Research ArticleSensorless Rotor-Field Oriented Controlled InductionMotor Drive with Particle Swarm Optimization AlgorithmSpeed Controller Design Strategy

Yung-Chang Luo Zhi-Sheng Ke and Ying-Piao Kuo

Department of Electrical Engineering National Chin-Yi University of Technology No 57 Section 2 Zhongshan RoadTaiping District Taichung 41170 Taiwan

Correspondence should be addressed to Yung-Chang Luo luoycncutedutw

Received 26 February 2014 Accepted 16 April 2014 Published 12 June 2014

Academic Editor Her-Terng Yau

Copyright copy 2014 Yung-Chang Luo et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

A sensorless rotor-field oriented control inductionmotor drive with particle swarm optimization algorithm speed controller designstrategy is presented First the rotor-field oriented control scheme of inductionmotor is establishedThen the current-and-voltageserial-model rotor-flux estimator is developed to identify synchronous speed for coordinate transformation Third the rotor-shaftspeed on-line estimation is established applying themodel reference adaptive systemmethod based on estimated rotor-flux Fourththe speed controller of sensorless induction motor drive is designed using particle swarm optimization algorithm Simulation andexperimental results confirm the effectiveness of the proposed approach

1 Introduction

Automatic production facilities require numerous motorsto actuate mechanical load Direct current (DC) motorsdemand frequent maintenance requirements and are unsuit-able for dirty and explosive environments because of thepresence of brushes and commutators Induction motors(IM) possess lower volume and weight are more reliableand efficient and require fewer maintenance requirementsHowever the control of an IMdrive ismore complicated thanaDCmotor drive Since Blaschke presented the field orientedcontrol (FOC) theory of an IM [1] it is through suitablecoordinate transformation that the nonlinear coupling andtime-varying model of IM can be converted as a DC sepa-rately excited motor which field and armature voltage canbe independently controlled and DC like drive performancecan be achieved Nevertheless the implementation of FOCrequires rotor-shaft encoder to detect rotor-shaft positionThis position sensor however reduces the drive reliabilityand is unsuitable for hostile environment Hence the sen-sorless FOC approaches which utilize flux linkage and speedestimationmethods have been extensively used to replace theconventional FOC IM drives [2 3]

Model reference adaptive system (MRAS) method hasbeen applied to estimate rotor-shaft speed for speed sen-sorless IM drive [4] which has a number of advantagesincluding easy implementation simple structure and lowerparameters sensitivity

Particle swarm optimization (PSO) algorithm is oneof the optimum control approaches which possesses rapidconvergence and lesser adjusting parameters and which issuitable for dynamic conditions application [5] Hence thespeed controller design procedure is developed based on PSOalgorithm for sensorless rotor FOC IM drive in this paper

2 Rotor-Field Oriented Control InductionMotor Drive

The stator and rotor voltage state equations of IM in thesynchronous reference coordinate frame are [6]

V119904= 119877119904

119894119904+ 119895120596119890

120582119904+ 119901

120582119904 (1)

0 = 119877119903

119894119903+ 119895120596119904119897

120582119903+ 119901

120582119903 (2)

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 861462 13 pageshttpdxdoiorg1011552014861462

2 Mathematical Problems in Engineering

where V119904= V119889119904

+ 119895V119902119904is the stator voltage

119894119904= 119894119889119904

+ 119895119894119902119904is the

stator current 120582119904= 120582119889119904

+ 119895120582119902119904is the stator flux linkage

119894119903=

119894119889119903

+ 119895119894119902119903is the rotor current

120582119903= 120582119889119903

+ 119895120582119902119903is the rotor-flux

linkage119877119904is the stator resistance119877

119903is the rotor resistance120596

119890

is the speed of the synchronous reference coordinate frame120596119904119897

= 120596119890minus 120596119903is the slip speed 120596

119903is the electric speed of the

rotor and 119901 = 119889119889119905 is the differential operatorThe stator androtor-flux linkage are given by

120582119904= 119871119904

119894119904+ 119871119898

119894119903 (3)

120582119903= 119871119903

119894119903+ 119871119898

119894119904 (4)

where 119871119904is the stator inductance 119871

119903is the rotor inductance

and 119871119898is the mutual inductance

The developed electromagnetic torque of IM can beobtained by

119879119890=

3119875

4

119871119898

(119894119902119904119894119889119903

minus 119894119889119904119894119902119903) (5)

where 119875 is the pole number of the motor The mechanicalequation of the motor is

119869119898119901120596119903119898

+ 119861119898120596119903119898

+ 119879119871= 119879119890 (6)

where 119869119898is the inertia of the motor 119861

119898is the viscous friction

coefficient 119879119871is the load torque and 120596

119903119898is the mechanical

speed of the motor rotor-shaftThe speed of the motor rotor-shaft can also be expressed as

120596119903119898

=

2

119875

120596119903 (7)

Under the rotor-field oriented control (RFOC) condition set120582119902119903

= 0 in (2) and (4) the estimated slip speed can be derivedas

119904119897

=

119871119898119894119902119904

120591119903120582119889119903

(8)

where 120591119903= 119871119903119877119903is the rotor time constant and the rotor flux

linkage is obtained by

120582119889119903

=

119871119898119894119889119904

1 + 120591119903119904

(9)

where 119904 is the Laplace operator The developed electromag-netic torque of IM under RFOC condition can be derived as

119879119890=

3119875

4

119871119898

119871119903

120582119889119903119894119902119904 (10)

Hence the dynamic equations of IM under RFOC can beexpressed as

119901[

[

119894119889119904

119894119902119904

120582119889119903

]

]

=

[

[

[

[

[

[

[

[

[

[

[

[

minus

119877119904

120590119871119904

minus

1 minus 120590

120590120591119903

120596119890

1 minus 120590

120590119871119898120591119903

minus120596119890

minus

119877119904

120590119871119904

minus

(1 minus 120590) 120596119890

120590119871119898

119871119898

120591119903

0 minus

1

120591119903

]

]

]

]

]

]

]

]

]

]

]

]

[

[

119894119889119904

119894119902119904

120582119889119903

]

]

+

1

120590119871119904

[

[

V119889119904

V119902119904

0

]

]

(11)

where 120590 = 1 minus 119871119898

2

(119871119904119871119903)

Examining (11) as nonlinear and coupling differentialequations the linear control can be acquired by utilizingfeedforward voltage compensation skill The linear outputsignal of the 119902-axis stator current control loop can beexpressed as

V1015840119902119904

= (119870119901119902

+

119870119894119902

119904

) (119894

lowast

119902119904minus 119894119902119904) (12)

where 119894

lowast

119902119904is the command of the 119902-axis stator current and119870

119901119902

and119870119894119902are the proportion and integral gain parameter of the

119902-axis stator current controller respectivelyThe second row of (11) through the decoupling procedure

can be expressed as

119901119894119902119904

= minus

119877119904

120590119871119904

119894119902119904

+ V1015840119902119904 (13)

Comparing (13) with the second row of (11) the decou-pling control of the 119902-axis stator current control loop can beobtained by defining the feedforward voltage compensationas

120590119871119904(120596119890119894119889119904

+

1 minus 120590

120590119871119898

120596119890

120582119889119903) (14)

where 120582119889119903

is the estimated 119889-axis rotor-flux linkage Conse-quently the decoupling voltage equation of the 119902-axis statorcurrent control loop is derived as

Vlowast119902119904

= 120590119871119904(V1015840119902119904

+ 120596119890119894119889119904

+

1 minus 120590

120590119871119898

120596119890

120582119889119903) (15)

where Vlowast119902119904is the command of the 119902-axis stator voltage

Similarly the feedforward voltage compensation of the 119889-axis stator current control loop should be defined as

120590119871119904(minus120596119890119894119902119904

minus

1 minus 120590

120590120591119903119871119898

120582119889119903) (16)

Mathematical Problems in Engineering 3

Kpr

Kir

rarr

iss +

+ +

+

+

+

+

+minus minus

minus

minus

Lm

120591r

1

s

1

s

1

s

Rs

Lr

Lm

120590

1 minus 120590Lm

Voltage model

Current modelr

rarr

ss

rarr120582

s

ri rarr120582

s

rv

rarr120582

s

s

( 1120591r

minus )jr

rarr120582

s

ri

Figure 1 Current-and-voltage serial-model rotor-flux estimator

Then the decoupling control of the 119889-axis stator currentcontrol loop can be acquired and the decoupling voltageequation of the 119889-axis stator current control loop is derivedas

Vlowast119889119904

= 120590119871119904(V1015840119889119904

minus 120596119890119894119902119904

minus

1 minus 120590

120590120591119903119871119898

120582119889119903) (17)

where Vlowast119889119904is the command of the 119889-axis stator voltage and V1015840

119889119904

is the linear output signal of the 119889-axis stator current controlloop

3 Sensorless RFOC Induction Motor Drive

It is necessary to design a speed estimator to replace thefeedback speed in the sensorless RFOC induction motordrive and the speed estimator can be acquired from the rotor-flux estimator

31 Rotor-Flux Estimator The stator current and rotor-fluxlinkage are chosen as state variables in RFOC schemeRewrite (4) as

119894119903=

1

119871119903

(

120582119903minus 119871119898

119894119904) (18)

Then substituting (18) into (3) the stator flux linkage canbe expressed as the function of stator current and rotor-fluxlinkage that is

120582119904= 120590119871119904

119894119904+

119871119898

119871119903

120582119903 (19)

Substituting (19) into (1) the stator voltage equation canbe also expressed by

V119904= (119877119904+ 119895120596119890120590119871119904+ 120590119871119904119901)

119894119904+

119871119898

119871119903

(119895120596119890+ 119901)

120582119903 (20)

Set 120596119890= 0 in (20) the voltage-model rotor-flux estimator can

be derived as

119901

120582

119904

119903V =

119871119903

119871119898

[V119904119904minus (119877119904+ 120590119871119904119901)

119894

119904

119904] (21)

where the superscript ldquo119904rdquo is represented in the stationarycoordinate frame

Then substituting (18) into (2) and setting also 120596119890

= 0the current-model rotor-flux estimator can be derived as

119901

120582

119904

119903119894=

119871119898

120591119903

119894

119904

119904minus (

1

120591119903

minus 119895120596119903)

120582

119904

119903119894 (22)

Both voltage-model and current-model rotor-flux esti-mators are open loop estimators The current-model fluxestimator is affected by the rotor resistance variation at lowspeeds which is affected by the rotor resistance and mutualinductance variation at high speeds The voltage-model fluxestimator is affected by the stator resistance variation and themagnitude of stator voltage at low speeds but is less affected bythe parameters variation at high speeds Hence the current-model rotor-flux estimator is applied for low speeds and thevoltage-model rotor-flux estimator is suitable for high speeds[6] In this paper the closed loop type current-and-voltageserial-model rotor-flux estimator is proposed to improve theestimated rotor-flux for entire speeds and that is shown inFigure 1

Applying the estimated 119889-axis rotor-flux linkage 120582

119904

119889119903and

estimated 119902-axis rotor-flux linkage 120582

119904

119902119903 which are acquired

from Figure 1 the synchronous angular speed for coordinatetransformation between the stationary reference frame andsynchronous reference frame can be obtained that is

120579119890= tanminus1(

120582

119904

119902119903

120582

119904

119889119903

) (23)

4 Mathematical Problems in Engineering

Reference model

Adjustable model

120576

Kp +Ki

s

p =Lr

Lm

s

dris

qr minus s

qris

dr

Adaptationmechanism

rarr

iss

rarr

iss

r

r

rarr

ssrarr

ss[ minus (Rs + 120590Lsp) ]

p =Lm

120591rminus ( 1

120591rminus )rarr

iss jr

rarr120582

s

ri

rarr120582

s

ri

rarr120582

s

rv

Figure 2 MRAS rotor speed estimator based on estimated rotor-flux linkage

32 MRAS Rotor Speed On-Line Estimated Scheme Theestimated synchronous angular speed

119890is derived from the

current-and-voltage serial-model rotor-flux estimator andthe estimated rotor speed

119903can be obtained by subtracting

slip speed 119904119897from

119890

According to MRAS speed estimated scheme which isproposed by Schauder [7] the on-lineMRAS estimated rotorelectrical speed is shown in Figure 2 The voltage-modelrotor-flux estimator relying on (21) is chosen as the referencemodel and the current-model rotor-flux estimator relyingon (22) is chosen as the adjustable model then the errorbetween the reference model and the adjustable model canbe expressed as (24) where the error is passed through anadaptation mechanism to estimate the rotor electrical speedin Figure 2 Consider

120576 =120582

119904

119889119903119894

120582

119904

119902119903V minus120582

119904

119902119903119894

120582

119904

119889119903V (24)

33 PSO Speed Controller Design Strategy PSO is originallyproposed by Kennedy and Eberhart [5 8] which is devisedto simulate social behavior The iterative method is appliedin PSO to improve candidate solution (called particles)to acquire prescribed measure of quality These particlesare moved around in the search-space according to theirposition and velocity Each particle possesses individualoptimum searching variable to correct searching directionin the search-space and that is called particle cognition-onlymodel Comparing individual optimum searching variablewith swarm searching variables and then updating swarmsearching variables to correct searching velocity of theparticles is called swarm social-only model Hence theacquired optimum solution of a problem is according to thebest adaptation value in PSO

Conventional PSO algorithm has a disadvantage of localsolution rapid convergence Consequently some modifiedPSO algorithms are presented which include inertia weightmethod tracking dynamic system method and constrictionfactors method [9] The inertia weight method is applied inthis paper which provides PSO with the ability to searchrapidly for optimum solution at initial stage and possesses

Computeadaptation value

of the particle

Number ofiterations

End

No

Initialize positionand velocity of

the particle

Update the bestvalue of individual

particle Pbest

Update the bestvalue of swarmparticles Gbest

Figure 3 The flowchart of PSO algorithm

effective convergence at later stage the position and velocityupdated formulae are described as follows

119881119894(119896 + 1) = 119908 times 119881

119894(119896) + 119862

1times Rand times (119875best minus 119909

119894)

+ 1198622times Rand times (119866best minus 119909

119894)

119909119894(119896 + 1) = 119909

119894(119896) + 119881

119894(119896 + 1)

(25)

where 119881119894(119896) and 119909

119894(119896) are the velocity and position of the

particle respectively 119875best and119866best are the optimum solutionposition of the individual particle and swarm particlesrespectively119908 is theweighting factor119862

1and119862

2are the learn-

ing factors and Rand is the uniform distribution randomvariable over [0 1]

The flowchart of PSO algorithm is shown in Figure 3The first particle is produced randomly and the best

function value can be found by iteration searching in PSOalgorithmThe best solution is obtained by applying 119875best and119866best to compute optimum variable The design procedure ofPSO algorithms is as follows

Step 1 Create initial position and velocity of the particle in119889-dimension space randomly

Step 2 Apply objective function to compute the adaptationvalue of each particle

Step 3 Compare the position of the present particle with thesearching best solution position 119875best of individual particleIf the new searching adaptation value of the present particleis better to 119875best then update 119875best with the new searchingadaptation value of the present particle

Step 4 Compare the position of the present particle with thesearching best solution position 119866best of swarm particles If

Mathematical Problems in Engineering 5

2

P

PSO speedcontroller

Rotorspeed

estimation

r

Tlowaste 4Lr

3PLm120582lowastr

minusminus

minusminus

+ +

+

+

+

+

++120590Ls

120590Ls

e

e

MRAS for 120596eidentification

Rotor-fluxestimator

Inverter

IM

120596lowastrm

rm

ilowastqs

ilowastds

dr

Kpf +Kif

s

120582lowastr

Kpq +Kiq

s

Kpd +Kid

s

s

dr

120596e +1 minus 120590

120590Lm

120596edrids

120596e +1 minus 120590

120590120591rLm

iqs dr

998400qs lowastqs

998400ds lowastds

idsiqs

iasibsics

lowastas

isqs

isds

lowastbslowastcs

2e⟹2s 2s⟹3

2e

⟹

2s

2e

⟹

2s 2s

⟹

3

slowast

qs

slowast

ds

Figure 4 Sensorless RFOC IM drive with PSO algorithm speed controller design

the new searching adaptation value of the present particleis better to 119866best then update 119866best with the new searchingadaptation value of the present particle

Step 5 Utilizing (25) update the position and velocity of theparticle

Step 6 Repeat Step 2simStep 5 until the desired accuracy isobtained

4 Simulation and Experimental

The block diagram of the proposed sensorless RFOC IMdrive with PSO algorithm speed controller is shown inFigure 4 which includes PSO algorithm speed controllerflux controller 119902-axis and 119889-axis stator current controllersvoltage decouple coordinate transformation MRAS basedrotor speed estimator and current-and-voltage serial-modelrotor-flux estimator In this system the speed control loopis designed using PSO algorithm the flux control loop 119889-axis and 119902-axis stator current control loops are designedproportion-integral (PI) type controller based on the root-locus method The Bode plot of the proposed speed controlloop based on PSO design is shown in Figure 5 The pro-portion gain (119870

119901) integral gain (119870

119894) and bandwidth (119861119882)

for four controllers are shown in Table 1 The simulationscheme that was designed utilizing toolbox MatlabSimulinkis shown in Figure 6

To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller design

10

0

minus10

minus20

minus30

minus400

minus45

minus90

Bode diagram

Frequency (rads)10minus1 100 101 102 103 104

Phas

e (de

g)M

agni

tude

(dB)

System sysFrequency (rads) 109

Magnitude (dB) minus3

Figure 5 Bode plot of the speed control loop based on PSO design

Table 1 Controller parameters and its bandwidth

119870119901

119870119894

BWSpeed controller 09898 14847 109Flux controller 48655 9015 1060119902-axis stator current controller 61651 41099 2970119889-axis stator current controller 89549 44784 3970

a 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM (the parameters of the used IM are listed in Table 2)

6 Mathematical Problems in Engineering

1000

pi30Gain

+minus

+minus

Clock t

t

+

s

120596m

Transfer Fcn

F lowast r

Flux generator

times

divide

Divide

+

s

Transfer Fcn1

Transfer Fcn3

Transfer Fcn2

Transfer Fcn4

4 lowast Lr

3 lowast P lowast Lm +

s

+

s

120596e

120596e

Fedr

Fedr

Fsdr

Fsqr

qe

qe

qe

qe

ids

iqs

fds

fqs

Speed estimation

Series

Fdr

Fqr

120596r

VqsVds

2s to 2e

2s to 2e

isq

isd

Ieqs

Ieqs

Ieds

120596e

Fedr

Ieds

Out1

Out1

Subsystem

Subsystem1

3s to 2s

Isq

Isd

Ias

Ibs

Ics

Le lowast Ls

Le lowast Ls

Gain1

Gain2

Veqs

Veds

VasVsq Vsq

Vbs

Vsd VsdVcs

2e to 2s 2s to 3s

ias

ibs

ics

Te120596m

qm

an

bn

cn

TL

IM

30pirads to rpm

0

Constantqmqm120596rm

120596rm

TeTe

idsiqs

+minus

+minus

+minus

++

120596rm

Kpsmiddots

Kpfmiddots

Kpqmiddots

Kpdmiddots

Kis

Kiq

Kif Kid

Figure 6 Simulation scheme for sensorless RFOC IM drive with PSO algorithm speed controller design

Table 2 The parameters of the used IM

Poles 4119877119904(Ω) 285

119877119903(Ω) 23433

119871119904(H) 01967

119871119903(H) 01967

119871119898(H) 01886

119869119898(Nt-s2m) 0009

119861119898(Nt-s2m2) 000825

is used which serves as the controlled plant for experimenta-tion To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller designa 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM is used which serves as the controlled plant forexperimentation In a running cycle the speed commandis designed as follows forward direction acceleration from119905 = 0 to 119905 = 1 sec forward direction steady-state operationduring 1 le 119905 le 2 sec forward direction braking operationto reach zero speed in the interval 2 le 119905 le 3 sec reversedirection acceleration from 119905 = 3 to 119905 = 4 sec reversedirection steady-state operation during 4 le 119905 le 5 sec andreverse direction braking operation to reach zero speed inthe interval 5 le 119905 le 6 sec The simulated and measured

responses are shown in Figures 7ndash18 Each figure containsfour responses the actual shaft speed the estimated shaftspeed the rotor-flux linkage locus and the estimated elec-tromagnetic torque The simulated and measured responseswith no-load for reversible steady-state speed commandsplusmn300 rpm plusmn900 rpm and plusmn1800 rpm are shown in Figures7 8 9 10 11 and 12 respectively And the simulated andmeasured responseswith loading 2N-m for reversible steady-state speed commands plusmn300 rpm plusmn900 rpm and plusmn1800 rpmare shown in Figures 13 14 15 16 17 and 18 respectively

Based on the simulated and experimental results fordifferent operational speeds as shown in Figures 7ndash18 theproposed MRAS rotor-shaft speed on-line estimation sen-sorless RFOC IM drive with PSO algorithm speed controllerdesign strategy has shown that the desired performance canbe acquired

5 Conclusions

A sensorless RFOC based on current-and-voltage serial-model rotor-flux estimator with PSO algorithm speed con-troller design strategy has been proposed to control an IMdrive The proposed rotor-flux estimator acquired exactlyestimation flux angle position of coordinate transforma-tion between the synchronous reference coordinate frameand the stationary reference coordinate frame The flux

Mathematical Problems in Engineering 7

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 7 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 8 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Mathematical Problems in Engineering

where V119904= V119889119904

+ 119895V119902119904is the stator voltage

119894119904= 119894119889119904

+ 119895119894119902119904is the

stator current 120582119904= 120582119889119904

+ 119895120582119902119904is the stator flux linkage

119894119903=

119894119889119903

+ 119895119894119902119903is the rotor current

120582119903= 120582119889119903

+ 119895120582119902119903is the rotor-flux

linkage119877119904is the stator resistance119877

119903is the rotor resistance120596

119890

is the speed of the synchronous reference coordinate frame120596119904119897

= 120596119890minus 120596119903is the slip speed 120596

119903is the electric speed of the

rotor and 119901 = 119889119889119905 is the differential operatorThe stator androtor-flux linkage are given by

120582119904= 119871119904

119894119904+ 119871119898

119894119903 (3)

120582119903= 119871119903

119894119903+ 119871119898

119894119904 (4)

where 119871119904is the stator inductance 119871

119903is the rotor inductance

and 119871119898is the mutual inductance

The developed electromagnetic torque of IM can beobtained by

119879119890=

3119875

4

119871119898

(119894119902119904119894119889119903

minus 119894119889119904119894119902119903) (5)

where 119875 is the pole number of the motor The mechanicalequation of the motor is

119869119898119901120596119903119898

+ 119861119898120596119903119898

+ 119879119871= 119879119890 (6)

where 119869119898is the inertia of the motor 119861

119898is the viscous friction

coefficient 119879119871is the load torque and 120596

119903119898is the mechanical

speed of the motor rotor-shaftThe speed of the motor rotor-shaft can also be expressed as

120596119903119898

=

2

119875

120596119903 (7)

Under the rotor-field oriented control (RFOC) condition set120582119902119903

= 0 in (2) and (4) the estimated slip speed can be derivedas

119904119897

=

119871119898119894119902119904

120591119903120582119889119903

(8)

where 120591119903= 119871119903119877119903is the rotor time constant and the rotor flux

linkage is obtained by

120582119889119903

=

119871119898119894119889119904

1 + 120591119903119904

(9)

where 119904 is the Laplace operator The developed electromag-netic torque of IM under RFOC condition can be derived as

119879119890=

3119875

4

119871119898

119871119903

120582119889119903119894119902119904 (10)

Hence the dynamic equations of IM under RFOC can beexpressed as

119901[

[

119894119889119904

119894119902119904

120582119889119903

]

]

=

[

[

[

[

[

[

[

[

[

[

[

[

minus

119877119904

120590119871119904

minus

1 minus 120590

120590120591119903

120596119890

1 minus 120590

120590119871119898120591119903

minus120596119890

minus

119877119904

120590119871119904

minus

(1 minus 120590) 120596119890

120590119871119898

119871119898

120591119903

0 minus

1

120591119903

]

]

]

]

]

]

]

]

]

]

]

]

[

[

119894119889119904

119894119902119904

120582119889119903

]

]

+

1

120590119871119904

[

[

V119889119904

V119902119904

0

]

]

(11)

where 120590 = 1 minus 119871119898

2

(119871119904119871119903)

Examining (11) as nonlinear and coupling differentialequations the linear control can be acquired by utilizingfeedforward voltage compensation skill The linear outputsignal of the 119902-axis stator current control loop can beexpressed as

V1015840119902119904

= (119870119901119902

+

119870119894119902

119904

) (119894

lowast

119902119904minus 119894119902119904) (12)

where 119894

lowast

119902119904is the command of the 119902-axis stator current and119870

119901119902

and119870119894119902are the proportion and integral gain parameter of the

119902-axis stator current controller respectivelyThe second row of (11) through the decoupling procedure

can be expressed as

119901119894119902119904

= minus

119877119904

120590119871119904

119894119902119904

+ V1015840119902119904 (13)

Comparing (13) with the second row of (11) the decou-pling control of the 119902-axis stator current control loop can beobtained by defining the feedforward voltage compensationas

120590119871119904(120596119890119894119889119904

+

1 minus 120590

120590119871119898

120596119890

120582119889119903) (14)

where 120582119889119903

is the estimated 119889-axis rotor-flux linkage Conse-quently the decoupling voltage equation of the 119902-axis statorcurrent control loop is derived as

Vlowast119902119904

= 120590119871119904(V1015840119902119904

+ 120596119890119894119889119904

+

1 minus 120590

120590119871119898

120596119890

120582119889119903) (15)

where Vlowast119902119904is the command of the 119902-axis stator voltage

Similarly the feedforward voltage compensation of the 119889-axis stator current control loop should be defined as

120590119871119904(minus120596119890119894119902119904

minus

1 minus 120590

120590120591119903119871119898

120582119889119903) (16)

Mathematical Problems in Engineering 3

Kpr

Kir

rarr

iss +

+ +

+

+

+

+

+minus minus

minus

minus

Lm

120591r

1

s

1

s

1

s

Rs

Lr

Lm

120590

1 minus 120590Lm

Voltage model

Current modelr

rarr

ss

rarr120582

s

ri rarr120582

s

rv

rarr120582

s

s

( 1120591r

minus )jr

rarr120582

s

ri

Figure 1 Current-and-voltage serial-model rotor-flux estimator

Then the decoupling control of the 119889-axis stator currentcontrol loop can be acquired and the decoupling voltageequation of the 119889-axis stator current control loop is derivedas

Vlowast119889119904

= 120590119871119904(V1015840119889119904

minus 120596119890119894119902119904

minus

1 minus 120590

120590120591119903119871119898

120582119889119903) (17)

where Vlowast119889119904is the command of the 119889-axis stator voltage and V1015840

119889119904

is the linear output signal of the 119889-axis stator current controlloop

3 Sensorless RFOC Induction Motor Drive

It is necessary to design a speed estimator to replace thefeedback speed in the sensorless RFOC induction motordrive and the speed estimator can be acquired from the rotor-flux estimator

31 Rotor-Flux Estimator The stator current and rotor-fluxlinkage are chosen as state variables in RFOC schemeRewrite (4) as

119894119903=

1

119871119903

(

120582119903minus 119871119898

119894119904) (18)

Then substituting (18) into (3) the stator flux linkage canbe expressed as the function of stator current and rotor-fluxlinkage that is

120582119904= 120590119871119904

119894119904+

119871119898

119871119903

120582119903 (19)

Substituting (19) into (1) the stator voltage equation canbe also expressed by

V119904= (119877119904+ 119895120596119890120590119871119904+ 120590119871119904119901)

119894119904+

119871119898

119871119903

(119895120596119890+ 119901)

120582119903 (20)

Set 120596119890= 0 in (20) the voltage-model rotor-flux estimator can

be derived as

119901

120582

119904

119903V =

119871119903

119871119898

[V119904119904minus (119877119904+ 120590119871119904119901)

119894

119904

119904] (21)

where the superscript ldquo119904rdquo is represented in the stationarycoordinate frame

Then substituting (18) into (2) and setting also 120596119890

= 0the current-model rotor-flux estimator can be derived as

119901

120582

119904

119903119894=

119871119898

120591119903

119894

119904

119904minus (

1

120591119903

minus 119895120596119903)

120582

119904

119903119894 (22)

Both voltage-model and current-model rotor-flux esti-mators are open loop estimators The current-model fluxestimator is affected by the rotor resistance variation at lowspeeds which is affected by the rotor resistance and mutualinductance variation at high speeds The voltage-model fluxestimator is affected by the stator resistance variation and themagnitude of stator voltage at low speeds but is less affected bythe parameters variation at high speeds Hence the current-model rotor-flux estimator is applied for low speeds and thevoltage-model rotor-flux estimator is suitable for high speeds[6] In this paper the closed loop type current-and-voltageserial-model rotor-flux estimator is proposed to improve theestimated rotor-flux for entire speeds and that is shown inFigure 1

Applying the estimated 119889-axis rotor-flux linkage 120582

119904

119889119903and

estimated 119902-axis rotor-flux linkage 120582

119904

119902119903 which are acquired

from Figure 1 the synchronous angular speed for coordinatetransformation between the stationary reference frame andsynchronous reference frame can be obtained that is

120579119890= tanminus1(

120582

119904

119902119903

120582

119904

119889119903

) (23)

4 Mathematical Problems in Engineering

Reference model

Adjustable model

120576

Kp +Ki

s

p =Lr

Lm

s

dris

qr minus s

qris

dr

Adaptationmechanism

rarr

iss

rarr

iss

r

r

rarr

ssrarr

ss[ minus (Rs + 120590Lsp) ]

p =Lm

120591rminus ( 1

120591rminus )rarr

iss jr

rarr120582

s

ri

rarr120582

s

ri

rarr120582

s

rv

Figure 2 MRAS rotor speed estimator based on estimated rotor-flux linkage

32 MRAS Rotor Speed On-Line Estimated Scheme Theestimated synchronous angular speed

119890is derived from the

current-and-voltage serial-model rotor-flux estimator andthe estimated rotor speed

119903can be obtained by subtracting

slip speed 119904119897from

119890

According to MRAS speed estimated scheme which isproposed by Schauder [7] the on-lineMRAS estimated rotorelectrical speed is shown in Figure 2 The voltage-modelrotor-flux estimator relying on (21) is chosen as the referencemodel and the current-model rotor-flux estimator relyingon (22) is chosen as the adjustable model then the errorbetween the reference model and the adjustable model canbe expressed as (24) where the error is passed through anadaptation mechanism to estimate the rotor electrical speedin Figure 2 Consider

120576 =120582

119904

119889119903119894

120582

119904

119902119903V minus120582

119904

119902119903119894

120582

119904

119889119903V (24)

33 PSO Speed Controller Design Strategy PSO is originallyproposed by Kennedy and Eberhart [5 8] which is devisedto simulate social behavior The iterative method is appliedin PSO to improve candidate solution (called particles)to acquire prescribed measure of quality These particlesare moved around in the search-space according to theirposition and velocity Each particle possesses individualoptimum searching variable to correct searching directionin the search-space and that is called particle cognition-onlymodel Comparing individual optimum searching variablewith swarm searching variables and then updating swarmsearching variables to correct searching velocity of theparticles is called swarm social-only model Hence theacquired optimum solution of a problem is according to thebest adaptation value in PSO

Conventional PSO algorithm has a disadvantage of localsolution rapid convergence Consequently some modifiedPSO algorithms are presented which include inertia weightmethod tracking dynamic system method and constrictionfactors method [9] The inertia weight method is applied inthis paper which provides PSO with the ability to searchrapidly for optimum solution at initial stage and possesses

Computeadaptation value

of the particle

Number ofiterations

End

No

Initialize positionand velocity of

the particle

Update the bestvalue of individual

particle Pbest

Update the bestvalue of swarmparticles Gbest

Figure 3 The flowchart of PSO algorithm

effective convergence at later stage the position and velocityupdated formulae are described as follows

119881119894(119896 + 1) = 119908 times 119881

119894(119896) + 119862

1times Rand times (119875best minus 119909

119894)

+ 1198622times Rand times (119866best minus 119909

119894)

119909119894(119896 + 1) = 119909

119894(119896) + 119881

119894(119896 + 1)

(25)

where 119881119894(119896) and 119909

119894(119896) are the velocity and position of the

particle respectively 119875best and119866best are the optimum solutionposition of the individual particle and swarm particlesrespectively119908 is theweighting factor119862

1and119862

2are the learn-

ing factors and Rand is the uniform distribution randomvariable over [0 1]

The flowchart of PSO algorithm is shown in Figure 3The first particle is produced randomly and the best

function value can be found by iteration searching in PSOalgorithmThe best solution is obtained by applying 119875best and119866best to compute optimum variable The design procedure ofPSO algorithms is as follows

Step 1 Create initial position and velocity of the particle in119889-dimension space randomly

Step 2 Apply objective function to compute the adaptationvalue of each particle

Step 3 Compare the position of the present particle with thesearching best solution position 119875best of individual particleIf the new searching adaptation value of the present particleis better to 119875best then update 119875best with the new searchingadaptation value of the present particle

Step 4 Compare the position of the present particle with thesearching best solution position 119866best of swarm particles If

Mathematical Problems in Engineering 5

2

P

PSO speedcontroller

Rotorspeed

estimation

r

Tlowaste 4Lr

3PLm120582lowastr

minusminus

minusminus

+ +

+

+

+

+

++120590Ls

120590Ls

e

e

MRAS for 120596eidentification

Rotor-fluxestimator

Inverter

IM

120596lowastrm

rm

ilowastqs

ilowastds

dr

Kpf +Kif

s

120582lowastr

Kpq +Kiq

s

Kpd +Kid

s

s

dr

120596e +1 minus 120590

120590Lm

120596edrids

120596e +1 minus 120590

120590120591rLm

iqs dr

998400qs lowastqs

998400ds lowastds

idsiqs

iasibsics

lowastas

isqs

isds

lowastbslowastcs

2e⟹2s 2s⟹3

2e

⟹

2s

2e

⟹

2s 2s

⟹

3

slowast

qs

slowast

ds

Figure 4 Sensorless RFOC IM drive with PSO algorithm speed controller design

the new searching adaptation value of the present particleis better to 119866best then update 119866best with the new searchingadaptation value of the present particle

Step 5 Utilizing (25) update the position and velocity of theparticle

Step 6 Repeat Step 2simStep 5 until the desired accuracy isobtained

4 Simulation and Experimental

The block diagram of the proposed sensorless RFOC IMdrive with PSO algorithm speed controller is shown inFigure 4 which includes PSO algorithm speed controllerflux controller 119902-axis and 119889-axis stator current controllersvoltage decouple coordinate transformation MRAS basedrotor speed estimator and current-and-voltage serial-modelrotor-flux estimator In this system the speed control loopis designed using PSO algorithm the flux control loop 119889-axis and 119902-axis stator current control loops are designedproportion-integral (PI) type controller based on the root-locus method The Bode plot of the proposed speed controlloop based on PSO design is shown in Figure 5 The pro-portion gain (119870

119901) integral gain (119870

119894) and bandwidth (119861119882)

for four controllers are shown in Table 1 The simulationscheme that was designed utilizing toolbox MatlabSimulinkis shown in Figure 6

To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller design

10

0

minus10

minus20

minus30

minus400

minus45

minus90

Bode diagram

Frequency (rads)10minus1 100 101 102 103 104

Phas

e (de

g)M

agni

tude

(dB)

System sysFrequency (rads) 109

Magnitude (dB) minus3

Figure 5 Bode plot of the speed control loop based on PSO design

Table 1 Controller parameters and its bandwidth

119870119901

119870119894

BWSpeed controller 09898 14847 109Flux controller 48655 9015 1060119902-axis stator current controller 61651 41099 2970119889-axis stator current controller 89549 44784 3970

a 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM (the parameters of the used IM are listed in Table 2)

6 Mathematical Problems in Engineering

1000

pi30Gain

+minus

+minus

Clock t

t

+

s

120596m

Transfer Fcn

F lowast r

Flux generator

times

divide

Divide

+

s

Transfer Fcn1

Transfer Fcn3

Transfer Fcn2

Transfer Fcn4

4 lowast Lr

3 lowast P lowast Lm +

s

+

s

120596e

120596e

Fedr

Fedr

Fsdr

Fsqr

qe

qe

qe

qe

ids

iqs

fds

fqs

Speed estimation

Series

Fdr

Fqr

120596r

VqsVds

2s to 2e

2s to 2e

isq

isd

Ieqs

Ieqs

Ieds

120596e

Fedr

Ieds

Out1

Out1

Subsystem

Subsystem1

3s to 2s

Isq

Isd

Ias

Ibs

Ics

Le lowast Ls

Le lowast Ls

Gain1

Gain2

Veqs

Veds

VasVsq Vsq

Vbs

Vsd VsdVcs

2e to 2s 2s to 3s

ias

ibs

ics

Te120596m

qm

an

bn

cn

TL

IM

30pirads to rpm

0

Constantqmqm120596rm

120596rm

TeTe

idsiqs

+minus

+minus

+minus

++

120596rm

Kpsmiddots

Kpfmiddots

Kpqmiddots

Kpdmiddots

Kis

Kiq

Kif Kid

Figure 6 Simulation scheme for sensorless RFOC IM drive with PSO algorithm speed controller design

Table 2 The parameters of the used IM

Poles 4119877119904(Ω) 285

119877119903(Ω) 23433

119871119904(H) 01967

119871119903(H) 01967

119871119898(H) 01886

119869119898(Nt-s2m) 0009

119861119898(Nt-s2m2) 000825

is used which serves as the controlled plant for experimenta-tion To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller designa 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM is used which serves as the controlled plant forexperimentation In a running cycle the speed commandis designed as follows forward direction acceleration from119905 = 0 to 119905 = 1 sec forward direction steady-state operationduring 1 le 119905 le 2 sec forward direction braking operationto reach zero speed in the interval 2 le 119905 le 3 sec reversedirection acceleration from 119905 = 3 to 119905 = 4 sec reversedirection steady-state operation during 4 le 119905 le 5 sec andreverse direction braking operation to reach zero speed inthe interval 5 le 119905 le 6 sec The simulated and measured

responses are shown in Figures 7ndash18 Each figure containsfour responses the actual shaft speed the estimated shaftspeed the rotor-flux linkage locus and the estimated elec-tromagnetic torque The simulated and measured responseswith no-load for reversible steady-state speed commandsplusmn300 rpm plusmn900 rpm and plusmn1800 rpm are shown in Figures7 8 9 10 11 and 12 respectively And the simulated andmeasured responseswith loading 2N-m for reversible steady-state speed commands plusmn300 rpm plusmn900 rpm and plusmn1800 rpmare shown in Figures 13 14 15 16 17 and 18 respectively

Based on the simulated and experimental results fordifferent operational speeds as shown in Figures 7ndash18 theproposed MRAS rotor-shaft speed on-line estimation sen-sorless RFOC IM drive with PSO algorithm speed controllerdesign strategy has shown that the desired performance canbe acquired

5 Conclusions

A sensorless RFOC based on current-and-voltage serial-model rotor-flux estimator with PSO algorithm speed con-troller design strategy has been proposed to control an IMdrive The proposed rotor-flux estimator acquired exactlyestimation flux angle position of coordinate transforma-tion between the synchronous reference coordinate frameand the stationary reference coordinate frame The flux

Mathematical Problems in Engineering 7

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 7 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 8 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 3

Kpr

Kir

rarr

iss +

+ +

+

+

+

+

+minus minus

minus

minus

Lm

120591r

1

s

1

s

1

s

Rs

Lr

Lm

120590

1 minus 120590Lm

Voltage model

Current modelr

rarr

ss

rarr120582

s

ri rarr120582

s

rv

rarr120582

s

s

( 1120591r

minus )jr

rarr120582

s

ri

Figure 1 Current-and-voltage serial-model rotor-flux estimator

Then the decoupling control of the 119889-axis stator currentcontrol loop can be acquired and the decoupling voltageequation of the 119889-axis stator current control loop is derivedas

Vlowast119889119904

= 120590119871119904(V1015840119889119904

minus 120596119890119894119902119904

minus

1 minus 120590

120590120591119903119871119898

120582119889119903) (17)

where Vlowast119889119904is the command of the 119889-axis stator voltage and V1015840

119889119904

is the linear output signal of the 119889-axis stator current controlloop

3 Sensorless RFOC Induction Motor Drive

It is necessary to design a speed estimator to replace thefeedback speed in the sensorless RFOC induction motordrive and the speed estimator can be acquired from the rotor-flux estimator

31 Rotor-Flux Estimator The stator current and rotor-fluxlinkage are chosen as state variables in RFOC schemeRewrite (4) as

119894119903=

1

119871119903

(

120582119903minus 119871119898

119894119904) (18)

Then substituting (18) into (3) the stator flux linkage canbe expressed as the function of stator current and rotor-fluxlinkage that is

120582119904= 120590119871119904

119894119904+

119871119898

119871119903

120582119903 (19)

Substituting (19) into (1) the stator voltage equation canbe also expressed by

V119904= (119877119904+ 119895120596119890120590119871119904+ 120590119871119904119901)

119894119904+

119871119898

119871119903

(119895120596119890+ 119901)

120582119903 (20)

Set 120596119890= 0 in (20) the voltage-model rotor-flux estimator can

be derived as

119901

120582

119904

119903V =

119871119903

119871119898

[V119904119904minus (119877119904+ 120590119871119904119901)

119894

119904

119904] (21)

where the superscript ldquo119904rdquo is represented in the stationarycoordinate frame

Then substituting (18) into (2) and setting also 120596119890

= 0the current-model rotor-flux estimator can be derived as

119901

120582

119904

119903119894=

119871119898

120591119903

119894

119904

119904minus (

1

120591119903

minus 119895120596119903)

120582

119904

119903119894 (22)

Both voltage-model and current-model rotor-flux esti-mators are open loop estimators The current-model fluxestimator is affected by the rotor resistance variation at lowspeeds which is affected by the rotor resistance and mutualinductance variation at high speeds The voltage-model fluxestimator is affected by the stator resistance variation and themagnitude of stator voltage at low speeds but is less affected bythe parameters variation at high speeds Hence the current-model rotor-flux estimator is applied for low speeds and thevoltage-model rotor-flux estimator is suitable for high speeds[6] In this paper the closed loop type current-and-voltageserial-model rotor-flux estimator is proposed to improve theestimated rotor-flux for entire speeds and that is shown inFigure 1

Applying the estimated 119889-axis rotor-flux linkage 120582

119904

119889119903and

estimated 119902-axis rotor-flux linkage 120582

119904

119902119903 which are acquired

from Figure 1 the synchronous angular speed for coordinatetransformation between the stationary reference frame andsynchronous reference frame can be obtained that is

120579119890= tanminus1(

120582

119904

119902119903

120582

119904

119889119903

) (23)

4 Mathematical Problems in Engineering

Reference model

Adjustable model

120576

Kp +Ki

s

p =Lr

Lm

s

dris

qr minus s

qris

dr

Adaptationmechanism

rarr

iss

rarr

iss

r

r

rarr

ssrarr

ss[ minus (Rs + 120590Lsp) ]

p =Lm

120591rminus ( 1

120591rminus )rarr

iss jr

rarr120582

s

ri

rarr120582

s

ri

rarr120582

s

rv

Figure 2 MRAS rotor speed estimator based on estimated rotor-flux linkage

32 MRAS Rotor Speed On-Line Estimated Scheme Theestimated synchronous angular speed

119890is derived from the

current-and-voltage serial-model rotor-flux estimator andthe estimated rotor speed

119903can be obtained by subtracting

slip speed 119904119897from

119890

According to MRAS speed estimated scheme which isproposed by Schauder [7] the on-lineMRAS estimated rotorelectrical speed is shown in Figure 2 The voltage-modelrotor-flux estimator relying on (21) is chosen as the referencemodel and the current-model rotor-flux estimator relyingon (22) is chosen as the adjustable model then the errorbetween the reference model and the adjustable model canbe expressed as (24) where the error is passed through anadaptation mechanism to estimate the rotor electrical speedin Figure 2 Consider

120576 =120582

119904

119889119903119894

120582

119904

119902119903V minus120582

119904

119902119903119894

120582

119904

119889119903V (24)

33 PSO Speed Controller Design Strategy PSO is originallyproposed by Kennedy and Eberhart [5 8] which is devisedto simulate social behavior The iterative method is appliedin PSO to improve candidate solution (called particles)to acquire prescribed measure of quality These particlesare moved around in the search-space according to theirposition and velocity Each particle possesses individualoptimum searching variable to correct searching directionin the search-space and that is called particle cognition-onlymodel Comparing individual optimum searching variablewith swarm searching variables and then updating swarmsearching variables to correct searching velocity of theparticles is called swarm social-only model Hence theacquired optimum solution of a problem is according to thebest adaptation value in PSO

Conventional PSO algorithm has a disadvantage of localsolution rapid convergence Consequently some modifiedPSO algorithms are presented which include inertia weightmethod tracking dynamic system method and constrictionfactors method [9] The inertia weight method is applied inthis paper which provides PSO with the ability to searchrapidly for optimum solution at initial stage and possesses

Computeadaptation value

of the particle

Number ofiterations

End

No

Initialize positionand velocity of

the particle

Update the bestvalue of individual

particle Pbest

Update the bestvalue of swarmparticles Gbest

Figure 3 The flowchart of PSO algorithm

effective convergence at later stage the position and velocityupdated formulae are described as follows

119881119894(119896 + 1) = 119908 times 119881

119894(119896) + 119862

1times Rand times (119875best minus 119909

119894)

+ 1198622times Rand times (119866best minus 119909

119894)

119909119894(119896 + 1) = 119909

119894(119896) + 119881

119894(119896 + 1)

(25)

where 119881119894(119896) and 119909

119894(119896) are the velocity and position of the

particle respectively 119875best and119866best are the optimum solutionposition of the individual particle and swarm particlesrespectively119908 is theweighting factor119862

1and119862

2are the learn-

ing factors and Rand is the uniform distribution randomvariable over [0 1]

The flowchart of PSO algorithm is shown in Figure 3The first particle is produced randomly and the best

function value can be found by iteration searching in PSOalgorithmThe best solution is obtained by applying 119875best and119866best to compute optimum variable The design procedure ofPSO algorithms is as follows

Step 1 Create initial position and velocity of the particle in119889-dimension space randomly

Step 2 Apply objective function to compute the adaptationvalue of each particle

Step 3 Compare the position of the present particle with thesearching best solution position 119875best of individual particleIf the new searching adaptation value of the present particleis better to 119875best then update 119875best with the new searchingadaptation value of the present particle

Step 4 Compare the position of the present particle with thesearching best solution position 119866best of swarm particles If

Mathematical Problems in Engineering 5

2

P

PSO speedcontroller

Rotorspeed

estimation

r

Tlowaste 4Lr

3PLm120582lowastr

minusminus

minusminus

+ +

+

+

+

+

++120590Ls

120590Ls

e

e

MRAS for 120596eidentification

Rotor-fluxestimator

Inverter

IM

120596lowastrm

rm

ilowastqs

ilowastds

dr

Kpf +Kif

s

120582lowastr

Kpq +Kiq

s

Kpd +Kid

s

s

dr

120596e +1 minus 120590

120590Lm

120596edrids

120596e +1 minus 120590

120590120591rLm

iqs dr

998400qs lowastqs

998400ds lowastds

idsiqs

iasibsics

lowastas

isqs

isds

lowastbslowastcs

2e⟹2s 2s⟹3

2e

⟹

2s

2e

⟹

2s 2s

⟹

3

slowast

qs

slowast

ds

Figure 4 Sensorless RFOC IM drive with PSO algorithm speed controller design

the new searching adaptation value of the present particleis better to 119866best then update 119866best with the new searchingadaptation value of the present particle

Step 5 Utilizing (25) update the position and velocity of theparticle

Step 6 Repeat Step 2simStep 5 until the desired accuracy isobtained

4 Simulation and Experimental

The block diagram of the proposed sensorless RFOC IMdrive with PSO algorithm speed controller is shown inFigure 4 which includes PSO algorithm speed controllerflux controller 119902-axis and 119889-axis stator current controllersvoltage decouple coordinate transformation MRAS basedrotor speed estimator and current-and-voltage serial-modelrotor-flux estimator In this system the speed control loopis designed using PSO algorithm the flux control loop 119889-axis and 119902-axis stator current control loops are designedproportion-integral (PI) type controller based on the root-locus method The Bode plot of the proposed speed controlloop based on PSO design is shown in Figure 5 The pro-portion gain (119870

119901) integral gain (119870

119894) and bandwidth (119861119882)

for four controllers are shown in Table 1 The simulationscheme that was designed utilizing toolbox MatlabSimulinkis shown in Figure 6

To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller design

10

0

minus10

minus20

minus30

minus400

minus45

minus90

Bode diagram

Frequency (rads)10minus1 100 101 102 103 104

Phas

e (de

g)M

agni

tude

(dB)

System sysFrequency (rads) 109

Magnitude (dB) minus3

Figure 5 Bode plot of the speed control loop based on PSO design

Table 1 Controller parameters and its bandwidth

119870119901

119870119894

BWSpeed controller 09898 14847 109Flux controller 48655 9015 1060119902-axis stator current controller 61651 41099 2970119889-axis stator current controller 89549 44784 3970

a 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM (the parameters of the used IM are listed in Table 2)

6 Mathematical Problems in Engineering

1000

pi30Gain

+minus

+minus

Clock t

t

+

s

120596m

Transfer Fcn

F lowast r

Flux generator

times

divide

Divide

+

s

Transfer Fcn1

Transfer Fcn3

Transfer Fcn2

Transfer Fcn4

4 lowast Lr

3 lowast P lowast Lm +

s

+

s

120596e

120596e

Fedr

Fedr

Fsdr

Fsqr

qe

qe

qe

qe

ids

iqs

fds

fqs

Speed estimation

Series

Fdr

Fqr

120596r

VqsVds

2s to 2e

2s to 2e

isq

isd

Ieqs

Ieqs

Ieds

120596e

Fedr

Ieds

Out1

Out1

Subsystem

Subsystem1

3s to 2s

Isq

Isd

Ias

Ibs

Ics

Le lowast Ls

Le lowast Ls

Gain1

Gain2

Veqs

Veds

VasVsq Vsq

Vbs

Vsd VsdVcs

2e to 2s 2s to 3s

ias

ibs

ics

Te120596m

qm

an

bn

cn

TL

IM

30pirads to rpm

0

Constantqmqm120596rm

120596rm

TeTe

idsiqs

+minus

+minus

+minus

++

120596rm

Kpsmiddots

Kpfmiddots

Kpqmiddots

Kpdmiddots

Kis

Kiq

Kif Kid

Figure 6 Simulation scheme for sensorless RFOC IM drive with PSO algorithm speed controller design

Table 2 The parameters of the used IM

Poles 4119877119904(Ω) 285

119877119903(Ω) 23433

119871119904(H) 01967

119871119903(H) 01967

119871119898(H) 01886

119869119898(Nt-s2m) 0009

119861119898(Nt-s2m2) 000825

is used which serves as the controlled plant for experimenta-tion To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller designa 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM is used which serves as the controlled plant forexperimentation In a running cycle the speed commandis designed as follows forward direction acceleration from119905 = 0 to 119905 = 1 sec forward direction steady-state operationduring 1 le 119905 le 2 sec forward direction braking operationto reach zero speed in the interval 2 le 119905 le 3 sec reversedirection acceleration from 119905 = 3 to 119905 = 4 sec reversedirection steady-state operation during 4 le 119905 le 5 sec andreverse direction braking operation to reach zero speed inthe interval 5 le 119905 le 6 sec The simulated and measured

responses are shown in Figures 7ndash18 Each figure containsfour responses the actual shaft speed the estimated shaftspeed the rotor-flux linkage locus and the estimated elec-tromagnetic torque The simulated and measured responseswith no-load for reversible steady-state speed commandsplusmn300 rpm plusmn900 rpm and plusmn1800 rpm are shown in Figures7 8 9 10 11 and 12 respectively And the simulated andmeasured responseswith loading 2N-m for reversible steady-state speed commands plusmn300 rpm plusmn900 rpm and plusmn1800 rpmare shown in Figures 13 14 15 16 17 and 18 respectively

Based on the simulated and experimental results fordifferent operational speeds as shown in Figures 7ndash18 theproposed MRAS rotor-shaft speed on-line estimation sen-sorless RFOC IM drive with PSO algorithm speed controllerdesign strategy has shown that the desired performance canbe acquired

5 Conclusions

A sensorless RFOC based on current-and-voltage serial-model rotor-flux estimator with PSO algorithm speed con-troller design strategy has been proposed to control an IMdrive The proposed rotor-flux estimator acquired exactlyestimation flux angle position of coordinate transforma-tion between the synchronous reference coordinate frameand the stationary reference coordinate frame The flux

Mathematical Problems in Engineering 7

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 7 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 8 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Mathematical Problems in Engineering

Reference model

Adjustable model

120576

Kp +Ki

s

p =Lr

Lm

s

dris

qr minus s

qris

dr

Adaptationmechanism

rarr

iss

rarr

iss

r

r

rarr

ssrarr

ss[ minus (Rs + 120590Lsp) ]

p =Lm

120591rminus ( 1

120591rminus )rarr

iss jr

rarr120582

s

ri

rarr120582

s

ri

rarr120582

s

rv

Figure 2 MRAS rotor speed estimator based on estimated rotor-flux linkage

32 MRAS Rotor Speed On-Line Estimated Scheme Theestimated synchronous angular speed

119890is derived from the

current-and-voltage serial-model rotor-flux estimator andthe estimated rotor speed

119903can be obtained by subtracting

slip speed 119904119897from

119890

According to MRAS speed estimated scheme which isproposed by Schauder [7] the on-lineMRAS estimated rotorelectrical speed is shown in Figure 2 The voltage-modelrotor-flux estimator relying on (21) is chosen as the referencemodel and the current-model rotor-flux estimator relyingon (22) is chosen as the adjustable model then the errorbetween the reference model and the adjustable model canbe expressed as (24) where the error is passed through anadaptation mechanism to estimate the rotor electrical speedin Figure 2 Consider

120576 =120582

119904

119889119903119894

120582

119904

119902119903V minus120582

119904

119902119903119894

120582

119904

119889119903V (24)

33 PSO Speed Controller Design Strategy PSO is originallyproposed by Kennedy and Eberhart [5 8] which is devisedto simulate social behavior The iterative method is appliedin PSO to improve candidate solution (called particles)to acquire prescribed measure of quality These particlesare moved around in the search-space according to theirposition and velocity Each particle possesses individualoptimum searching variable to correct searching directionin the search-space and that is called particle cognition-onlymodel Comparing individual optimum searching variablewith swarm searching variables and then updating swarmsearching variables to correct searching velocity of theparticles is called swarm social-only model Hence theacquired optimum solution of a problem is according to thebest adaptation value in PSO

Conventional PSO algorithm has a disadvantage of localsolution rapid convergence Consequently some modifiedPSO algorithms are presented which include inertia weightmethod tracking dynamic system method and constrictionfactors method [9] The inertia weight method is applied inthis paper which provides PSO with the ability to searchrapidly for optimum solution at initial stage and possesses

Computeadaptation value

of the particle

Number ofiterations

End

No

Initialize positionand velocity of

the particle

Update the bestvalue of individual

particle Pbest

Update the bestvalue of swarmparticles Gbest

Figure 3 The flowchart of PSO algorithm

effective convergence at later stage the position and velocityupdated formulae are described as follows

119881119894(119896 + 1) = 119908 times 119881

119894(119896) + 119862

1times Rand times (119875best minus 119909

119894)

+ 1198622times Rand times (119866best minus 119909

119894)

119909119894(119896 + 1) = 119909

119894(119896) + 119881

119894(119896 + 1)

(25)

where 119881119894(119896) and 119909

119894(119896) are the velocity and position of the

particle respectively 119875best and119866best are the optimum solutionposition of the individual particle and swarm particlesrespectively119908 is theweighting factor119862

1and119862

2are the learn-

ing factors and Rand is the uniform distribution randomvariable over [0 1]

The flowchart of PSO algorithm is shown in Figure 3The first particle is produced randomly and the best

function value can be found by iteration searching in PSOalgorithmThe best solution is obtained by applying 119875best and119866best to compute optimum variable The design procedure ofPSO algorithms is as follows

Step 1 Create initial position and velocity of the particle in119889-dimension space randomly

Step 2 Apply objective function to compute the adaptationvalue of each particle

Step 3 Compare the position of the present particle with thesearching best solution position 119875best of individual particleIf the new searching adaptation value of the present particleis better to 119875best then update 119875best with the new searchingadaptation value of the present particle

Step 4 Compare the position of the present particle with thesearching best solution position 119866best of swarm particles If

Mathematical Problems in Engineering 5

2

P

PSO speedcontroller

Rotorspeed

estimation

r

Tlowaste 4Lr

3PLm120582lowastr

minusminus

minusminus

+ +

+

+

+

+

++120590Ls

120590Ls

e

e

MRAS for 120596eidentification

Rotor-fluxestimator

Inverter

IM

120596lowastrm

rm

ilowastqs

ilowastds

dr

Kpf +Kif

s

120582lowastr

Kpq +Kiq

s

Kpd +Kid

s

s

dr

120596e +1 minus 120590

120590Lm

120596edrids

120596e +1 minus 120590

120590120591rLm

iqs dr

998400qs lowastqs

998400ds lowastds

idsiqs

iasibsics

lowastas

isqs

isds

lowastbslowastcs

2e⟹2s 2s⟹3

2e

⟹

2s

2e

⟹

2s 2s

⟹

3

slowast

qs

slowast

ds

Figure 4 Sensorless RFOC IM drive with PSO algorithm speed controller design

the new searching adaptation value of the present particleis better to 119866best then update 119866best with the new searchingadaptation value of the present particle

Step 5 Utilizing (25) update the position and velocity of theparticle

Step 6 Repeat Step 2simStep 5 until the desired accuracy isobtained

4 Simulation and Experimental

The block diagram of the proposed sensorless RFOC IMdrive with PSO algorithm speed controller is shown inFigure 4 which includes PSO algorithm speed controllerflux controller 119902-axis and 119889-axis stator current controllersvoltage decouple coordinate transformation MRAS basedrotor speed estimator and current-and-voltage serial-modelrotor-flux estimator In this system the speed control loopis designed using PSO algorithm the flux control loop 119889-axis and 119902-axis stator current control loops are designedproportion-integral (PI) type controller based on the root-locus method The Bode plot of the proposed speed controlloop based on PSO design is shown in Figure 5 The pro-portion gain (119870

119901) integral gain (119870

119894) and bandwidth (119861119882)

for four controllers are shown in Table 1 The simulationscheme that was designed utilizing toolbox MatlabSimulinkis shown in Figure 6

To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller design

10

0

minus10

minus20

minus30

minus400

minus45

minus90

Bode diagram

Frequency (rads)10minus1 100 101 102 103 104

Phas

e (de

g)M

agni

tude

(dB)

System sysFrequency (rads) 109

Magnitude (dB) minus3

Figure 5 Bode plot of the speed control loop based on PSO design

Table 1 Controller parameters and its bandwidth

119870119901

119870119894

BWSpeed controller 09898 14847 109Flux controller 48655 9015 1060119902-axis stator current controller 61651 41099 2970119889-axis stator current controller 89549 44784 3970

a 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM (the parameters of the used IM are listed in Table 2)

6 Mathematical Problems in Engineering

1000

pi30Gain

+minus

+minus

Clock t

t

+

s

120596m

Transfer Fcn

F lowast r

Flux generator

times

divide

Divide

+

s

Transfer Fcn1

Transfer Fcn3

Transfer Fcn2

Transfer Fcn4

4 lowast Lr

3 lowast P lowast Lm +

s

+

s

120596e

120596e

Fedr

Fedr

Fsdr

Fsqr

qe

qe

qe

qe

ids

iqs

fds

fqs

Speed estimation

Series

Fdr

Fqr

120596r

VqsVds

2s to 2e

2s to 2e

isq

isd

Ieqs

Ieqs

Ieds

120596e

Fedr

Ieds

Out1

Out1

Subsystem

Subsystem1

3s to 2s

Isq

Isd

Ias

Ibs

Ics

Le lowast Ls

Le lowast Ls

Gain1

Gain2

Veqs

Veds

VasVsq Vsq

Vbs

Vsd VsdVcs

2e to 2s 2s to 3s

ias

ibs

ics

Te120596m

qm

an

bn

cn

TL

IM

30pirads to rpm

0

Constantqmqm120596rm

120596rm

TeTe

idsiqs

+minus

+minus

+minus

++

120596rm

Kpsmiddots

Kpfmiddots

Kpqmiddots

Kpdmiddots

Kis

Kiq

Kif Kid

Figure 6 Simulation scheme for sensorless RFOC IM drive with PSO algorithm speed controller design

Table 2 The parameters of the used IM

Poles 4119877119904(Ω) 285

119877119903(Ω) 23433

119871119904(H) 01967

119871119903(H) 01967

119871119898(H) 01886

119869119898(Nt-s2m) 0009

119861119898(Nt-s2m2) 000825

is used which serves as the controlled plant for experimenta-tion To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller designa 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM is used which serves as the controlled plant forexperimentation In a running cycle the speed commandis designed as follows forward direction acceleration from119905 = 0 to 119905 = 1 sec forward direction steady-state operationduring 1 le 119905 le 2 sec forward direction braking operationto reach zero speed in the interval 2 le 119905 le 3 sec reversedirection acceleration from 119905 = 3 to 119905 = 4 sec reversedirection steady-state operation during 4 le 119905 le 5 sec andreverse direction braking operation to reach zero speed inthe interval 5 le 119905 le 6 sec The simulated and measured

responses are shown in Figures 7ndash18 Each figure containsfour responses the actual shaft speed the estimated shaftspeed the rotor-flux linkage locus and the estimated elec-tromagnetic torque The simulated and measured responseswith no-load for reversible steady-state speed commandsplusmn300 rpm plusmn900 rpm and plusmn1800 rpm are shown in Figures7 8 9 10 11 and 12 respectively And the simulated andmeasured responseswith loading 2N-m for reversible steady-state speed commands plusmn300 rpm plusmn900 rpm and plusmn1800 rpmare shown in Figures 13 14 15 16 17 and 18 respectively

Based on the simulated and experimental results fordifferent operational speeds as shown in Figures 7ndash18 theproposed MRAS rotor-shaft speed on-line estimation sen-sorless RFOC IM drive with PSO algorithm speed controllerdesign strategy has shown that the desired performance canbe acquired

5 Conclusions

A sensorless RFOC based on current-and-voltage serial-model rotor-flux estimator with PSO algorithm speed con-troller design strategy has been proposed to control an IMdrive The proposed rotor-flux estimator acquired exactlyestimation flux angle position of coordinate transforma-tion between the synchronous reference coordinate frameand the stationary reference coordinate frame The flux

Mathematical Problems in Engineering 7

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 7 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 8 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 5

2

P

PSO speedcontroller

Rotorspeed

estimation

r

Tlowaste 4Lr

3PLm120582lowastr

minusminus

minusminus

+ +

+

+

+

+

++120590Ls

120590Ls

e

e

MRAS for 120596eidentification

Rotor-fluxestimator

Inverter

IM

120596lowastrm

rm

ilowastqs

ilowastds

dr

Kpf +Kif

s

120582lowastr

Kpq +Kiq

s

Kpd +Kid

s

s

dr

120596e +1 minus 120590

120590Lm

120596edrids

120596e +1 minus 120590

120590120591rLm

iqs dr

998400qs lowastqs

998400ds lowastds

idsiqs

iasibsics

lowastas

isqs

isds

lowastbslowastcs

2e⟹2s 2s⟹3

2e

⟹

2s

2e

⟹

2s 2s

⟹

3

slowast

qs

slowast

ds

Figure 4 Sensorless RFOC IM drive with PSO algorithm speed controller design

the new searching adaptation value of the present particleis better to 119866best then update 119866best with the new searchingadaptation value of the present particle

Step 5 Utilizing (25) update the position and velocity of theparticle

Step 6 Repeat Step 2simStep 5 until the desired accuracy isobtained

4 Simulation and Experimental

The block diagram of the proposed sensorless RFOC IMdrive with PSO algorithm speed controller is shown inFigure 4 which includes PSO algorithm speed controllerflux controller 119902-axis and 119889-axis stator current controllersvoltage decouple coordinate transformation MRAS basedrotor speed estimator and current-and-voltage serial-modelrotor-flux estimator In this system the speed control loopis designed using PSO algorithm the flux control loop 119889-axis and 119902-axis stator current control loops are designedproportion-integral (PI) type controller based on the root-locus method The Bode plot of the proposed speed controlloop based on PSO design is shown in Figure 5 The pro-portion gain (119870

119901) integral gain (119870

119894) and bandwidth (119861119882)

for four controllers are shown in Table 1 The simulationscheme that was designed utilizing toolbox MatlabSimulinkis shown in Figure 6

To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller design

10

0

minus10

minus20

minus30

minus400

minus45

minus90

Bode diagram

Frequency (rads)10minus1 100 101 102 103 104

Phas

e (de

g)M

agni

tude

(dB)

System sysFrequency (rads) 109

Magnitude (dB) minus3

Figure 5 Bode plot of the speed control loop based on PSO design

Table 1 Controller parameters and its bandwidth

119870119901

119870119894

BWSpeed controller 09898 14847 109Flux controller 48655 9015 1060119902-axis stator current controller 61651 41099 2970119889-axis stator current controller 89549 44784 3970

a 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM (the parameters of the used IM are listed in Table 2)

6 Mathematical Problems in Engineering

1000

pi30Gain

+minus

+minus

Clock t

t

+

s

120596m

Transfer Fcn

F lowast r

Flux generator

times

divide

Divide

+

s

Transfer Fcn1

Transfer Fcn3

Transfer Fcn2

Transfer Fcn4

4 lowast Lr

3 lowast P lowast Lm +

s

+

s

120596e

120596e

Fedr

Fedr

Fsdr

Fsqr

qe

qe

qe

qe

ids

iqs

fds

fqs

Speed estimation

Series

Fdr

Fqr

120596r

VqsVds

2s to 2e

2s to 2e

isq

isd

Ieqs

Ieqs

Ieds

120596e

Fedr

Ieds

Out1

Out1

Subsystem

Subsystem1

3s to 2s

Isq

Isd

Ias

Ibs

Ics

Le lowast Ls

Le lowast Ls

Gain1

Gain2

Veqs

Veds

VasVsq Vsq

Vbs

Vsd VsdVcs

2e to 2s 2s to 3s

ias

ibs

ics

Te120596m

qm

an

bn

cn

TL

IM

30pirads to rpm

0

Constantqmqm120596rm

120596rm

TeTe

idsiqs

+minus

+minus

+minus

++

120596rm

Kpsmiddots

Kpfmiddots

Kpqmiddots

Kpdmiddots

Kis

Kiq

Kif Kid

Figure 6 Simulation scheme for sensorless RFOC IM drive with PSO algorithm speed controller design

Table 2 The parameters of the used IM

Poles 4119877119904(Ω) 285

119877119903(Ω) 23433

119871119904(H) 01967

119871119903(H) 01967

119871119898(H) 01886

119869119898(Nt-s2m) 0009

119861119898(Nt-s2m2) 000825

is used which serves as the controlled plant for experimenta-tion To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller designa 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM is used which serves as the controlled plant forexperimentation In a running cycle the speed commandis designed as follows forward direction acceleration from119905 = 0 to 119905 = 1 sec forward direction steady-state operationduring 1 le 119905 le 2 sec forward direction braking operationto reach zero speed in the interval 2 le 119905 le 3 sec reversedirection acceleration from 119905 = 3 to 119905 = 4 sec reversedirection steady-state operation during 4 le 119905 le 5 sec andreverse direction braking operation to reach zero speed inthe interval 5 le 119905 le 6 sec The simulated and measured

responses are shown in Figures 7ndash18 Each figure containsfour responses the actual shaft speed the estimated shaftspeed the rotor-flux linkage locus and the estimated elec-tromagnetic torque The simulated and measured responseswith no-load for reversible steady-state speed commandsplusmn300 rpm plusmn900 rpm and plusmn1800 rpm are shown in Figures7 8 9 10 11 and 12 respectively And the simulated andmeasured responseswith loading 2N-m for reversible steady-state speed commands plusmn300 rpm plusmn900 rpm and plusmn1800 rpmare shown in Figures 13 14 15 16 17 and 18 respectively

Based on the simulated and experimental results fordifferent operational speeds as shown in Figures 7ndash18 theproposed MRAS rotor-shaft speed on-line estimation sen-sorless RFOC IM drive with PSO algorithm speed controllerdesign strategy has shown that the desired performance canbe acquired

5 Conclusions

A sensorless RFOC based on current-and-voltage serial-model rotor-flux estimator with PSO algorithm speed con-troller design strategy has been proposed to control an IMdrive The proposed rotor-flux estimator acquired exactlyestimation flux angle position of coordinate transforma-tion between the synchronous reference coordinate frameand the stationary reference coordinate frame The flux

Mathematical Problems in Engineering 7

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 7 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 8 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Mathematical Problems in Engineering

1000

pi30Gain

+minus

+minus

Clock t

t

+

s

120596m

Transfer Fcn

F lowast r

Flux generator

times

divide

Divide

+

s

Transfer Fcn1

Transfer Fcn3

Transfer Fcn2

Transfer Fcn4

4 lowast Lr

3 lowast P lowast Lm +

s

+

s

120596e

120596e

Fedr

Fedr

Fsdr

Fsqr

qe

qe

qe

qe

ids

iqs

fds

fqs

Speed estimation

Series

Fdr

Fqr

120596r

VqsVds

2s to 2e

2s to 2e

isq

isd

Ieqs

Ieqs

Ieds

120596e

Fedr

Ieds

Out1

Out1

Subsystem

Subsystem1

3s to 2s

Isq

Isd

Ias

Ibs

Ics

Le lowast Ls

Le lowast Ls

Gain1

Gain2

Veqs

Veds

VasVsq Vsq

Vbs

Vsd VsdVcs

2e to 2s 2s to 3s

ias

ibs

ics

Te120596m

qm

an

bn

cn

TL

IM

30pirads to rpm

0

Constantqmqm120596rm

120596rm

TeTe

idsiqs

+minus

+minus

+minus

++

120596rm

Kpsmiddots

Kpfmiddots

Kpqmiddots

Kpdmiddots

Kis

Kiq

Kif Kid

Figure 6 Simulation scheme for sensorless RFOC IM drive with PSO algorithm speed controller design

Table 2 The parameters of the used IM

Poles 4119877119904(Ω) 285

119877119903(Ω) 23433

119871119904(H) 01967

119871119903(H) 01967

119871119898(H) 01886

119869119898(Nt-s2m) 0009

119861119898(Nt-s2m2) 000825

is used which serves as the controlled plant for experimenta-tion To confirm the effectiveness of the proposed sensorlessRFOC IM drive with PSO algorithm speed controller designa 3-phase 220V 075 kW Δ-connected standard squirrel-cage IM is used which serves as the controlled plant forexperimentation In a running cycle the speed commandis designed as follows forward direction acceleration from119905 = 0 to 119905 = 1 sec forward direction steady-state operationduring 1 le 119905 le 2 sec forward direction braking operationto reach zero speed in the interval 2 le 119905 le 3 sec reversedirection acceleration from 119905 = 3 to 119905 = 4 sec reversedirection steady-state operation during 4 le 119905 le 5 sec andreverse direction braking operation to reach zero speed inthe interval 5 le 119905 le 6 sec The simulated and measured

responses are shown in Figures 7ndash18 Each figure containsfour responses the actual shaft speed the estimated shaftspeed the rotor-flux linkage locus and the estimated elec-tromagnetic torque The simulated and measured responseswith no-load for reversible steady-state speed commandsplusmn300 rpm plusmn900 rpm and plusmn1800 rpm are shown in Figures7 8 9 10 11 and 12 respectively And the simulated andmeasured responseswith loading 2N-m for reversible steady-state speed commands plusmn300 rpm plusmn900 rpm and plusmn1800 rpmare shown in Figures 13 14 15 16 17 and 18 respectively

Based on the simulated and experimental results fordifferent operational speeds as shown in Figures 7ndash18 theproposed MRAS rotor-shaft speed on-line estimation sen-sorless RFOC IM drive with PSO algorithm speed controllerdesign strategy has shown that the desired performance canbe acquired

5 Conclusions

A sensorless RFOC based on current-and-voltage serial-model rotor-flux estimator with PSO algorithm speed con-troller design strategy has been proposed to control an IMdrive The proposed rotor-flux estimator acquired exactlyestimation flux angle position of coordinate transforma-tion between the synchronous reference coordinate frameand the stationary reference coordinate frame The flux

Mathematical Problems in Engineering 7

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 7 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 8 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 7

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 7 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

1

0

minus1

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 8 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Mathematical Problems in Engineering

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 9 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus20 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 10 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 9

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 11 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 12 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with no-load atreversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed (blueline) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

10 Mathematical Problems in Engineering

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 13 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

Estim

ated

spee

d (r

adm

in) 400

200

0

minus200

minus400

0 3 6 9 12

Time (s)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

2

0

minus2

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 14 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 300 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 11

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 15 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

1200

800

400

0

minus400

minus800

minus1200

(a)

0 3 6 9 12

Time (s)

1200

800

400

0

minus400

minus800

minus1200Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

3

0

minus3

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 16 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 900 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

12 Mathematical Problems in Engineering

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

6

0

minus6

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 17 Simulated responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Spee

d (r

adm

in)

(a)

2000

1000

0

minus1000

minus2000

0 3 6 9 12

Time (s)

Estim

ated

spee

d (r

adm

in)

(b)

05

05

0

0

minus05

minus05

fqs

fds

(c)

4

0

minus4

0 3 6 9 12

Time (s)

Estim

ated

Te

(N-m

)

(d)

Figure 18 Measured responses of MRAS sensorless RFOC IM dive with PSO algorithm speed controller design strategy with loading 2N-mat reversible steady-state speed command 1800 rpm (a) Command speed (blue line) and actual shaft speed (red line) (b) command speed(blue line) and estimated shaft speed (red line) (c) rotor flux linkage locus (d) estimated electromagnetic torque

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Mathematical Problems in Engineering 13

estimator based MRAS scheme can accurately identifythe rotor-shaft speed on-line The speed controller designstrategy utilizing PSO algorithm obtained superior speedresponse The simulated and experimental responses at dif-ferent reversible steady-state speed commands (plusmn300 rpmplusmn900 rpm and plusmn1800 rpm) confirm the effectiveness of theproposed approach

Conflict of Interests

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

References

[1] F Blaschke ldquoThe principle of field orientation as applied to thenew transvektor closed-loop control system for rotating-fieldmachinesrdquo Siemens Review vol 39 no 5 pp 217ndash220 1972

[2] H Tajima and Y Hori ldquoSpeed sensorless field-orientation con-trol of the induction machinerdquo IEEE Transactions on IndustryApplications vol 29 no 1 pp 175ndash180 1993

[3] Y C Luo and W X Chen ldquoSensorless stator field orientationcontrolled induction motor drive with fuzzy speed controllerrdquoComputers andMathematics with Applications vol 64 no 5 pp1206ndash1216 2012

[4] Y D Landau Adaptive Control The Model Reference Approachvol 8 Marcel Dekker New York NY USA 1979

[5] J Kennedy and R C Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks vol 4 pp 1942ndash1948 IEEE Perth Australia Decem-ber 1995

[6] C H Liu Control of AC Electrical Machines Tunghua TaipeiTaiwan 4th edition 2008 (Chinese)

[7] C Schauder ldquoAdaptive speed identification for vector controlof induction motors without rotational transducersrdquo IEEETransactions on Industry Applications vol 28 no 5 pp 1054ndash1061 1992

[8] R Eberhart and J Kennedy ldquoA New optimizer using particleswarm theoryrdquo in Proceedings of the 6th International Sympo-sium on Micro Machine and Human Science pp 39ndash43 IEEENagoya Japan October 1995

[9] Y Shi and R Eberhart ldquoModified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of