(Nlowast

m)

01 02 03 04 05 060t (s)

(a) DTC

01 02 03 04 05 060t (s)

minus5

0

5

10

15

20

Te

(Nlowast

m)

(b) SMVS-DTC


DTCSMVS-DTC

01 02 03 04 05 06t (s)

0100020003000400050006000

n(r

min

)







0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC


minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC


01 02 03 04 05 060t (s)


00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC


00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC


MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)






PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







(24)



(25)


119860 = [[[[[

120597 11991011205971199061120597 11991011205971199062

120597 11991021205971199061120597 11991021205971199062

]]]]]= 119870119898119898 [ 1205951120572 1205951120573minus1205951120573 1205951120572] (26)



1199061 = 119898119870119898 (12059521120572 + 12059521120573) (12059511205721206011 minus 12059511205731206012 +

11989611990411989811990911205951120572

minus 11989611990411989811990921205951120573 minus 1198921205951120573) 1199062 = 119898

119870119898 (12059521120572 + 12059521120573) (12059511205731206011 + 12059511205721206012 +11989611990411989811990911205951120573

+ 11989611990411989811990921205951120572 + 1198921205951120572)

(27)










1205951120572 = 1205951119904120572 minus 119871111990411989711989411199041205721205951120573 = 1205951119904120573 minus 11987111199041198971198941119904120573 (31)





Speed regulator


Torque calculation

SMVS-DTC

Inverter

x2s3s

CRPWM


y

BIM

SMVS Inversesystem

i1s120572

i1s120573

i1s120572

i1s120572

i1s120573

i1s120573

i1s120572i1s120573

u1s120572

u1s120573

u1s120572

u1s120573

R1s

minus

minus

+

+

minus+

minus+

1205951s

120595lowast1s

120596r

120596r

1205951s120572

1205951s120572

1205951s120573

1205951s120573

xlowast

ylowast

1206011

1206012

1205951120572 1205951120573

ilowast2s120572

ilowast2s120573

Te

Tlowaste

u1sa

u1sb

u1sc

120596lowastr

i2sa

i2sb

i2sc

ilowast2sa

ilowast2sb

ilowast2sc












1205951s (Wb)

minus1

minus05

0

05

1

1205951s

(Wb)

(a) DTC

minus1

minus05

0

05

1

1205951s

(Wb)

1205951s (Wb)minus11 05 0 minus05

(b) SMVS-DTC


minus505

10152025

Te

(Nlowast

m)

01 02 03 04 05 060t (s)

(a) DTC

01 02 03 04 05 060t (s)

minus5

0

5

10

15

20

Te

(Nlowast

m)

(b) SMVS-DTC


DTCSMVS-DTC

01 02 03 04 05 06t (s)

0100020003000400050006000

n(r

min

)







0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC


minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC


01 02 03 04 05 060t (s)


00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC


00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC


MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)






PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Speed regulator


Torque calculation

SMVS-DTC

Inverter

x2s3s

CRPWM


y

BIM

SMVS Inversesystem

i1s120572

i1s120573

i1s120572

i1s120572

i1s120573

i1s120573

i1s120572i1s120573

u1s120572

u1s120573

u1s120572

u1s120573

R1s

minus

minus

+

+

minus+

minus+

1205951s

120595lowast1s

120596r

120596r

1205951s120572

1205951s120572

1205951s120573

1205951s120573

xlowast

ylowast

1206011

1206012

1205951120572 1205951120573

ilowast2s120572

ilowast2s120573

Te

Tlowaste

u1sa

u1sb

u1sc

120596lowastr

i2sa

i2sb

i2sc

ilowast2sa

ilowast2sb

ilowast2sc












1205951s (Wb)

minus1

minus05

0

05

1

1205951s

(Wb)

(a) DTC

minus1

minus05

0

05

1

1205951s

(Wb)

1205951s (Wb)minus11 05 0 minus05

(b) SMVS-DTC


minus505

10152025

Te

(Nlowast

m)

01 02 03 04 05 060t (s)

(a) DTC

01 02 03 04 05 060t (s)

minus5

0

5

10

15

20

Te

(Nlowast

m)

(b) SMVS-DTC


DTCSMVS-DTC

01 02 03 04 05 06t (s)

0100020003000400050006000

n(r

min

)







0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC


minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC


01 02 03 04 05 060t (s)


00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC


00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC


MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)






PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






1205951s (Wb)

minus1

minus05

0

05

1

1205951s

(Wb)

(a) DTC

minus1

minus05

0

05

1

1205951s

(Wb)

1205951s (Wb)minus11 05 0 minus05

(b) SMVS-DTC


minus505

10152025

Te

(Nlowast

m)

01 02 03 04 05 060t (s)

(a) DTC

01 02 03 04 05 060t (s)

minus5

0

5

10

15

20

Te

(Nlowast

m)

(b) SMVS-DTC


DTCSMVS-DTC

01 02 03 04 05 06t (s)

0100020003000400050006000

n(r

min

)







0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC


minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC


01 02 03 04 05 060t (s)


00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC


00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC


MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)






PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0 001 002minus001minus002 003X (mm)

minus002

minus001

0

001

002

003Y

(mm

)

(a) DTC


minus002

minus0015

minus001

minus0005

0

0005

001

0015

002

Y (m

m)

(b) SMVS-DTC


01 02 03 04 05 060t (s)


00015

0030045

Radi

al d

ispla

cem

ent (

mm

)

(a) DTC


00005

0010015

Radi

al d

ispla

cem

ent (

mm

)

01 02 03 04 05 060t (s)

(b) SMVS-DTC


MeasuredPreset

035minus001

0001002003004005006007008

Radi

al d

ispla

cem

ent (

mm

)

026 027 028 029 03 031 032 033 034025t (s)






PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





PWM1ndash6 IPM

LEM voltagesensor

DSP

LEM currentsensor

Speed closed loop

Isolation drive

PWM7ndash12

LEM currentsensor



Suspension control

Torque winding

BIM

Suspensionwinding


SMVS-DTC

IPMIsolation drive



Time (100 msdiv)

y(

100

md

iv)

x(

100

md

iv)


5 Conclusion






Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





Time (100 msdiv)

Spee

d (1

000

rpm

div

)T

Te

(1Nlowast

md

iv)

(a) DTC

Time (100 msdiv)

Spee

d (1

000

rpm

div

)

T

Te

(1Nlowast

md

iv)

(b) SMVS-DTC




Acknowledgments


References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






















Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




a bearingless induction motor direct torque control and

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