EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
EMR coupled with Power-Oriented
Graphs for automotive application
Dr. Federica GROSSI, Prof. Roberto ZANASI
Università di Modena, Italy
federica.grossi@unimore.it, roberto.zanasi@unimore.it
Dr.Walter LHOMME, Prof. Alain BOUSCAYROL
L2EP, University Lille1, MEGEVH network,
Walter.Lhomme@univ-lille1.fr, Alain.Bouscayrol@univ-lille1.fr
EMR coupled with Power-Oriented Graphs for automotive application
Outline
EMR’11 summer school, Lausanne, July 2011
1. Power-Oriented Graphs basic features
2. The studied system: simplified model of a
vehicle with tire-soil interaction
3. Control structure
4. Simulations
5. Comparison with EMR
6. Conclusion
2
EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
1. Power-Oriented Graphs
basic features
EMR coupled with Power-Oriented Graphs for automotive application
Power-Oriented Graphs (POG) basic features
EMR’11 summer school, Lausanne, July 2011
The Power-Oriented Graphs (POG) are ''block diagrams'' with a ''modular'' structure
based on two blocks:
Positive power flows
Dashed line =
power flowing
through that
section
Product of conjugated
variables = power
Elaboration block
Connection block
Store and dissipate
or generate energy
Only transform
the energy
Direct correspondence between POG and state space equations
4
EMR coupled with Power-Oriented Graphs for automotive application
Dynamic modeling: electrical exemples
EMR’11 summer school, Lausanne, July 2011
IR
IR
II
Vc
Vc
R
C
Kirchhoff’s
current law
5
R
VO
C
Kirchhoff’s
voltage law
EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
2. The studied system: simplified
model of a vehicle with tire-soil
interaction
EMR coupled with Power-Oriented Graphs for automotive application
Simplified vehicle: the bicycle model
EMR’11 summer school, Lausanne, July 2011
7
• 2D model with 3 rigid bodies
• motion possible in plane (xy)
• no suspensions
• interaction with the ground by means
of tires
Energetic model of the tire-soil
interaction
Degrees of freedom:
2 translational (wheels are solidly connected to chassis for translations)
3 rotational (wheels are independent from chassis for rotations)
EMR coupled with Power-Oriented Graphs for automotive application
Tire-road interaction: elastic dynamic model
EMR’11 summer school, Lausanne, July 2011
Main drawbacks of Pacejka’s formulas:
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1. The slip ratio
can be used only
when vx>0 ( or R>0)
2. They mix together the slip and
skid phenomena.
New definition for the slip ratio:
elastic element
SLIPPING
Only when both the contact force in the x-direction and the angular
velocity of the wheel in the y-direction are not zero.
SKIDDING
Only when the force vector exceeds the skidding threshold. The
contact area changes its dimensions according to the adherence
conditions.
EMR coupled with Power-Oriented Graphs for automotive application
POG scheme of the simplified vehicle
EMR’11 summer school, Lausanne, July 2011
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Contact point
2D mechanical
dynamics of chassis
and wheels
Coordinate
transformation
Elastic element Both blocks have a force
describing the tire as input and give a
velocity as output
EMR coupled with Power-Oriented Graphs for automotive application
POG scheme: mathematical details
EMR’11 summer school, Lausanne, July 2011
Differential equations of the whole system:
Mass and
inertia matrix
Velocity
vector
Transformation
matrices
Stiffness and
damping matrices
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EMR coupled with Power-Oriented Graphs for automotive application
POG and EMR of the vehicle
EMR’11 summer school, Lausanne, July 2011
Frx
.
xm
Env. x
.
xm
2
tot
tot
Fry
MS2
2– m
tot
ym
.
r
ym
V
1
Fpx
.
Env. y
Fpy
.
Xc
Fc
S+S
MS1
1– m
Fr
Fc
Vcsl + Vcsk
11
EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
3. Control Structure
EMR coupled with Power-Oriented Graphs for automotive application
Maximum Control Structure
EMR’11 summer school, Lausanne, July 2011
input torques
coupling
inertias
coupling
masses
Frx
environment
.
Tuning
chain
xm
Env. x
.
xm
2
tot
tot
Fry
MS2
2– m
ym
E
Env. y
Fpy
elastic element
.
V
1
Xc
skidding and
M
slipping
R
Fc
Inversion
S+S
MS1
1-ref
ym
.
r
tot
Fpx
.
Fr
1– m
Fc
Vcsl + Vcsk
coupling
2-mes
r1meas
tot-ref
fcx1-meas
1-ref
1-ref
.
Xc- ref
fcx2-meas
fcx1-ref
Frx-ref
Frx-ref
.
xm-ref
M
C
S
Maximum
Control
Structure
13
EMR coupled with Power-Oriented Graphs for automotive application
Model and control without the contact law
EMR’11 summer school, Lausanne, July 2011
input torques
coupling
Equivalent wheel
mas
Frx
environment
Vrx
Env. x
Fpx
2
tot
E
Vrx
MS2
2– m
M
tot
1
R
Simplified
Model
MS1
1-ref
1– m
2-mes
M
tot-ref
C
S
Frx-ref
Vrx-ref
Simplified
Control
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EMR coupled with Power-Oriented Graphs for automotive application
Simplified control with the complete model
EMR’11 summer school, Lausanne, July 2011
input torques
coupling
inertias
coupling
masses
environment
Frx
Env. x
Fpx
2
tot
tot
Fry
MS2
Env. y
2– m
tot
r
Fpy elastic element
1
V
skidding and
slipping
M
R
Fc
MS1
1-ref
E
Complete
Model
S+S
1– m
Fr
Fc
Vcsl + Vcsk
2-mes
P
tot-ref
C
S
Frx-ref
Vrx-ref
Simplified
Control
15
EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
4. Simulation
EMR coupled with Power-Oriented Graphs for automotive application
Matlab-Simulink implementation
EMR’11 summer school, Lausanne, July 2011
17
Global structure:
EMR
Inner structure:
POG
EMR coupled with Power-Oriented Graphs for automotive application
Simulation results: complete model and control
EMR’11 summer school, Lausanne, July 2011
reference
real
slip
skid
•Electric vehicle with DC
machine
• Control of velocity: structure
based on inversion (MCS)
The tire starts skidding
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EMR coupled with Power-Oriented Graphs for automotive application
Simulation results: Model and control without the contact law
EMR’11 summer school, Lausanne, July 2011
• First order
dynamic system
• No information on
tires slipping
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EMR coupled with Power-Oriented Graphs for automotive application
Simulation results: complete model and simplified control
EMR’11 summer school, Lausanne, July 2011
slip
skid
• Good control of the speed
• Bad behavior of tire skidding
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EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
5. Comparison POG - EMR
EMR coupled with Power-Oriented Graphs for automotive application
POG and EMR: comparison
EMR’11 summer school, Lausanne, July 2011
POG
EMR
Analysis
Control structure
All known
All known
Scalar and vectorial
Scalar and vectorial
Firestone’s
Maxwell’s
Integral and differential
Integral
2
4 main elements,
several symbols
Coupling
Implicit
Explicit
Variable direction
Explicit
Explicit
Power direction
Implicit
Not visible
Mathematical model from
the graphical scheme
Directly obtainable
Not directly obtainable
Simulation
Directly in Simulink
Simulink library
Linear
Planar
No methodology
Methodology through
inversion rules
Objective
Energetic domains
Power variables
Analogy between
energetic domains
Causality
Nr. Basic elements
Graphical representation
Control structure
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EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
6. Conclusion
EMR coupled with Power-Oriented Graphs for automotive application
Conclusion
EMR’11 summer school, Lausanne, July 2011
• Power-Oriented Graphs (POG) and Energetic Macroscopic
Representation (EMR) are energy-based techniques that
can be used for modelling all types of physical systems
involving power flows
• Cooperation of both POG and EMR is proposed
• A simplified vehicle model is given in POG and EMR
formalisms
• An elastic dynamic model of the interaction between tires
and ground has been used
• The MCS is given in order to control the longitudinal
velocity of the vehicle
• A simplified control is also proposed
• Simulations in Matlab-Simulink
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EMR’11
Lausanne
July 2011
Joint Summer School EMR’11
“Energetic Macroscopic Representation”
« BIOGRAPHIES AND REFERENCES »
EMR coupled with Power-Oriented Graphs for automotive application
- Authors EMR’11 summer school, Lausanne, July 2011
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Dr. Federica GROSSI
University of Modena, Italy
PhD in Information and Telecommunication Tech. at University of Modena (2010)
Research topics: graphical modelling techniques applied to electro-mechanical systems
and hybrid automotive systems.
Prof. Roberto ZANASI
University of Modena, Italy
PhD in System Engineering at University of Bologna (1992)
Research topics: POG modelling of complex physical systems, advanced control
techniques, trajectory planning, control in automotive systems
Dr. Walter LHOMME
L2EP, University Lille1, MEGEVH, France
PhD on Hybrid Electric Vehicles at University Lille1, 2007
Engineer at AVL (UK) (2007-2008) Associate Prof. at Univ. Lille1 (2008)
Research topics: EMR, EVs and HEVs
Prof. Alain BOUSCAYROL
University Lille 1, L2EP, MEGEVH, France
Coordinator of MEGEVH, French network on HEVs
PhD in Electrical Engineering at University of Toulouse (1995)
Research topics: EMR, HIL simulation, tractions systems, EVs and HEVs
EMR coupled with Power-Oriented Graphs for automotive application
References
EMR’11 summer school, Lausanne, July 2011
[1] F. Grossi, W. Lhomme, R. Zanasi, A. Bouscayrol, “Modelling and control of a vehicle with tireroad interaction using POG and EMR formalisms”, ELECTROMOTION 2009, EPE Chapter
“Electric Drives” 8th International Symposium on Advanced Electromechanical Motion Systems,
Lille, France, July 2009 (common paper University of Modena and L2EP Lille)
[2] F. Grossi, W. Lhomme, R. Zanasi, A. Bouscayrol, “Modelling and control of a vehicle with tireroad interaction using energy-based techniques” IEEE VPPC 2009 (Vehicular Power and
Propulsion Conference), Dearborn, Michigan, USA, September 2009 common paper University
of Modena and L2EP Lille).
[3] R. Zanasi, F. Grossi, “Modelling Hybrid Automotive Systems with the POG Technique”, Journal
of Asian Electric Vehicles, Vol. 8, Nr. 1, June 2010.
[4] R. Zanasi “The Power-Oriented Graphs Technique: system modeling and basic properties”, IEEE
VPPC 2010 (Vehicular Power and Propulsion Conference), Lille, France, September 2010.
[5] W. Lhomme, R. Zanasi, G.-H. Geitner, A. Bouscayrol, “Different graphical descriptions of clutch
modelling for traction systems”, ElectrIMACS’08, Québec (Canada), May 2008 (common paper
L2EP Lille, University of Modena and University of Dresden)
[6] F.Grossi, “Dynamic Modeling and Control of Hybrid Automotive Systems”, PhD Dissertation
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