analysis and design of an electric vehicle using matlab...

Analysis and Design of an Electric Vehicle usingMatlab and Simulink

James T. Allison

Advanced Support GroupJanuary 22, 2009

James T. Allison EV Modeling and Design

2003-2007: University of Michigan

Research: Optimal System Partitioning and Coordination

Original System: Partitioned System: Coordination:


Optimal Partitioning and Coordination Decisionsin Decomposition-based Design Optimization


Application: Integrated Design of an Electric Vehicle


Vehicle Layout

sprung mass center

battery

b!max!e

xb b!

bw

front control arm

available battery space

rear trailing arm

W

L

!1 !2

!3

pulley drive system

traction motorx

y

forward direction of travel


Powertrain Simulation

Vehicle model: backward-looking Simulink model thataccounts for vehicle pitch motion and tire slip

Motor model: computes power loss map from geometricdesign variables

Battery model: Li-ion Simulink model (Fuller et al. 1994, Han2008). Battery parameters computed using artificial neuralnetwork.


Powertrain Simulation

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

time (sec)

vel

oci

ty (

m/s

ec)

SFUDS cycle Vehicle model Motor model

0.4

0.40.4 0.4

0.4

0.4

0.4

0.4

0.4

0.4

0.6

0.60.6

0.6

0.6

0.6

0.6

0.6

0.6

0.8 0.8

0.8

0.8

0.8

0.8

0.8

0.8

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.9

0.91

0.91

0.91

0.91

0.91

0.91

0.91

0.91

0.91

0.92

0.92

0.92

0.92

0.92

0.92

0.92

0.92

0.92

0.93

0.93

0.93

0.93

0.93

0.93

0.94

0.94

0.95

0.95

0.96

0.96

0.97

0.97

0.98

0.98

0.99

0.99

1

1

1

0 100 200 300 400 500 600 700

!250

!200

!150

!100

!50

0

50

100

150

200

v(t)!(t)

!(t)

Battery model

P (t)

Power History P(t):

0 50 100 150 200 250 300 350 400−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5 x 104 Power Requirements

battery output powermechanical power


Powertrain Simulation: Vehicle Model

v(t) Frx(t)

Net LongitudinalForce

Aero Drag Force

Fa(t)

Vehicle Pitch Model

Ffz(t)

Frz(t)

Tire Drag Model

+ Frt(t)

Fft(t)

Rear Tire Slip Model

!r(t)

Net Drive Torque

!r(t)

Belt Model

1/2

Single Wheel Torque

!m(t)

Motor Inertia Model

!b(t)

!m(t)

Belt Model

Motor Power Loss Map

P (t)


Vehicle Pitch Model

Frz

Ffz

!p

z

!1

!2

static height of mass center

z

θpz

θp

=

0 0 1 00 0 0 1

− kf +kr

ms

`2kr−`1kf

ms− cf +cr

ms

`2cr−`1cf

ms

`2kr−`1kf

Iy− `2

2kr+`21kf

Iy`2cr−`1cf

Iy− `2

2cr−`21cf

Iy

zθpz

θp

+

000Mp

Iy


Tire Slip Model

ωr =v(i + 1)

r(v)

Slip data obtained for a high efficiency tire from Bridgestone:

−0.4

−0.3

−0.2

−0.2

−0.1

−0.1

−0.1

00

0

0.1

0.1

0.1

0.2

0.20.3

0.4

Fx

F z

−1500 −1000 −500 0 500 1000 15000

500

1000

1500

Dynamic radius model constructed from Bridgestone data:

r(v) = Ct1 + Ct2v + Ct3v2


Induction Motor Model

rotor

stator

output shaft

Vs Lm

Rs Lls Llr

Rr/s

increasing sconstant Vs/!e

!e

!b

constant flux region flux weakening region

!em

!e

Motor Efficiency Map

!m (rad/sec)

!net

(N)


Power Demand Calculation

SFUDS Profile

0 50 100 150 200 250 300 350 4000

5

10

15

20

25

time (sec)

velo

city

(m/se

c)

Power Demand History

0 50 100 150 200 250 300 350 400−1.5

−1

−0.5

0

0.5

1

1.5

2

2.5 x 104 Power Requirements

battery output powermechanical power

τ and ω points visited

!m (rad/sec)

!net

(N)

!60000

!60000!40

000

!40000 !40000

!20

000

!20000!20000

00

00

00

20000

2000020000

40000

40000

40000

60000 60000

Torque/Speed Points Visited

0 100 200 300 400 500 600 700

!250

!200

!150

!100

!50

0

50

100

150

200


Battery Simulation

Li-ion Battery Construction

(a) cell winding

cu

rre

nt

co

lle

cto

r

ele

ctr

od

e

ele

ctr

od

e

cu

rre

nt

co

lle

cto

r

se

pa

rato

r

(a) Cell widings (b) Flat-wound lithium-ion cell

width

height

Vehicle Range Simulation

0 2000 4000 6000 8000 10000 12000−6

−4

−2

0

2

4

6

8

10 x 104

time (sec)

pow

er (W

)

P(t)Pu(t)

Pl(t)

Lumped parameter dynamic model

Hybrid pulse power characterization (HPPC) test computes:

Polarization resistance curvePolarization time constant

HHPC results modeled with a neural network


Vehicle Dynamics Simulation

Quarter-car model: state-space model used to simulate vehiclecomfort, roadholding, rattle space, and suspension forces

Static bicycle model: analytical model used to assessdirectional stability

Dynamic bicycle model: state-space model used to simulatesteering responsiveness


Quarter-car Model

v

ks cs

ktct

z0

zus

zs

ms/4

mus/4

d

dt

2664zus − z0

zuszs − zus

zs

3775 =

266640 1 0 0

− 4ktmus

− 4(cs+ct )mus

4ksmus

4csmus

0 −1 0 1

0 4csms

− 4ksms

− 4csms

377752664

zus − z0zus

zs − zuszs

3775 +

2664−14ctmus00

3775 z0


Road Profile Model

Begin with random data from a gaussian distributionApply color and moving average filtersCheck IRI using quarter-car model with golden parameters

IRI = 4.20: driver discomfort simulationIRI = 7.37: roadholding metric

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.06

−0.04

−0.02

0

0.02

0.04

0.06

Longitudinal Position (m)

Elev

atio

n (m

)

unfiltered datalow−pass filtermoving average filter


Steering Responsiveness (Step Input)

Lower yaw rate (Ω) rise time ⇒ more responsive handling

[vy

Ωz

]=

[− a3

a1− a2

a1

− b3

b1− b2

b1

] [vy

Ωz

]+

[ a4

a1b4

a1

]δf

a1 = m

a2 = m +2(`1Cαf − `2Cαr )

v

a3 =2(Cαf + Cαr )

v

a4 = 2Cαf

b1 = Iz

b2 =2(`2

1Cαf + `22Cαr )

v

b3 =2(`2

1Cαf − `22Cαr )

v

b4 = 2`1Cαf


Directional Stability

Stable at speeds up to vmax if:

Ds = L +v2max

gKus≥ 0

where:

Kus =

(Wf

Cαf− Wr

Cαr

)

Modeled Cαf and Cαr dependence on normal forces based ondata from Bridgestone.


Vehicle Structure Simulation

ANSYS R© finite element model used to predict:

bending and torsional stiffnessbending and torsional stresses

Surrogate model created using artificial neural network toreduce simulation time


EV Subsystem Interactions

Modeling these system interactions required the flexibility ofMatlab and Simulink

PT

ST

V D

M

Suspensionparameters

Suspens

ion

forces

Frame mass and inertia

Vehi

cle

mas

s an

d in

ertiaBattery m

ass and geom

etry

Vehicle mass and inertia

Battery mass and geometry


Electric Vehicle Design Problem

Design Objective and Constraints:

minimize 1/mpg equivalent fuel consumptionsubject to g1−2 ≤ 0 motor feasibility

g3 0-60 time ≤ 10 secg4 ≤ 0 urban range ≥ 100 mig5−6 ≤ 0 battery power and capacity constraintsg7 ≤ 0 directional stability constraintg8 ≤ 0 steering responsiveness constraintg9 ≤ 0 maximum rattle space constraintg10 ≤ 0 road holding constraintg11 ≤ 0 passenger comfort constraintg12 ≤ 0 geometric frame constraintg13−14 ≤ 0 frame stress constraintsg15−16 ≤ 0 frame stiffness constraintsg17−18 ≤ 0 battery packaging constraints


Electric Vehicle Design Problem

Design Variables:

x1−2 suspension parametersx3 pulley speed ratiox4−7 motor geometry and rotor resistancex8−10 battery geometryx11−12 frame geometryx13 battery position


Electric Vehicle Project Summary

Developed powertrain and chassis models from scratch inMatlab and Simulink

Developed structural model using ANSYS, constructed neuralnetwork model

Quantified vehicle system interactions

Used as a case study for system optimization research

Design results:

> 200 mpg equiv. (with AC and other loads)

100 mile range

0-60 mph in 10 seconds


EV Lessons Learned

Modeling system interactions is difficult, but essential

Requires flexible modeling environmentMass change propagation is significantEnables exploitation of synergy

EV technology can provide substantial energy savings

Explored tradeoffs between performance and efficiency


analysis and design of an electric vehicle using matlab...

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