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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)|
The expression of 119909[119890(119896)] can be described as
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
4 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 5
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
6 Mathematical Problems in Engineering
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)
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 7
Time (s)
Curr
ent (
A)
0 1 2 3 4 5 6
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 8 The simulation result of three-phase current
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
8 Mathematical Problems in Engineering
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
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Complex AnalysisJournal of
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OptimizationJournal of
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CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
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Operations ResearchAdvances in
Journal of
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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
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)|
The expression of 119909[119890(119896)] can be described as
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
4 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 5
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
6 Mathematical Problems in Engineering
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)
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 7
Time (s)
Curr
ent (
A)
0 1 2 3 4 5 6
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 8 The simulation result of three-phase current
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
8 Mathematical Problems in Engineering
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
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
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)|
The expression of 119909[119890(119896)] can be described as
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
4 Mathematical Problems in Engineering
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
Mathematical Problems in Engineering 5
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
6 Mathematical Problems in Engineering
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)
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 7
Time (s)
Curr
ent (
A)
0 1 2 3 4 5 6
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 8 The simulation result of three-phase current
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
8 Mathematical Problems in Engineering
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
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
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
Mathematical Problems in Engineering 5
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
6 Mathematical Problems in Engineering
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)
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 7
Time (s)
Curr
ent (
A)
0 1 2 3 4 5 6
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 8 The simulation result of three-phase current
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
8 Mathematical Problems in Engineering
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
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
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
6 Mathematical Problems in Engineering
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)
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 7
Time (s)
Curr
ent (
A)
0 1 2 3 4 5 6
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 8 The simulation result of three-phase current
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
8 Mathematical Problems in Engineering
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
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
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)
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 7
Time (s)
Curr
ent (
A)
0 1 2 3 4 5 6
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 8 The simulation result of three-phase current
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
8 Mathematical Problems in Engineering
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
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
Time (s)
Curr
ent (
A)
0 1 2 3 4 5 6
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6
Curr
ent (
A)
0
200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 8 The simulation result of three-phase current
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
8 Mathematical Problems in Engineering
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
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
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(a) Three-phase current with PID controller
Time (s)0 1 2 3 4 5 6 7 8
Curr
ent (
A)
0
200
400
minus200
minus400
(b) Three-phase current with variable gain PID controller
Time (s)0 1 2 3 4 5 6 7 8
0
Curr
ent (
A) 200
400
minus200
minus400
(c) Three-phase current with improved variable gain PID controller
Figure 10 The simulation result of three-phase current
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
In Figure 10 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
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
Improved variable gain PID controllerVariable gain PID controllerPID controller
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
Mathematical Problems in Engineering 9
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
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
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
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