research article vector control algorithm for electric...

Research ArticleVector Control Algorithm for Electric Vehicle AC InductionMotor Based on Improved Variable Gain PID Controller

Gang Qin1 Mushuang Liu2 Jianxiao Zou1 and Xiaoshuai Xin1

1School of Automation Engineering University of Electronic Science and Technology of China Chengdu 610023 China2School of Microelectronics and Solid-State Electronics University of Electronic Science and Technology of ChinaChengdu 610023 China

Correspondence should be addressed to Mushuang Liu lxwgws163com

Received 3 December 2014 Revised 28 December 2014 Accepted 28 December 2014

Academic Editor Hui Zhang

Copyright copy 2015 Gang Qin et alThis is an open access article distributed under theCreativeCommonsAttribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The acceleration performance of EV which affects a lot of performances of EV such as start-up overtaking driving safety and ridecomfort has become increasingly popular in recent researches An improved variable gain PID control algorithm to improve theacceleration performance is proposed in this paper The results of simulation with MatlabSimulink demonstrate the effectivenessof the proposed algorithm through the control performance of motor velocity motor torque and three-phase current of motorMoreover it is investigated that the proposed controller is valid by comparison with the other PID controllers Furthermore theAC induction motor experiment set is constructed to verify the effect of proposed controller

1 Introduction

With the increased emphasis on saving energy and reducingemission electric vehicles (EVs) have emerged as very strongcandidates to achieve these goals [1ndash5]Moreover the acceler-ation performance of EV which affects a lot of performancesof EV such as start ability passing ability driving safety andride comfort is the key point of EV researches

Vector control algorithm which can accurately controlthe torque and has a wide control range of motor velocity andalso has a current loop which can be used for current limitingprotection is widely used in EVdriving control However thevelocity loop controller of vector control algorithm whichuses traditional PID control algorithm generally limits thedynamic performance of driving system and the accelerationperformance of EV During the last few years the velocityloop controller of EVAC inductionmotor (ACIM) controllersystem is researched and improved unceasingly and manymethods are presented One method is using the fuzzycontroller to replace velocity loop traditional PID controllerand current loop traditional PID controller of vector controlalgorithm [6ndash8] which can make the control system trackthe different given velocity rapidly and without overshoot in

different load and has strong ability against load disturbancebut its steady-state accuracy is not high because of no existingintegration element Another method is using the neutralnetwork PID controller to replace velocity loop traditionalPID controller of vector control algorithm [9ndash11] which hasthe advantages of adjusting velocity rapidly zero overshootsmooth and small-fluctuation control signals and goodsystem tracking but it reduces the EV control performancedue to learning slowly in learning process and long responsetime Literature [12] also presented amethod using the fuzzy-PI controller which executes fuzzy control algorithm whenvelocity deviation is greater than given threshold and executestraditional PID control algorithm when velocity deviation isless instead of velocity loop traditional PID controller [13]The method can make velocity response rapidly with smallovershoot [14] but it is difficult to achieve completely smoothswitching andmay cause velocity hopwhen control algorithmswitches thereby affecting the driving safety and ride comfortwhen EV accelerates

In this paper we design a vector control algorithm forvehicle asynchronousmotor based on improved variable gainPID controller which can make motor velocity rise rapidlyand no overshoot Moreover it can satisfy the demands of

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 875843 9 pageshttpdxdoiorg1011552015875843

2 Mathematical Problems in Engineering

EV driving system dynamic performance and accelerationperformance no matter whether the EV runs in low velocitynormal velocity high velocity or variable velocity

The sections are organized as follows In Section 2 asyn-chronous motor model is studied In Section 3 improvedvariable gain PID control algorithm is designed to improvethe acceleration performance In Section 4 vector controlalgorithm for EV asynchronous motor based on improvedvariable gain PID controller is proposed Furthermore thestability condition is given In Section 5 the effectivenessof controller is demonstrated by simulation with Mat-labSimulink (Figure 4) Section 6 presents some concludingremarks

2 AC Induction Motor Model

ACIM is widely applied to EV driving system which hasmany good characteristics such as robustness durabilitysimple structure reliable operation low cost low torqueripple low noise no position sensor and high velocity limitThe design of ACIM for EV which is different from normalACIM and must satisfy the power performance of EV musthave the following characteristics (1) constant power outputand big velocity adjustable range for satisfying the demandsfor flat road overtaking and so on when run in highlowvelocity (2) smaller mass and volume in the condition ofcertain power level and (3) robust structure and resistanceto vibrations [15]

This paper which takes ACIM for example researchesmotor mathematical model of EV driving system The math-ematical model of ACIM is a nonlinear high order closecoupling multivariable system Ignore these factors such ascore loss space harmonics the change of frequency thechange of temperature and the saturation of magnetic circuiton the impact ofwinding resistanceswhen establishingmotormodel [16]

A physical model of ACIM is shown in Figure 1 Thethree-phase winding resistances which are 120∘ phase differ-ent in the space are symmetrical and the mutual inductanceand self-inductance of every winding resistance are constantThe mathematical models of ACIM which consist of voltagematrix equation magnetic linkage matrix equation andtorque equation can be obtained according to the physicalmodel of ACIM

Based on the voltage balance principle of three-phasestator winding resistances the voltage matrix equation [17]can be written as

[[[[[[[

[

119906119860

119906119861

119906119862

119906119886

119906119887

119906119888

]]]]]]]

]

=

[[[[[[[

[

1198771199040 0 0 0 0

0 1198771199040 0 0 0

0 0 1198771199040 0 0

0 0 0 1198771199030 0

0 0 0 0 1198771199030

0 0 0 0 0 119877119903

]]]]]]]

]

[[[[[[[

[

119894119860

119894119861

119894119862

119894119886

119894119887

119894119888

]]]]]]]

]

+ 119901

[[[[[[[

[

120595119860

120595119861

120595119862

120595119886

120595119887

120595119888

]]]]]]]

]

(1)

where 119906119860 119906119861 and 119906

119862are stator phase voltage 119906

119886 119906119887 and 119906

119888

are rotor phase voltage 119894119860 119894119861 and 119894

119862are stator phase current

119894119886 119894119887 and 119894

119888are rotor phase current 120595

119860 120595119861 and 120595

119862are

magnetic linkage of stator winding resistance 120595119886 120595119887 and 120595

119888

B

b

120596uB

iB

ubib uaia

a

120579

A

uAiA

uc

ic

c

C

uC

iC

Figure 1 The physical model of ACIM

are magnetic linkage of rotor winding resistance 119877119904is stator

resistance119877119903is rotor resistance and119901 is differential operator

Based on the principle that the magnetic linkage of everywinding resistance is equal to its self-inductance magneticlinkage plus mutual inductance magnetic linkage with otherwinding resistances the magnetic linkage matrix equationcan be written as

[[[[[[[

[

120595119860

120595119861

120595119862

120595119886

120595119887

120595119888

]]]]]]]

]

=

[[[[[[[

[

119871119860119860

119871119860119861119871119860119862119871119860119886119871119860119887119871119860119888

119871119861119860119871119861119861119871119861119862119871119861119886119871119861119887119871119861119888

119871119862119860119871119862119861119871119862119862119871119862119886119871119862119887119871119862119888

119871119886119860

119871119886119861119871119886119862119871119886119886119871119886119887119871119886119888

119871119887119860119871119887119861119871119887119862119871119887119886119871119887119887119871119887119888

119871119888119860

119871119888119861119871119888119862119871119888119886119871119888119887119871119888119888

]]]]]]]

]

[[[[[[[

[

119894119860

119894119861

119894119862

119894119886

119894119887

119894119888

]]]]]]]

]

(2)

where 119871119860119860

is self-inductance and 119871119860119861

is mutual inductanceThe torque equation can be expressed as

119879119890= 119899119901119871119898[(119894119860119894119886+ 119894119861119894119887+ 119894119862119894119888) sin 120579

+ (119894119860119894119887+ 119894119861119894119888+ 119894119862119894119886) sin (120579 + 120∘)

+ (119894119860119894119888+ 119894119861119894119886+ 119894119862119894119887) sin (120579 minus 120∘)]

(3)

where 119899119901is pole pairs 119871

119898is mutual inductance and 120579 is

electrical degree difference between 119886 axis and 119860 axisThe ACIM whose mathematical model is very complex

is very difficult to be controlled in practical applicationThe vector control algorithm controls ACIM as DC motorthrough coordinate transformation for the problem that themathematical model ACIM is very complex so that thegoverning performance of ACIM can be comparable withDCmotor

Mathematical Problems in Engineering 3

3 Improved Variable Gain PID ControlAlgorithm Design

The fundamental thought of traditional variable gain PIDcontrol algorithm is matching the cumulative velocity ofintegral value with the magnitude of deviation The integralaction reduces to nothing for preventing integral saturationwhen system deviation is large and is reinforced for improv-ing the stability of velocity when system deviation is smallThe more desirable situation is matching the magnitudeof proportional coefficient with deviation The action ofproportional part is reinforced for improving the dynamicperformance of system when system deviation is large andreduces for preventing overshoot when system deviation issmall This paper designs an improved variable gain PIDcontrol algorithm based on improving the variable gain PIDcontrol algorithm

The proportional and integral term of improved variablegain PID control algorithm can be expressed as

119906 (119896) = (119896119901+ 119909 [119890 (119896)]) 119890 (119896)

+ 119896119894

119896minus1

sum119894=0

119890 (119894) + 119910 [119890 (119896)] 119890 (119896)119879

(4)

where 119909[119890(119896)] and 119910[119890(119896)] are the functions of deviation 119890(119896)As 119890(119896) increases 119909[119890(119896)] increases and 119910[119890(119896)] reduces As119890(119896) reduces 119909[119890(119896)] reduces and 119910[119890(119896)] increases

The expression of 119909[119890(119896)] can be described as

119909 [119890 (119896)]

=

1198961015840

1199011

|119890 (119896)| le 1198902

11989610158401199012

minus 11989610158401199011

1198901

(|119890 (119896)| minus 1198902) + 11989610158401199011

1198902lt |119890 (119896)| le 119890

1+ 1198902

11989610158401199012

|119890 (119896)| gt 1198901+ 1198902

(5)

where parameters 1198901 1198902 11989610158401199011

and 11989610158401199012

are necessary to beensured 0 le 1198961015840

1199011

lt 11989610158401199012

On one hand the chosen valuesof these four parameters must satisfy the condition of systemstability On the other hand the chosen values of 119890

1and 1198961015840

1199012

must meet the condition of velocity and the chosen values of1198902and 11989610158401199011

must meet the condition of no velocity overshootThe value of 119909[119890(119896)] varies in the range of interval

[11989610158401199011

11989610158401199012

]When |119890(119896)| gt 119890

1+ 1198902 119909[119890(119896)] is equal to 1198961015840

1199012

and theproportional coefficient of control algorithm is equal to 119896

119901+

11989610158401199012

for improving the dynamic performance of systemWhen |119890(119896)| le 119890

2 119909[119890(119896)] is equal to 1198961015840

1199011

and theproportional coefficient of control algorithm is equal to theminimum value 119896

119901+ 11989610158401199011

for preventing overshootWhen 119890

2lt |119890(119896)| le 119890

1+ 1198902 the value of 119909[119890(119896)] which

is in the range of interval [11989610158401199011

11989610158401199012

] and the proportionalcoefficient of control algorithm which is in the range ofinterval [119896

119901+11989610158401199011

119896119901+11989610158401199012

] vary with the magnitude of |119890(119896)|


119910 [119890 (119896)]

=

1 |119890 (119896)| le 1198904

1198961015840119894

minus 1

1198903

(|119890 (119896)| minus 1198904) + 1 119890

4lt |119890 (119896)| le 119890

3+ 1198904

1198961015840119894

|119890 (119896)| gt 1198903+ 1198904

(6)

where parameters 1198903 1198904 and 1198961015840

119894

are necessary to be ensured0 le 1198961015840

119894

lt 1 On one hand the chosen values of these threeparameters must satisfy the condition of system stabilityOn the other hand the chosen values of 119890

3and 1198961015840

119894

mustmeet the condition of no integral saturation and velocityovershoot and the chosen value of 119890

4must make velocity

stability rapidlyThe value of 119910[119890(119896)] varies in the range of interval [1198961015840

119894

1]When |119890(119896)| gt 119890

3+1198904 the value of119910[119890(119896)] is equal to 1198961015840

119894

forreducing the integral action to the lowest or not accumulatingthe current value of 119890(119896)

When |119890(119896)| le 1198904 the integral term is the same as the

general for increasing the integral action to the highest andaccumulating the current value of 119890(119896)

When 1198904lt |119890(119896)| le 119890

3+ 1198904 the value of 119910[119890(119896)] which is

in the range of interval [1198961015840119894

1] varies with the magnitude of|119890(119896)| and the integral term accumulates part current value of119890(119896)Thus the integral velocity is in the range of 119896

119894sum119896minus1

119894=0

119890(119894)+

1198961015840119894

119890(119896)119879 to 119896119894sum119896

119894=0

119890(119894)119879In order to increase the regulating range of improved

variable gain PID control algorithm the values of parameters1198901 1198902 1198903 and 119890

4must be decided by the maximum value of

deviation after desired value varies which are not fixed valuesThus we can get

1198901=1003816100381610038161003816119890max

1003816100381610038161003816 1198981

1198902=1003816100381610038161003816119890max

1003816100381610038161003816 1198982

1198903=1003816100381610038161003816119890max

1003816100381610038161003816 1198983

1198904=1003816100381610038161003816119890max

1003816100381610038161003816 1198984

(7)

where 119890max is the maximum value of deviation betweendesired value and feedback value after the desired value ofcontroller input changes and parameters119898

111989821198983 and119898

4

are necessary to be ensured which must satisfy 0 lt 119898119894lt 1

119894 = 1 2 3 4 0 lt 1198981+ 1198982lt 1 and 0 lt 119898

3+ 1198984lt

1 First of all the chosen values of these four parametersmust satisfy the condition of system stability Secondly thechosen value of 119898

1must make velocity stability rapidly

and the chosen value of 1198982must meet the condition of no

velocity overshoot and the chosen value of1198983must meet the

condition of no integral saturation and velocity overshootand the chosen value of 119898

4must make velocity stability

rapidly


Three-phase invert

erSVPWM

Clarktransformation

Parkinverse

transformationFlux

linkage observer

Parktransformation

ACR

ACR

Weakmagneticalgorithm

Decoupling

algorithmTorquecurrent

transformation

AVRminus

+minus

+

minus

+

120596lowastr

Tlowaste ilowastsq

ilowastsd

usd

usq

us120572

us120573

Vdc

iAiBiC

M

120596r

is120572is120573isd

isq

120596e ilowastsd i

lowastsq 120579

usm ism

Figure 2 The block diagram of vector control algorithm based on improved variable gain PID controller motor

minus

+120596lowastr Tlowast

eTe 120596rC(s)

1

Tcqs + 1

1

Js

Figure 3 The transfer function block diagram of vector controlalgorithm based on improved variable gain PID controller

Finally the improved variable gain PID control algorithmis obtained as

119906 (119896) = (119896119901+ 119909 [119890 (119896)]) 119890 (119896)

+ 119896119894

119896minus1

sum119894=0

119890 (119894) + 119910 [119890 (119896)] 119890 (119896)119879

+ 119896119889

119890 (119896) minus 119890 (119896 minus 1)

119879

(8)

Because requirement of improved variable gain PIDcontrol algorithm to the values of parameters 119898

1 1198982 1198983

1198984 11989610158401199011

11989610158401199012

and 1198961015840119894

is not accurate the values are easy to beensured

4 Vector Control Algorithm for VehicleAsynchronous Motor Based on ImprovedVariable Gain PID Controller

The block diagram of vector control algorithm for EV ACIMbased on improved variable gain PID controller is obtainedin Figure 2 This algorithm which uses rotator flux orienteduses velocity and current double closed-loop control algo-rithm in control structure

In outer loop control collect motor rotor velocity 120596119903via

revolution velocity transducer from the ACIM side Thenset the deviation between expected rotor velocity 120596lowast

119903

andfeedback rotor velocity 120596

119903as the input of automatic voltage

regulator (AVR) and the output is expected electromagnetic

torque 119879lowast119890

The expected electromagnetic torque via torque-current transformation and slicing obtains the inner loopexpected torque current 119894lowast

119904119902

The requisite parameter 120579 of Parktransformation and Park inverse transformation is providedby flux linkage observer The inputs of weak magnetic blockare 119906119904120572 119906119904120573 the maximum output voltage value of inverter is

119906119904119898 and the maximum motor current value in safe running

is 119894119904119898 and the outputs are the slicing values of expected

excitation current 119894lowast119904119889

and expected torque current 119894lowast119904119902

The transfer function block diagram of vector control

algorithm for EV asynchronous motor based on improvedvariable gain PID controller can be obtained in Figure 2

In Figure 3 1119879119888119902119904 + 1 is closed-loop transfer function of

torque control system So the transfer function of controlledobject can be expressed as

119866 (119904) =1

119879119888119902119904 + 1

lowast1

119869119904=

1

(120590119871119904119896119894119902) 119904 + 1

lowast1

119869119904 (9)

where 119896119894119902

is 119902 loop integral coefficient of vector controlalgorithm current loop 120590 is leakage inductance coefficient ofACIM 119871

119904is stator inductance of ACIM and 119869 is moment of

inertia of ACIMThe differentiation element of PID control algorithm

which is sensitive to the noise of input signal is not usedin the system which has bigger noise in general Thus onlyPI control in the velocity loop controller of vector controlalgorithm for EV ACIM in general is used

The transfer function of velocity loop controller basedon improved variable gain PID control algorithm is givenas

119862 (119904) =(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

119904 (10)

where 119896119901is proportional coefficient of traditional PID control

algorithm 119896119894is integral coefficient of PID control algorithm

11989610158401199011

le 119909[119890(119896)] le 11989610158401199012

and 1198961015840119894

le 119910[119890(119896)] le 1 Here 11989610158401199011

11989610158401199012

and 1198961015840119894

are parameters of improved variable gain PID controlalgorithm to be determined


GivenReal

Out

SectionPI

GivenReal Out

qPI

Discrete

Powergui

GivenReal Out

dPI

Wm

SinTetaCosTeta

fcn

Udq2UaUb

IabcCosTetaSinTeta

SVPWM2

Induction motor

35

+

-

IGBT inverter

Gain2

Gain1

wm

Demux

Decoupling

Battery

ETe Out

SinTetaCosTetaVetInputWewm

Idlowast

Udlowast

Uqlowast

Id

Iq

Id

id

Iq

Id

Iq

Ud

Uq

dq

120572

120573

U120572

U120573

A

B

C

A

B

C

g

-k-

-k-

Zminus1

Zminus1

m

m

ltm

gtTm+

minus

is abc

VetInput We

+Ts = Ts s

Figure 4 Simulation diagram constructed by MatlabSimulink

0 1 2 3 4 5 60

10

20

30

40

50

60

Time (s)

Velo

city

(rad

s)

Improved variable gain PID controllerVariable gain PID controllerPID controller

Figure 5 The simulation result of motor in low-velocity range

Therefore the closed-loop transfer function of system isobtained as

120593 (119904) =119862 (119904) 119866 (119904)

1 + 119862 (119904) 119866 (119904)

=(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(120590119871119904119869119896119894119902) 1199043 + 1198691199042 + (119896

119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(11)

Using Routh stability criterion [18] to judge the stabilityof system can obtain the stability condition of system as

1198961015840

1199011

gt120590119871119904119896119894

119896119894119902

minus 119896119901

1198961015840

119894

gt 0

(12)

The system can be stable if the values of parameters 11989610158401199011

and 1198961015840119894

satisfy the condition of (9) when designing the vectorcontrol algorithm for EV ACIM based on improved variablegain PID controller

5 Simulation and Interpretation of Results

To study the improvements of the improved variable gainPID control algorithm it is imperative to compare it to clas-sical PID control algorithm through simulation The motorparameters of 20 kW ACIM which is used in simulation aregiven in Table 1

Through debugging the simulation model of specificACIM described in Table 1 proportional and integral gainsas 063797 and 30158 respectively can be obtained and thevalues of parameters of improved variable gain PID controlalgorithm in the velocity loop controller are 119896

119901= 226 119896

119894=

3581198981= 006119898

2= 1198983= 004119898

4= 016 1198961015840

1199011

= 0 11989610158401199012

= 4and 1198961015840

119894

= 001 11989610158401199011

gt 120590119871119904119896119894119896119894119902minus 119896119901= minus22538 and 1198961015840

119894

gt 0these satisfy the stability condition of system

As shown in Figure 3 take a PID controller for examplefor comparison Sample time 119879

119904is 500120583s which is the sample

period of the closed-loop system

51 Low-Velocity Range EV low running velocity is about10 kmh and the corresponding motor velocity is about


0

100

200

Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

minus100

minus200

(a) Three-phase current with PID controller

Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200

(b) Three-phase current with variable gain PID controller

Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200

(c) Three-phase current with improved variable gain PID controller

Figure 6 The simulation result of three-phase current

Table 1 The parameters of ACIM

Rated line voltage 119880119873

180VRated torque 119879

119890119873

53NmRated velocity 119899

119873

3600 rpmStator resistance 119877

1

00205 ohmRotor resistance 119877

2

00097 ohmStator leakage inductance 119871 ls 92668e minus 05HRotor leakage inductance 119871 lr 109033e minus 07HMutual inductance 119871

119898

00055887HPole pairs 2

50 rads If the expected velocity is motor nominal velocityof 50 rads in simulation the control result is illustrated inFigure 5

In Figure 5 the response time of the PID controller isabout 3 s and the overshoot is about 14 The response timeof variable gain PID controller is about 2 s and the overshootis 0 However the proposed controller can still track thedesired velocity less than 1 s without 0 overshoots

In Figure 6 compared with PID controller and variablegain PID controller the peak of three-phase current is less

Time (s)


0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

Velo

city

(rad

s)

Figure 7 The simulation result of motor in moderate-velocityrange


Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400




0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)

Figure 9 The simulation result of motor in high-velocity range

than 100A In addition it is investigated that the proposedcontroller is valid by comparison with the other PID con-trollers

52 Moderate-Velocity Range EV normal running velocity is80 kmh to 100 kmh and the corresponding motor velocityis about 370 rads If the expected velocity is motor nominalvelocity of 370 rads in simulation the control result isillustrated in Figure 7

In Figure 7 the response time of the PID controller isabout 35 s and the overshoot is about 108 The responsetime of variable gain PID controller is about 3 s and theovershoot is 0 However the proposed controller can stilltrack the desired velocity less than 2 s without 0 overshoots

In Figure 8 compared with PID controller and variablegain PID controller three-phase current changes slowly andthe response time is smaller In addition it is investigated thatthe proposed controller is valid by comparison with the otherPID controllers

53 High-Velocity Range EV high running velocity is about120 kmh and the corresponding motor velocity is about


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400



630 rads If the given expected velocity is motor nominalvelocity of 630 rads in simulation the control result isillustrated in Figure 9

In Figure 9 the response time of the PID controller isabout 5 s and the overshoot is about 111The response timeof variable gain PID controller is about 7 s and the overshootis 0 However the proposed controller can still track thedesired velocity less than 4 s without 0 overshoots


54 Variable Velocity Range In order to test wheter themethod designed in this paper can satisfy the applicationneeds in velocity we make simulation of motor in variablevelocity range with the initial expected velocity as 630 radsand turn to 300 rads at the 4th second The control result isillustrated in Figure 11

As shown in Figure 11 the response time of the PIDcontroller is about 25 s and the overshoot is about 79 Theresponse time of variable gain PID controller is about 3 s and


0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)

Figure 11 The simulation result of motor in variable velocity range


the overshoot is 0 However the proposed controller can stilltrack the desired velocity less than 4 s without 0 overshoots

6 Conclusion

This paper has presented a novel approach in the automotivefield to implement the improved variable gain PID controllerto control EV ACIM In this paper the design of variablegain PID controller and stability analysis have been presentedalong with simulation The simulation results qualitativelydemonstrate that the improved variable gain PID controllercould improve on the control of motor velocity in the EVversus using the classical PID control method In additionthis control method can satisfy the demands of EV drivingsystem dynamic performance and acceleration performancewhen EV runs in low velocity moderate velocity highvelocity and variable velocity

Conflict of Interests

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

References

[1] C Larish D Piyabongkarn V Tsourapas and R Rajamani ldquoAnew predictive lateral load transfer ratio for rollover preventionsystemsrdquo IEEETransactions onVehicular Technology vol 62 no7 pp 2928ndash2936 2013

[2] S-I Sakai H Sado and Y Hori ldquoMotion control in an elec-tric vehicle with four independently driven in-wheel motorsrdquoIEEEASME Transactions on Mechatronics vol 4 no 1 pp 9ndash16 1999

[3] Q Li Z Zhang and W Zhao ldquoDynamic control for four-wheel independent drive electric vehiclerdquo in Proceedings of theInternational Conference on Computer Science and ElectronicsEngineering (ICCSEE rsquo12) vol 3 pp 252ndash256Hangzhou ChinaMarch 2012

[4] T Shim and D Margolis ldquoModel-based road friction estima-tionrdquoVehicle SystemDynamics vol 41 no 4 pp 249ndash276 2004

[5] D Chabrol C Aussagues andV David ldquoA spatial and temporalpartitioning approach for dependable automotive systemsrdquo inProceedings of the IEEE Conference on Emerging Technologiesamp Factory Automation (ETFA rsquo09) pp 1ndash8 Mallorca SpainSeptember 2009

[6] M Stecher N Jensen M Denison et al ldquoKey technologies forsystem-integration in the automotive and industrial applica-tionsrdquo IEEE Transactions on Power Electronics vol 20 no 3 pp537ndash549 2005

[7] D Zhang and L Yu ldquoExponential state estimation for Marko-vian jumping neural networks with time-varying discrete anddistributed delaysrdquo Neural Networks vol 35 pp 103ndash111 2012

[8] V P Petkov G K Balachandran and J Beintner ldquoA fully dif-ferential charge-balanced accelerometer for electronic stabilitycontrolrdquo IEEE Journal of Solid-State Circuits vol 49 no 1 pp262ndash269 2014

[9] C F Caruntu M Lazar R H Gielen P P J van den Boschand SDiCairano ldquoLyapunov based predictive control of vehicledrivetrains over CANrdquo Control Engineering Practice vol 21 no12 pp 1884ndash1898 2013

[10] J Cheng H Zhu S Zhong F Zheng and Y Zeng ldquoFinite-timefiltering for switched linear systems with a mode-dependentaverage dwell timerdquoNonlinear Analysis Hybrid Systems vol 15pp 145ndash156 2015

[11] M B G Cloosterman N D van de Wouw M P M HHeemels and H Nijmeijer ldquoRobust stability of networkedcontrol systems with time-varying network-induced delaysrdquoin Proceedings of the 45th IEEE Conference on Decision andControl pp 4980ndash4985 December 2006

[12] S Olaru and S Niculescu ldquoPredictive control for linear systemswith delayed input subject to constraintsrdquo in Proceedings of the17th World Congress the International Federation of AutomaticControl (IFAC rsquo08) pp 11208ndash11213 Seoul South Korea July2008

[13] L Hetel J Daafouz and C Iung ldquoStabilization of arbitraryswitched linear systems with unknown time-varying delaysrdquoIEEE Transactions on Automatic Control vol 51 no 10 pp1668ndash1674 2006

[14] RHGielen SOlaruM LazarW PHeemels N van deWouwand S-I Niculescu ldquoOn polytopic inclusions as a modelingframework for systems with time-varying delaysrdquo Automaticavol 46 no 3 pp 615ndash619 2010

[15] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[16] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[17] G Zheng J D Wu M W Kuang D Zhang and Y Yang ldquoAdisturbance rejection strategy for asynchronous motor of theelectric vehicle in speed-open-loop operating moderdquo AdvancedMaterials Research vol 479-481 pp 71ndash75 2012

[18] R H Gielen and M Lazar ldquoStabilization of networked controlsystems via non-monotone control Lyapunov functionsrdquo inProceedings of the 48th IEEE Conference on Decision andControl Held Jointly with the 28th Chinese Control Conference(CDCCCC rsquo09) pp 7942ndash7948 Shanghai China December2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


EV driving system dynamic performance and accelerationperformance no matter whether the EV runs in low velocitynormal velocity high velocity or variable velocity

The sections are organized as follows In Section 2 asyn-chronous motor model is studied In Section 3 improvedvariable gain PID control algorithm is designed to improvethe acceleration performance In Section 4 vector controlalgorithm for EV asynchronous motor based on improvedvariable gain PID controller is proposed Furthermore thestability condition is given In Section 5 the effectivenessof controller is demonstrated by simulation with Mat-labSimulink (Figure 4) Section 6 presents some concludingremarks

2 AC Induction Motor Model

ACIM is widely applied to EV driving system which hasmany good characteristics such as robustness durabilitysimple structure reliable operation low cost low torqueripple low noise no position sensor and high velocity limitThe design of ACIM for EV which is different from normalACIM and must satisfy the power performance of EV musthave the following characteristics (1) constant power outputand big velocity adjustable range for satisfying the demandsfor flat road overtaking and so on when run in highlowvelocity (2) smaller mass and volume in the condition ofcertain power level and (3) robust structure and resistanceto vibrations [15]

This paper which takes ACIM for example researchesmotor mathematical model of EV driving system The math-ematical model of ACIM is a nonlinear high order closecoupling multivariable system Ignore these factors such ascore loss space harmonics the change of frequency thechange of temperature and the saturation of magnetic circuiton the impact ofwinding resistanceswhen establishingmotormodel [16]

A physical model of ACIM is shown in Figure 1 Thethree-phase winding resistances which are 120∘ phase differ-ent in the space are symmetrical and the mutual inductanceand self-inductance of every winding resistance are constantThe mathematical models of ACIM which consist of voltagematrix equation magnetic linkage matrix equation andtorque equation can be obtained according to the physicalmodel of ACIM

Based on the voltage balance principle of three-phasestator winding resistances the voltage matrix equation [17]can be written as

[[[[[[[

[

119906119860

119906119861

119906119862

119906119886

119906119887

119906119888

]]]]]]]

]

=

[[[[[[[

[

1198771199040 0 0 0 0

0 1198771199040 0 0 0

0 0 1198771199040 0 0

0 0 0 1198771199030 0

0 0 0 0 1198771199030

0 0 0 0 0 119877119903

]]]]]]]

]

[[[[[[[

[

119894119860

119894119861

119894119862

119894119886

119894119887

119894119888

]]]]]]]

]

+ 119901

[[[[[[[

[

120595119860

120595119861

120595119862

120595119886

120595119887

120595119888

]]]]]]]

]

(1)

where 119906119860 119906119861 and 119906

119862are stator phase voltage 119906

119886 119906119887 and 119906

119888

are rotor phase voltage 119894119860 119894119861 and 119894

119862are stator phase current

119894119886 119894119887 and 119894

119888are rotor phase current 120595

119860 120595119861 and 120595

119862are

magnetic linkage of stator winding resistance 120595119886 120595119887 and 120595

119888

B

b

120596uB

iB

ubib uaia

a

120579

A

uAiA

uc

ic

c

C

uC

iC

Figure 1 The physical model of ACIM

are magnetic linkage of rotor winding resistance 119877119904is stator

resistance119877119903is rotor resistance and119901 is differential operator

Based on the principle that the magnetic linkage of everywinding resistance is equal to its self-inductance magneticlinkage plus mutual inductance magnetic linkage with otherwinding resistances the magnetic linkage matrix equationcan be written as

[[[[[[[

[

120595119860

120595119861

120595119862

120595119886

120595119887

120595119888

]]]]]]]

]

=

[[[[[[[

[

119871119860119860

119871119860119861119871119860119862119871119860119886119871119860119887119871119860119888

119871119861119860119871119861119861119871119861119862119871119861119886119871119861119887119871119861119888

119871119862119860119871119862119861119871119862119862119871119862119886119871119862119887119871119862119888

119871119886119860

119871119886119861119871119886119862119871119886119886119871119886119887119871119886119888

119871119887119860119871119887119861119871119887119862119871119887119886119871119887119887119871119887119888

119871119888119860

119871119888119861119871119888119862119871119888119886119871119888119887119871119888119888

]]]]]]]

]

[[[[[[[

[

119894119860

119894119861

119894119862

119894119886

119894119887

119894119888

]]]]]]]

]

(2)

where 119871119860119860

is self-inductance and 119871119860119861

is mutual inductanceThe torque equation can be expressed as

119879119890= 119899119901119871119898[(119894119860119894119886+ 119894119861119894119887+ 119894119862119894119888) sin 120579

+ (119894119860119894119887+ 119894119861119894119888+ 119894119862119894119886) sin (120579 + 120∘)

+ (119894119860119894119888+ 119894119861119894119886+ 119894119862119894119887) sin (120579 minus 120∘)]

(3)

where 119899119901is pole pairs 119871

119898is mutual inductance and 120579 is

electrical degree difference between 119886 axis and 119860 axisThe ACIM whose mathematical model is very complex

is very difficult to be controlled in practical applicationThe vector control algorithm controls ACIM as DC motorthrough coordinate transformation for the problem that themathematical model ACIM is very complex so that thegoverning performance of ACIM can be comparable withDCmotor





119906 (119896) = (119896119901+ 119909 [119890 (119896)]) 119890 (119896)

+ 119896119894

119896minus1

sum119894=0

119890 (119894) + 119910 [119890 (119896)] 119890 (119896)119879

(4)



119909 [119890 (119896)]

=

1198961015840

1199011

|119890 (119896)| le 1198902

11989610158401199012

minus 11989610158401199011

1198901

(|119890 (119896)| minus 1198902) + 11989610158401199011

1198902lt |119890 (119896)| le 119890

1+ 1198902

11989610158401199012

|119890 (119896)| gt 1198901+ 1198902

(5)


and 11989610158401199012


1199011

lt 11989610158401199012


1and 1198961015840

1199012



[11989610158401199011

11989610158401199012

]When |119890(119896)| gt 119890

1+ 1198902 119909[119890(119896)] is equal to 1198961015840

1199012


119901+

11989610158401199012


2 119909[119890(119896)] is equal to 1198961015840

1199011


119901+ 11989610158401199011


2lt |119890(119896)| le 119890



11989610158401199012


119901+11989610158401199011

119896119901+11989610158401199012



119910 [119890 (119896)]

=

1 |119890 (119896)| le 1198904

1198961015840119894

minus 1

1198903

(|119890 (119896)| minus 1198904) + 1 119890

4lt |119890 (119896)| le 119890

3+ 1198904

1198961015840119894

|119890 (119896)| gt 1198903+ 1198904

(6)


119894


119894


3and 1198961015840

119894


4must make velocity


119894

1]When |119890(119896)| gt 119890


119894




When 1198904lt |119890(119896)| le 119890




119894sum119896minus1

119894=0

119890(119894)+

1198961015840119894

119890(119896)119879 to 119896119894sum119896

119894=0





1198901=1003816100381610038161003816119890max

1003816100381610038161003816 1198981

1198902=1003816100381610038161003816119890max

1003816100381610038161003816 1198982

1198903=1003816100381610038161003816119890max

1003816100381610038161003816 1198983

1198904=1003816100381610038161003816119890max

1003816100381610038161003816 1198984

(7)


111989821198983 and119898

4


119894 = 1 2 3 4 0 lt 1198981+ 1198982lt 1 and 0 lt 119898

3+ 1198984lt







rapidly


Three-phase invert

erSVPWM

Clarktransformation

Parkinverse

transformationFlux

linkage observer

Parktransformation

ACR

ACR


Decoupling


transformation

AVRminus

+minus

+

minus

+

120596lowastr

Tlowaste ilowastsq

ilowastsd

usd

usq

us120572

us120573

Vdc

iAiBiC

M

120596r

is120572is120573isd

isq

120596e ilowastsd i

lowastsq 120579

usm ism


minus


eTe 120596rC(s)

1

Tcqs + 1

1

Js



119906 (119896) = (119896119901+ 119909 [119890 (119896)]) 119890 (119896)

+ 119896119894

119896minus1

sum119894=0

119890 (119894) + 119910 [119890 (119896)] 119890 (119896)119879

+ 119896119889

119890 (119896) minus 119890 (119896 minus 1)

119879

(8)


1 1198982 1198983

1198984 11989610158401199011

11989610158401199012

and 1198961015840119894






119903






119904119902










119866 (119904) =1

119879119888119902119904 + 1

lowast1

119869119904=

1

(120590119871119904119896119894119902) 119904 + 1

lowast1

119869119904 (9)

where 119896119894119902






119862 (119904) =(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

119904 (10)



11989610158401199011

le 119909[119890(119896)] le 11989610158401199012

and 1198961015840119894

le 119910[119890(119896)] le 1 Here 11989610158401199011

11989610158401199012

and 1198961015840119894



GivenReal

Out

SectionPI

GivenReal Out

qPI

Discrete

Powergui

GivenReal Out

dPI

Wm

SinTetaCosTeta

fcn

Udq2UaUb

IabcCosTetaSinTeta

SVPWM2

Induction motor

35

+

-

IGBT inverter

Gain2

Gain1

wm

Demux

Decoupling

Battery

ETe Out


Idlowast

Udlowast

Uqlowast

Id

Iq

Id

id

Iq

Id

Iq

Ud

Uq

dq

120572

120573

U120572

U120573

A

B

C

A

B

C

g

-k-

-k-

Zminus1

Zminus1

m

m

ltm

gtTm+

minus

is abc

VetInput We

+Ts = Ts s


0 1 2 3 4 5 60

10

20

30

40

50

60

Time (s)

Velo

city

(rad

s)




120593 (119904) =119862 (119904) 119866 (119904)

1 + 119862 (119904) 119866 (119904)

=(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(120590119871119904119869119896119894119902) 1199043 + 1198691199042 + (119896

119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(11)


1198961015840

1199011

gt120590119871119904119896119894

119896119894119902

minus 119896119901

1198961015840

119894

gt 0

(12)


and 1198961015840119894





119901= 226 119896

119894=

3581198981= 006119898

2= 1198983= 004119898

4= 016 1198961015840

1199011

= 0 11989610158401199012

= 4and 1198961015840

119894

= 001 11989610158401199011


119894







0

100

200

Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200






119890119873


119873


1


2


119898





Time (s)


0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

Velo

city

(rad

s)



Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400




0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)








Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400









0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)




6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119906 (119896) = (119896119901+ 119909 [119890 (119896)]) 119890 (119896)

+ 119896119894

119896minus1

sum119894=0

119890 (119894) + 119910 [119890 (119896)] 119890 (119896)119879

(4)



119909 [119890 (119896)]

=

1198961015840

1199011

|119890 (119896)| le 1198902

11989610158401199012

minus 11989610158401199011

1198901

(|119890 (119896)| minus 1198902) + 11989610158401199011

1198902lt |119890 (119896)| le 119890

1+ 1198902

11989610158401199012

|119890 (119896)| gt 1198901+ 1198902

(5)


and 11989610158401199012


1199011

lt 11989610158401199012


1and 1198961015840

1199012



[11989610158401199011

11989610158401199012

]When |119890(119896)| gt 119890

1+ 1198902 119909[119890(119896)] is equal to 1198961015840

1199012


119901+

11989610158401199012


2 119909[119890(119896)] is equal to 1198961015840

1199011


119901+ 11989610158401199011


2lt |119890(119896)| le 119890



11989610158401199012


119901+11989610158401199011

119896119901+11989610158401199012



119910 [119890 (119896)]

=

1 |119890 (119896)| le 1198904

1198961015840119894

minus 1

1198903

(|119890 (119896)| minus 1198904) + 1 119890

4lt |119890 (119896)| le 119890

3+ 1198904

1198961015840119894

|119890 (119896)| gt 1198903+ 1198904

(6)


119894


119894


3and 1198961015840

119894


4must make velocity


119894

1]When |119890(119896)| gt 119890


119894




When 1198904lt |119890(119896)| le 119890




119894sum119896minus1

119894=0

119890(119894)+

1198961015840119894

119890(119896)119879 to 119896119894sum119896

119894=0





1198901=1003816100381610038161003816119890max

1003816100381610038161003816 1198981

1198902=1003816100381610038161003816119890max

1003816100381610038161003816 1198982

1198903=1003816100381610038161003816119890max

1003816100381610038161003816 1198983

1198904=1003816100381610038161003816119890max

1003816100381610038161003816 1198984

(7)


111989821198983 and119898

4


119894 = 1 2 3 4 0 lt 1198981+ 1198982lt 1 and 0 lt 119898

3+ 1198984lt







rapidly


Three-phase invert

erSVPWM

Clarktransformation

Parkinverse

transformationFlux

linkage observer

Parktransformation

ACR

ACR


Decoupling


transformation

AVRminus

+minus

+

minus

+

120596lowastr

Tlowaste ilowastsq

ilowastsd

usd

usq

us120572

us120573

Vdc

iAiBiC

M

120596r

is120572is120573isd

isq

120596e ilowastsd i

lowastsq 120579

usm ism


minus


eTe 120596rC(s)

1

Tcqs + 1

1

Js



119906 (119896) = (119896119901+ 119909 [119890 (119896)]) 119890 (119896)

+ 119896119894

119896minus1

sum119894=0

119890 (119894) + 119910 [119890 (119896)] 119890 (119896)119879

+ 119896119889

119890 (119896) minus 119890 (119896 minus 1)

119879

(8)


1 1198982 1198983

1198984 11989610158401199011

11989610158401199012

and 1198961015840119894






119903






119904119902










119866 (119904) =1

119879119888119902119904 + 1

lowast1

119869119904=

1

(120590119871119904119896119894119902) 119904 + 1

lowast1

119869119904 (9)

where 119896119894119902






119862 (119904) =(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

119904 (10)



11989610158401199011

le 119909[119890(119896)] le 11989610158401199012

and 1198961015840119894

le 119910[119890(119896)] le 1 Here 11989610158401199011

11989610158401199012

and 1198961015840119894



GivenReal

Out

SectionPI

GivenReal Out

qPI

Discrete

Powergui

GivenReal Out

dPI

Wm

SinTetaCosTeta

fcn

Udq2UaUb

IabcCosTetaSinTeta

SVPWM2

Induction motor

35

+

-

IGBT inverter

Gain2

Gain1

wm

Demux

Decoupling

Battery

ETe Out


Idlowast

Udlowast

Uqlowast

Id

Iq

Id

id

Iq

Id

Iq

Ud

Uq

dq

120572

120573

U120572

U120573

A

B

C

A

B

C

g

-k-

-k-

Zminus1

Zminus1

m

m

ltm

gtTm+

minus

is abc

VetInput We

+Ts = Ts s


0 1 2 3 4 5 60

10

20

30

40

50

60

Time (s)

Velo

city

(rad

s)




120593 (119904) =119862 (119904) 119866 (119904)

1 + 119862 (119904) 119866 (119904)

=(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(120590119871119904119869119896119894119902) 1199043 + 1198691199042 + (119896

119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(11)


1198961015840

1199011

gt120590119871119904119896119894

119896119894119902

minus 119896119901

1198961015840

119894

gt 0

(12)


and 1198961015840119894





119901= 226 119896

119894=

3581198981= 006119898

2= 1198983= 004119898

4= 016 1198961015840

1199011

= 0 11989610158401199012

= 4and 1198961015840

119894

= 001 11989610158401199011


119894







0

100

200

Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200






119890119873


119873


1


2


119898





Time (s)


0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

Velo

city

(rad

s)



Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400




0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)








Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400









0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)




6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Three-phase invert

erSVPWM

Clarktransformation

Parkinverse

transformationFlux

linkage observer

Parktransformation

ACR

ACR


Decoupling


transformation

AVRminus

+minus

+

minus

+

120596lowastr

Tlowaste ilowastsq

ilowastsd

usd

usq

us120572

us120573

Vdc

iAiBiC

M

120596r

is120572is120573isd

isq

120596e ilowastsd i

lowastsq 120579

usm ism


minus


eTe 120596rC(s)

1

Tcqs + 1

1

Js



119906 (119896) = (119896119901+ 119909 [119890 (119896)]) 119890 (119896)

+ 119896119894

119896minus1

sum119894=0

119890 (119894) + 119910 [119890 (119896)] 119890 (119896)119879

+ 119896119889

119890 (119896) minus 119890 (119896 minus 1)

119879

(8)


1 1198982 1198983

1198984 11989610158401199011

11989610158401199012

and 1198961015840119894






119903






119904119902










119866 (119904) =1

119879119888119902119904 + 1

lowast1

119869119904=

1

(120590119871119904119896119894119902) 119904 + 1

lowast1

119869119904 (9)

where 119896119894119902






119862 (119904) =(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

119904 (10)



11989610158401199011

le 119909[119890(119896)] le 11989610158401199012

and 1198961015840119894

le 119910[119890(119896)] le 1 Here 11989610158401199011

11989610158401199012

and 1198961015840119894



GivenReal

Out

SectionPI

GivenReal Out

qPI

Discrete

Powergui

GivenReal Out

dPI

Wm

SinTetaCosTeta

fcn

Udq2UaUb

IabcCosTetaSinTeta

SVPWM2

Induction motor

35

+

-

IGBT inverter

Gain2

Gain1

wm

Demux

Decoupling

Battery

ETe Out


Idlowast

Udlowast

Uqlowast

Id

Iq

Id

id

Iq

Id

Iq

Ud

Uq

dq

120572

120573

U120572

U120573

A

B

C

A

B

C

g

-k-

-k-

Zminus1

Zminus1

m

m

ltm

gtTm+

minus

is abc

VetInput We

+Ts = Ts s


0 1 2 3 4 5 60

10

20

30

40

50

60

Time (s)

Velo

city

(rad

s)




120593 (119904) =119862 (119904) 119866 (119904)

1 + 119862 (119904) 119866 (119904)

=(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(120590119871119904119869119896119894119902) 1199043 + 1198691199042 + (119896

119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(11)


1198961015840

1199011

gt120590119871119904119896119894

119896119894119902

minus 119896119901

1198961015840

119894

gt 0

(12)


and 1198961015840119894





119901= 226 119896

119894=

3581198981= 006119898

2= 1198983= 004119898

4= 016 1198961015840

1199011

= 0 11989610158401199012

= 4and 1198961015840

119894

= 001 11989610158401199011


119894







0

100

200

Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200






119890119873


119873


1


2


119898





Time (s)


0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

Velo

city

(rad

s)



Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400




0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)








Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400









0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)




6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










GivenReal

Out

SectionPI

GivenReal Out

qPI

Discrete

Powergui

GivenReal Out

dPI

Wm

SinTetaCosTeta

fcn

Udq2UaUb

IabcCosTetaSinTeta

SVPWM2

Induction motor

35

+

-

IGBT inverter

Gain2

Gain1

wm

Demux

Decoupling

Battery

ETe Out


Idlowast

Udlowast

Uqlowast

Id

Iq

Id

id

Iq

Id

Iq

Ud

Uq

dq

120572

120573

U120572

U120573

A

B

C

A

B

C

g

-k-

-k-

Zminus1

Zminus1

m

m

ltm

gtTm+

minus

is abc

VetInput We

+Ts = Ts s


0 1 2 3 4 5 60

10

20

30

40

50

60

Time (s)

Velo

city

(rad

s)




120593 (119904) =119862 (119904) 119866 (119904)

1 + 119862 (119904) 119866 (119904)

=(119896119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(120590119871119904119869119896119894119902) 1199043 + 1198691199042 + (119896

119901+ 119909 [119890 (119896)]) 119904 + 119896

119894119910 [119890 (119896)]

(11)


1198961015840

1199011

gt120590119871119904119896119894

119896119894119902

minus 119896119901

1198961015840

119894

gt 0

(12)


and 1198961015840119894





119901= 226 119896

119894=

3581198981= 006119898

2= 1198983= 004119898

4= 016 1198961015840

1199011

= 0 11989610158401199012

= 4and 1198961015840

119894

= 001 11989610158401199011


119894







0

100

200

Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200






119890119873


119873


1


2


119898





Time (s)


0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

Velo

city

(rad

s)



Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400




0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)








Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400









0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)




6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

100

200

Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200


Time (s)

Curr

ent (

A)

0

100

200

0 1 2 3 4 5 6

minus100

minus200






119890119873


119873


1


2


119898





Time (s)


0 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

Velo

city

(rad

s)



Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400




0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)








Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400









0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)




6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Time (s)

Curr

ent (

A)

0 1 2 3 4 5 6

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6

Curr

ent (

A)

0

200

400

minus200

minus400




0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)








Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400









0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)




6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

Curr

ent (

A)

0

200

400

minus200

minus400


Time (s)0 1 2 3 4 5 6 7 8

0

Curr

ent (

A) 200

400

minus200

minus400









0

100

200

300

400

500

600

700

0 1 2 3 4 5 6 7 8Time (s)

Velo

city

(rad

s)




6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra











6 Conclusion




References


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article vector control algorithm for electric...

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