The Effect of Road constraints .doc

7/27/2019 The Effect of Road constraints .doc

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The Effect of Road constraints on the Behavior of Electric VehicleDrive Controlled by Space Vector Modulation Using Direct Torque

Control

Brahim Gasbaoui1, Chaker Abdelkader2

1,Bechar University, B.P 417 Bechar (08000), Algeria

Abstract:Electric vehicles (EV) undergo different road constraints which make the control of such vehicles very difficult usingclassical methods. To overcome this problem, space vector modulation technique based direct torque control (DTC-SVM) is proposed. The electric drive consists of two directing wheels and two rear propulsion wheels equipped withtwo light weight induction motors. Acceleration and steering are ensured by an electronic differential system whichmaintains robust control for all cases of vehicle behavior on the road. It also allows controlling independently everydriving wheel to turn at different speeds in any curve. The proposed control technique is simulated in MATLABSIMULINK environment. The results obtained reveals that the proposed method improves the efficiency andsatiability for EV in all type of road constraints such as straight, slope, descent and curved road.Keywords: Electric vehicle, Electronic differential, Induction motor, Space Vector Modulation, Traction, Direct torque control.

1 Introduction.Actually, electric vehicle (EV) including, full cell andhybrid vehicle have been developed very rapidly as asolution to energy and environmental problem.

Driven EVs are powered by electric motors throughtransmission and differential gears, while directly drivenvehicles are propelled by in-wheel or, simply, wheelmotors [1, 2]. The basic vehicle configurations of thisresearch has two directly driven wheel motors installedand operated inside the driving wheels on a pure EV.These wheel motors can be controlled independently andhave so quick and accurate response to the command thatthe vehicle chassis control or motion control becomesmore stable and robust, compared to indirectly drivenEVs. Like most research on the torque distributioncontrol of wheel motor, wheel motors [3, 15] proposed adynamic optimal tractive force distribution control for an

EV driven by four wheel motors, thereby improvingvehicle handling and stability [4, 5].The researchers assumed that wheel motors were all

identical with the same torque constant; neglecting motordynamics the output torque was simply proportional tothe input current with a prescribed torque constant.

Direct torque control has become one of the mostpopular methods of control for induction motor drivesystems [8, 13, 17]. DTC can decouple the interactionbetween flux and torque control, based on both torqueand flux instantaneous errors, and provide good torqueresponse in steady state and transient operationconditions. The main advantages of DTC are: absence ofcoordinate transformation and current regulator; absenceof separate voltage modulation block; the actual flux-linkage vector position does not have to be determined,but only the sector where the flux-linkage vector islocated, etc. In addition, DTC minimizes the use ofmachine parameters, so it is very little sensible to theparameters variation [3].

SVM-DTC method is an advanced, computationintensive PWM method and possibly the best among allthe PWM techniques for variable speed drivesapplication [19, 21]. Because of its superiorperformance characteristics, it has been findingwidespread application in recent years. With a machineload, the load neutral is normally isolated, which causesinteraction among the phases. This interaction was notconsidered before in the PWM discussion. Recently,fuzzy logic control has found many applications in thepast decades, which overcomes these drawbacks. Hence,fuzzy logic control has the capability to controlnonlinear, uncertain systems even in the case where nomathematical model is available for the controlledsystem.

The structure of the work presented in this paper is

organized in the following sequence: The principlecomponents of the Electric traction chain with theirequations model is set in section 2. Section 3 shows thedirect torque control of induction motor. Section 4 showsthe development space vector modulation techniquebased DTC for Electric vehicle motorization. Theproposed structure of the studied propulsion system isgiven in the section 6. The simulation results of thedifferent studied cases are presented in Section 5. Finally,the concluding remarks are given in section 6.

2 Electric traction system elementsmodeling.

Figure 1 represents the general diagram of an electrictraction system using an induction motor (IM) suppliedby voltage inverter [4, 8].

2.1. Energy source.

2.3. Traction motor.

The used motorization consist of three phaseinduction motor (IM) supplied by a voltage invertercontrolled by direct torque control. The dynamic modelof three-phase, induction motor can be expressed in thestator stationery reference as [3, 6, 7, 8]:

refernces

Gear

control

1

Fig.1 Electrical traction chain

Battery

motor

Induction

Inverter

Load

Vehicle


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srslsm

s

rslrr

sr

ms

ss

rr

rss

ss

rrr

ss

vpiL

pT

iT

L

vLT

kkpii

vL

kpT

ii

dt

d

1

1

1

++=

=

++=

+++=

(3)

Where is the coefficient of dispersion and is givenby:

rs

m

LL

L21= (4)

rs

m

LL

Lk

= (5)

s

r

mrs

L

L

LRR

2

2

+

=(6)

r

rr

R

LT = (7)

sL , rL , mL stator, rotor and mutualinductances;

sR , rR

stator and rotor resistances;

e, r

electrical and rotor angularfrequency;

sl Slip frequency ( )re ;r Rotor time constant ( )rr RL ;p Pole pairs

2.4. Mechanical part.

The developed globally traction chain model based onthe data uses is shown in figure 2:

Fig. 2 Electromechanical structure.

2.4.1. The vehicle load.

The vehicle is considered as a load is characterized bymany torques which are mostly considered as resistivetorques [4, 5, 16, 17]. The different torques includes:

The vehicle inertia torque defined by the followingrelationship:

dt

dwJT vvin .= (8)

2.4.2. Aerodynamics fore.

This part of the force is due to the friction of thevehicle body, moving through the air .It is q function ofthe frontal area shape protrusion such as side ,mirrors

,ducts and air passages spoilers ,and ;any other factor .theformula for this component is:

2...2

1vTSF xaero = (9)

The aerodynamics torque is:

2...2

1vRTST rxaero =

(10)

2.4.3. Rolling force.

The rolling resistance is primarily due to the tractionof the tire on the rode .Friction in bearing and thegearing systems also play their part. The rollingresistance is appositely constant, depend on vehicle speed.It is proportional to vehicle weight .The equation is.

.rtire MgfF = (11)

The rolling torque is:

rrtire RMgfT = (12)

2.4.4. Hill climbing force.

The force needed to drive the vehicle up a slope is the

most straightforward to find .It is simply the componentof the vehicle weight that acts along the slop. By simpleresolution the force we see that [18].

)sin(MgFslope = (13)

The slope torque is

We obtain finally the total resistive torque:

2.4.5. Gear.

The speed gear ensures the transmission of the motortorque to the driving wheels. The gear is modeled by thegear ratio, the transmission efficiency and its inertia.

The mechanical equation is given by [12]:

)Tp(Tfwdt

dwJ remm

me =+

(15)

With:

vred

r TNT

1=

rslpoe RMgT ).sin(= (14)

tireF

teF

Mg

aeroF

slopeF

Fig.3 The forces acting on a vehicle moving along a slope.

Inertie

RendementTorqueResistive

Load

Vehicle

m eTv vT

sT

Inertia


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3

(16)

2red

ve

N

JJJ

+=

(17)The modeling of the traction system allows the

implementation of some controls such as the vectorcontrol and the speed control in order to ensure theglobally system stability.

3 Direct torque control using space vectormodulation (SVM-DTC).With the development of microprocessors

and DSP techniques, the SVM technique hasbecome one of the most important PWMmethods for Voltage Source Inverter (VSI)since it gives a large linear control range, lessharmonic distortion, fast transient response,and simple digital implementation [21-22].The induction motor stator flux can beestimated by

dt)iRV( dsst

0 dsds= (18)

dt)iRV( qsst

0 qsqs = (18)2qs

2dss += (18)

= ds

qs1s tan

And electromagnetic torque emT can be calculatedby

)ii(p2

3T dsqsqsdsem = (19)

The SVM principle is based on the switchingbetween twoadjacent active vectors and two zero vectors

during one switching period. It uses the spacevector concept to compute the duty cycle ofthe switches. Fig. 4 shows a scheme of athree-phase two-level inverter with a star-connection load.From Fig.3, the output voltages of theinverter can be composed by eight states

710 u....u,u , corresponding to the switch

states )111(S),100(S),000(S 710 ,

respectively. These vectors can be plotted on

the complex plane )( as shown in Fig.4,

and are given by [3].

7,0kfor0

6,...2,1kforeV3

2

u)3/)(1k(j

dck

=

=

=

The rotating voltage vector within the sixsectors can be approximated by sampling thevector and switching between differentinverter states during the sampling period

[22]. The vector su is commonly split into

two nearest adjacent voltage vectors andzero u0 and u7 in an arbitrary sector. For

example, during one sampling interval,vector su in sector I can be expressed as

7s

72

s

21

s

10

s

0s u

T

Tu

T

Tu

T

Tu

T

T)t(u +++= (1

5)

Where 7210 T,T,T,T are the turn-on time of

the vectors 0u , 721 u,u,u and sT TS is the

sampling time.

.0T,0T,0TTTTT 707021s +=

The block diagram of the DTC-SVM controlscheme for voltage source inverter-fed IM isshown in figure 6. In this method two PIcontrollers are used for torque and flux

regulation. The outputs of the PI flux andtorque controllers generate the reference

stator voltage components .u,u dsqs

expressed in the stator flux oriented

coordinates ).qd( These components are

dc voltage commands and then transformed

into stationary coordinates ).( the

commanded values ss u,u are delivered to

space vector modulator (SVM), which

generates switching signals .S,S,S cba for

power transistors. [23-24].

au

cu

bu2

Vdc

2

Vdc

InductionMotor

Inverter

1S

2S

3S

4S

5S

6S

0u

N

3

Fig. 5 Phase voltage space vector.

Fig. 4 Three-phase two-level inverter


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Referring to figure 4.1 and 4.3 we can

calculate .uandu*qs

*ds

))(s

KK(u

*i

p*ds

+=

(15)

)TT)(s

KK(u

*em

*em

iT

pT*qs

em

em+=

(16)

Acclerator


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2. Electric Differentials and itImplementation.

The main of the control system should be summarizedas follows:

1) A speed network control is used to control eachmotor torque;

2) The speed of each rear wheel is controlled usingspeed difference feedback. Since the two rear wheels aredirectly driven by two separate motors, the speed of theouter wheel will need to be higher than the speed of the

inner wheel during steering maneuvers (and vice-versa).This condition can be easily met if the speed estimator isused to sense the angular speed of the steering wheel.The common reference speed ref is then set by theaccelerator pedal command. The actual reference speed

for the left drive*

left and the right drive*

right arethen obtained by adjusting the common reference speed

*

using the output signal from the DTC-SVM speedestimator. If the vehicle is turning right, the left wheelspeed is increased and the right wheel speed remainsequal to the common reference speed

*. If the vehicle

is turning left, the right wheel speed is increased and theleft wheel speed remains equal to the common referencespeed

*

[7 , 9, 11].Form the model figure 9, the following characteristic can

be calculated:

)(tg

LR w= (25)

Where is the steering angle. Therefore, the linearspeed of each wheel drive is given by

)2(

)2(

2

1

wv

wv

dRV

dRV

=

=

(26)

And their angular speed by

lmw

wwmL

rmw

wwrm

LdL

L

dL

)tan()2(

)tan()2(

=

=

(27)

Where vw is the vehicle angular speed according tothe

center of turn .The difference between wheel driveangular speeds is then

vw

wlmrm w

L

d )tan(** ==

(28)

And the steering angle indicates the trajectorydirection

leftTurn> 0 (29)

*sat

satpK

s

Ki

*dsu

*emT

sat

emT

satempTK

s

KemiT

*qsv

5

Wheel

Batter

Fig 6. DTC-SVM Controller

Fig.7 Flux controller

Fig. 8 Torque controller


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aheadStraight0= (30)

raightTurn


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Fig.10 Structure of vehicle in curve

7

1SVM

DTC

2SVM

DTC


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Fig.11 The driving wheels control system.


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3. Simulation results.Case1.In order to characterize the deriving wheel systembehavior were carried using the model of figure 10 .Forclarify and observe the effect of disturbances on thevehicle speed using DTC-SVM controlled. Firstly EV issubmitted a constant speed 80 km/h during simulation.The parameter of torque and flux controllers are

,2Kp = ,80Ki = ,200K empT = and

2000KTemi

= .Figure 12.1 show the system response in

DTC-SVM controller .We can summaries the vehiclespeed results in the following table:

Table.3 Performance of SVM-DTC in the speed response.

Results Rising

time

[Sec]

Overshoot

[%]

Steady

state

error [%]

DTC-SVM 0.752 0.310 0.080

The advantage of DTC-SVM control is its robustness,its capacity to maintain ideal trajectories for two wheels

control independently and ensure good disturbances

rejections stability of vehicle perfected ensured with the

speed variation and less error speed.

From the figure 12.1 and the table 3 we can say that: the

effect of the disturbance is neglected in the DTC-SVM

controller. It appears clearly that the classical control with

PI controller is easy to apply and gives satisfactory results.

In this propose the SVM-DTC is very uses in the electric

propulsion systems.

0

10

20

30

40

50

60

70

80

90

100

i

Vehiclespeed[km/h]

Refrence speed

Vehicle speed

Fig.12.1 Vehicle wheel speed

Case 2.

All simulation of electric vehicle is using the trajectoryshow in figure12.2, and for more detail show table1.Secondly application of DTC-SVM controller .EV hassubmitted a number of tests during the various routes.

At t = 0 s, the vehicle speed starts climbing to 70 km/h.figure 12.1.This forces the electromagnetic torque to attainmaximal value 346.70 Nm and calls an inrush currentmeasured 132.30 A. Each motor solicits a high current toattain the reference speed imposed by the driver.

Table 2 show below the time and nature of different road.

Table.2 Different paths driving by electric vehicle.

N[Paths]Time[s]

Designation

1 0


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direction but with different speeds. The Electronicdifferential acts on the two motor speeds by decreasing thespeed of the driving wheel on the right side situated insidethe curve, and on the other hand by increasing the wheelmotor speed in the external side of the curve. The behaviorof these speeds is given by 14.1.

At 4s


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Fig.12.8 Aerodynamic torque, Rolling torque, slop torque,Vehicle torque.

1: Variation of vehicle torque in different paths

t[s] T aero

[s]

T tire[s]

T slope

[s]

T v

[N]

0.678


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Angle grade of road rad

fr Wheels Rolling resistance coefficient

Vdc Battery voltage Volt

Angular speed variation given by electronicdifferential

Rad/sec

mr Right wheel angular speed Rad/sec

lr Left wheel angular speed Rad/secmr Right wheel angular speed of reference Rad/sec

lm Left wheel angular speed of reference rad

Reel angle wheel curves rad

Vehicle slip angle rad

References

[1] Y. P. Yang, C. P. Lo. Current Distribution Control of Dual DirectlyDriven Wheel Motors for Electric Vehicles. Control EngineeringPractice, vol. 16, no. 11, pp. 1285-1292, 2008.

[2] P. He, Y. Hori, M. Kamachi, K. Walters, H. Yoshida. Fu- tureMotion Control to be Realized by In-wheel Motored ElectricVehicle. In Proceedings of the 31st Annual Confer- ence of the IEEIndustrial Electronics Society, IEEE Press, Raliegh South Carolina,USA, pp. 2632-2637, 2005.

[3] Kang J. K., Sul S. K., New Direct Torque Control of InductionMotor for Minimum Torque Ripple and Constant SwitchingFrequency. IEEE Trans. Ind. Applicat., vol. 35, no. 5, p. 1076-1082, 1999.

[4] C. C. Chan et al., Electric vehicles charge forward, IEEE PowerEnergy Mag., vol. 2, no. 6, pp. 2433, 2004.

[5] Z. Zhu et al., Electrical machines and drives for electric, hybrid,and fuel cell vehicles, Proc. IEEE, vol. 95, no. 4, pp. 764765,2007.

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[8] Chen, L., Fang, K.L.: A Novel Direct Torque Control for Dual-Three-Phase Induction Motor. Conf. Rec. IEEE InternationalConference on Machine Learning and Cybernetics, pp. 876-88,2003.

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[17] M. Vasudevan, R. Arumugam, New direct torque control schemeof induction motor for electric vehicles. 5 th Asian Control

Conference, vol. 2, pp. 1377 1383, 2004.

[18] M. E. H. Benbouzid et al., Advanced fault-tolerant control ofinductionmotor drives for EV/HEV traction applications: Fromconventional to modern and intelligent control techniques, IEEETrans. Veh. Technol., vol. 56, no. 2, pp. 519528, Mar. 2007

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control of induction machines using space vector modulation,IEEETransaction on Industry Applications, Vol. 28, no. 5, pp. 1045-1053, septembre/October 1992.

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torque controlled space vector modulation (DTC-SVM) induction motor drives, in Proceedings of theIEEE ISIE'05, Dubrovnik (Croatia), pp. 951-956,June2005.

2Inverte

1_DTCSVM

2_DTCSVM

Electronicdifferential

dw

rR2

R

Inverter1

Battery

wheeldrivingrearRight

wheelfrontRight

v

1V2

V

Lw

wheelfrontLeft

The Effect of Road constraints .doc

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