Bond Graph for Modelling, Analysis, Control Design, Fault ... · Bond Graph for Modelling, Analysis, Control Design, Fault Diagnosis Geneviève Dauphin-Tanguy Christophe Sueur Laboratoire

Bond Graph for Modelling, Analysis,Control Design, Fault Diagnosis

Geneviève Dauphin-TanguyChristophe Sueur

Laboratoire d’Automatique et d’Informatique Industrielle de Lille

Bond Graph Research GroupLaboratoire d’Automatique et d’Informatique Industrielle de Lille

Ecole Centrale de Lille

• 6 academics (2 Profs, 2 associate profs, 2 assistant profs)• 10 PhD students

Application areas : power systems (electrical machines, photovoltaicsystems, fuel cells), thermofluid process, car industry

Rosario - 22/11/02 LAIL - Ecole Centrale de Lille 3

Studies performed in collaboration with Peugeot -Citroën

• Mechatronic design of an automatic gear box

• Clutch management and drive comfort

• Mechatronic design of an active hydraulic suspension

• Thermal comfort regulation in a car interior

• Modelling and simulation of a fuel cell system

• Analysis of structural properties of bond graph models

• Robustness of control laws for systems with parametric uncertainties

• …..


Why a bond graph approach ?

• Multidisciplinary systemsà need for a communication language between people from different physical domains

• Need for models with physical insight (virtual testing facility)

• Unified modelling methodology for knowledge storagein model libraries

• Integrated (« mechatronic ») design of controlled systems


Mechatronic design

Modelling Control

Diagnosis

IdentificationAnalysisValidationSimulation

SimplificationActuatorsSensors

Fault Detection andIsolation

Objectives

Faulty modeMaintaining


1 - Mechatronic design of an automatic gear box

engine torqueconverter

automatic gear box

vehicle

computer

Differential, Transmission shaftWheels, Vehicle mass, air resistance, road friction

Complete driveline



Problem statement

• Design control laws for the driving of an automatic gear box by a computer with the following objectives:– Complete satisfaction of the customer corresponding to a variation

of the engine torque as continue as possible (no jerk in acceleration during a shift)

– Respect of technological constraints (actuator response duration, minimization of the energy dissipated in the clutchs)

When to shift ? How to shift ?



Automatic gear box : physical scheme

Arrangement of 2 epicyclic gear trainswhich allows 3 ratios plus one reverse

Different ratios : one element blockedor 2 elements maintained at the same speed

Clutches between 2 rotating elementsBrakes between one element and the housing block

Planetcarrier

ω ringω

Planetω

mPCP

PCR =−−

ωωωω



Bond graph model of the automatic gear box

:Jinp

:friction:PC1_R2

:P1

:PC2

:housing

:m2

:1-m2

:1-m1

:m1

:R1

:input

:load

clutch 2

:housing

Clutch1

brake 2

brake 1

Free wheel



Bond graph model of a clutch or a brake

:pressure:friction_coeff

Coulomb friction depending on the pressure applied on the clutch disks, defining the « limited torque »

torque

slip

pressure

If clutch torque < limited torqueà clutch closed, all the torque transmittedIf clutch torque = limited torqueà clutch opened, slipping velocity



Decision block

Contains the schift schedule (diagram throttle position vs vehicle speed)which permits to know « when to shift »

Different programs: economical, sport, snow

When a shift is decided, the different pressures in the clutches are controlled

pressure

time

« How to shift » : - action on only 2 clutches or 2 brakes at the

same time,- control of the pressure to have a smooth shift and no jerk in acceleration



Bond graph model of the vehicle

differential

: AGB outputtorque

:Cwheel_r:Jwheel_r:Cshaft_r

:Cwheel_l:Cshaft_l:Jshaft_l

:air_friction

:Mveh

:Jwheel_l

:rwh_2

:rwh_1

:slope

:Jshaft_r

left_shaft left_wheelvehicle

right_wheel

right_shaft

:Idiff

:diff


2- Clutch management and drive comfort

• Ojectives: – Reduce the well-known fore and aft oscillation of a vehicle

occuring when a sudden torque variation takes place in thetransmission (throttle step sollicitation)

– Satisfy comfort and driving pleasure

• Means:– Define an hydraulic-electronic-mechanical actuator transforming

the numerical output into pressure on the plates of the clutch– Design control laws for this electrohydraulic servovalve


3 - Thermal comfort regulation in a car interior

Usual climate control

• Try to reach and maintain the passenger compartment temperature to a specified target temperature.

à The regulator acts on the mixing flap to increase or decrease the blown air temperature. Usually, a proportional strategy is used to control the mixing flap

CABMixing

FlapProp.+-

Tb,target Tbε

Ta

Ta,target


3 - Thermal comfort regulation in a car interiorUsual climate control

! Usually the air temperature in the compartment does not reach the target temperature.

0 500 1000 1500-10

-5

0

5

10

15

20

25

temps(s)

Tha

b(°C

)

Tcons

Text = -10°C

heating

0 500 1000 150018

19

20

21

22

23

24

25

temps(s)

Tha

b(°C

)

Tcons

Text = 25°C

cooling)


3 - Thermal comfort regulation in a car interiorComfort strategy

• comfort : much more than only thermal comfort. Our five senses, our cerebral state, our thermal state have an influence on our comfort estimating.

• thermal sensations rather than thermal comfort - a very subjective notion.

• in PSA Peugeot-Citroën, quantitative scale to evaluate a thermal sensation : an integer between 1 (very cold) and 9 (very hot) sensation.

Objectives: define a regulation strategy for a climate controller for car interior, taking into account the car passenger's thermal sensations.


3 - Thermal comfort regulation in a car interiorBlock representation of the model

climaticconditions

ACTUATORS

recycling flap

thermalcar

interiormodel

air temperature

walls temperatureair speed

interiorgeometry

materialsproperties

drivingconditions

mixing flap

compressor on/offblower tension

spreading air flaps

e

activity

physiologicalmodel thermal

feelings

clothes

SENSORSREGULATOR


3 - Thermal comfort regulation in a car interiorPhysiological model

à human body divided into seven parts called segments:the head, the trunk, the left arm, the right arm, the hands, the legs and the feet.

à head and hands segments are bare.

fat

center

muscle

skin

air

clothes

center

muscle

fatskin

bare segment dressed segment



CENTER MUSCLE FAT SKIN

BLOOD

conduction conduction conduction

convectionco

nvec

tion convection

convection

evap

orat

ion

wallsradiation

METABOLISM

AMBIENT

AIRO

RMEDIUM

AIR

respiration

shivers

Activity

Sunradiation

convection


For each segment


to the fat

Sf :Qsh (m)

1

R

0

T(m)Td (m)

Toth

ebl

ood

1B

cR

C:C

(m)

Td (c)

Sf:Qa (m

)SfQb(m)

Muscle layer

0

Tblood

C: Cblood

Bc(c)

Bc

(f)

Bc(s)

Bc

(m)

Blood layer


3 - Thermal comfort regulation in a car interiorPhysiological mathematical model

• x state vector (order = 57) : temperature, water mass, sudation production and water partial pressure of the layers.

• u input vector (size = 14) : air temperature and air speed of the ambient air close to the 7 segments.

• d disturbance vector (size = 35) : ambient air humidity, sun and wall radiation on clothes and skin layers.

• y output vector (size = 7) : thermal feelings of the 7 segments.

==

),,(

),,(

duxgy

duxfx&


3 - Thermal comfort regulation in a car interiorLinearized physiological mathematical model

• A nominal functioning point defined as a comfortable situation for the human (air temperature=299K, air speed=0.5m/s and humidity=50%).

• Two linear models containing saturations, because heat transfers are different whether the body is warm or cold.

– b = 1 if the body is cold, and 0 if not.– F vector that results from constant thresholds due to saturations.– K matrix selecting the x components concerning the saturations.

<⋅<⋅+⋅=

+⋅+⋅++=

MxKm

uDxCy

FdEuBxAbbAx wc )(&


3 - Thermal comfort regulation in a car interiorPhysiological model : simplifications

0 1000 2000 3000 4000 5000 6000 7000 80004.55

4.6

4.65

4.7

4.75

4.8comparison of order 57 and order 9 linear models

time(s)tr

unk

sens

atio

n

order 57 model

order 9 model

0 1000 2000 3000 4000 5000 6000 7000 8000 32.8

33

33.2

33.4

33.6

33.8

34

34.2

34.4

34.6 comparison of linear and non-linear

time (s )

tru

nk

ski

n

te

mp

er

atu

non linear model

linear model

air temperature=22°C

air humidity=50%

air speed=0.1m/s

Trunk sensationsTrunk skin temperature


3 - Thermal comfort regulation in a car interiorProposed comfort strategy

Control strategy based on the thermal feelings :

• Determine the air temperature close to the head driver to ensure him a comfortable thermal feeling (level 5 in PSA scale)

• Take into account the wall temperatures and the air flows in thecompartment.

• Compute the best air temperature target for the driver to be comfortable by using the inverted human model

In case of chilly driver, a target sensation superior to 5 can be asked for


3 - Thermal comfort regulation in a car interiorProposed comfort strategy

Thermalfeelings

MixingFlap

Cab HumanRegulatorInvertedhuman

Wall temp.model

Air temp.model

Tb,target TbThermalfeelingstarget

Ta ,target

Ta

Twall

Tair,model

+

-ε

Predictive control (GPC)


3 - Thermal comfort regulation in a car interiorComfort strategy - Air temperature model

linear convex formulation:

• Ta air temperature,

• Tout outside air temperature,• Tb blown air temperature,• V convex parameter depending essentially of the blown air flow and

the vehicle speed.

There are two dynamic modes : a fast mode caused by the mass transferand a slow mode caused by the thermal transfers with the outside.

baoutaa TTss

T )1()(1

1

1(

21

λλτα

τα

−++−

++

=


3 - Thermal comfort regulation in a car interiorComfort strategy - Wall temperature model

first order model:

• Tw the surface temperature,• Ta the air compartment temperature close to the surface.

Experiments in a wind tunnel to identify the parameters of each air temperaturemodel and wall temperature model : several wind-tunnel air flows (for the air flow due to the vehicle speed), severaloutside temperatures, several blown air temperatures and flows

))1()(1

1( awoutw

ww TT

sT λλ

τ−+

+=


3 - Thermal comfort regulation in a car interiorComfort strategy

0 200 400 600 800 1000 12000

2

4

6

time(s)

ther

mal

fee

ling

HEATING

0 200 400 600 800 1000 1200-10

0

10

20

30

time(s)

Ta(

°C)

0 200 400 600 800 1000 12004

5

6

7

8

9

time(s)

ther

mal

fee

ling

COOLING

0 200 400 600 800 1000 120020

25

30

35

40

45

time(s)

Ta(

°C)


4 – Modelling of a fuel cell system

FuelCell

engine

Ui

reforming

recoveringrecycling

Compressor

Humidifier

Compressorair

2H

air

2Hhumid

?maxP

)

, (

methanol

gaznatural

fuel


4 – Modelling of a fuel cellFuel cell : principle

load

anode cathodeelectrolyte

−2O

−e

2O2H

−− +→+ eOHOH 222

2−− →+ 2

221 2 OeO


4 – Modelling of a fuel cellFuel cell : tubular design

Fuel flow(hydrogen)

post combustion

air

interconnect

interconnect

anode

cathode

electrolyteelectrolyte

air,e

fuel,i fuel,o

air,s

Reaction zone

Anode canal

Cathode canal

anode active layer

Cathode active layer

Anode diffusion zone

Cathode diffusion layer

gaz,diffa

air,diffc

Q&

productedOvH2

½ anode interconnect

½ cathode i nterconnect

1α

1α

2α

2α

environment

mesh 2mesh 1


4 – Modelling of a fuel cellVariables

Pressure:Temperature:

Mass or molar flow rate:

Enthalpy flow

Fluid

TcmH p..&& =

nm && or

TP

Molar flow rate:

Chemical potential : Chemical reaction

n&

µ

Current: Voltage:

ElectricalU

i


electrolyte

cathode+

Cathodecanal

+interconnect

anode+

anodecanal

+interconnect

,consOn2

&

,consHn2

&Ov,prodHn

2&

gaz,em&

gaz,eH&air,eH&

air,em&

iU

HMSfHMSf

TMSfTMSf

eairm ,&

eairT ,

sairT , sgazT ,sairm ,& sgazm ,&

extP extP

MSe MSe

load

extP extP

aohmQ ,&

elaohmQ ,&

elcohmQ ,&

eohmQ ,&

cohmQ ,&

gfT

wfT environt

gfT

wfTenviront

SeSe

extT

extT

MSe

extT

MSe

extT

Electro-chemical reaction

FC Word BG


Anodeintercon

nect

Anodeactivelayer

anodediffusion

zone Anodecanal

Electrochemicalréaction

Ov,prodHn2

&,consHn2

&aohmQ ,

&

Ov,diffaHn2

&

Ar,diffan&

,diffaHn2

&

diffaQ&diffaQ&

,diffaHn2

&

Ar,diffan&

Ov,diffaHn2

&

gaz,sm&

gaz,eH&

gaz,em&

,consOn2

&

diffaOv,prodHn .2& diffaOv,prodHn .2

&

iU

diffagazH ,&

diffagazH ,&

sgazT ,extP

pbaQ&

gfT

wfT

Electrolyte

elaohmQ ,&

extT

FC AnodeWord BG


anodeJ-th diffusion zone

jth anodeinterconnect

C

0

0

0

0

ejHn ,2&

ejOvHn ,2&

ejArn ,&

cnlajHn ,2&

diffajHn ,2&

cnlajOvHn ,2&

diffajOvHn ,2&

cnlajArn ,&

difafjArn ,&

cnlaj

ejgazm ,&

ejgazH ,&

dpbajQ&

sjHn ,2&

sjArn ,&

sjOvHn ,2&

diffajgazH ,&

*

,2 cnlajHP

*

,cnlajArP

*

,2 cnlajOvHP

cnlajgazH ,&

cnlajT

sjgazm ,&

icnlaji Mx ,,ieji Mx ,,

diffajQ&

sjgazH ,&

cnlajP

diffajprodOvHn .,2&

cnlajT222

. . ,,, HejHejgazejH Mxmn && =

ejgazm ,&

Fuel supply

Anode canalBG


00

0,diffajHn

2&

,ejHn2

&

,sjHn2

&

diffajOv,prodHn .2&

Ov,ejHn2

&

Ar,ejn&Ov,sjHn

2&

*2Ov,cnlajHP

*Ar,cnlajP

Ar,sjn&Ar,diffajn&

ii,cnlaj Mx ,

gazjgaz,s mm && ou

pdcjR

)1(ou +jcnlaext PP

*2 ,cnlajHP

egazm ,&

0

sgazH ,&

diffajQ& )1(, ou −jgazegaz HH &&

)1(ou −ji,cnlai,e xxCOv,cnlajHn

2&

Ar,cnlajn&,cnlajHn

2&

cnlajgazH ,&

cnlajT

Ov,diffajHn2

&

cnlajC

cnlajP

diffajgazH ,&

R1

1

1

1

1

diffajR

1

0

0

0

prodjOvHn ,2&

ajohmQ ,&

0

Ov,diffajHn2

&

diffajQ&

,diffajHn2

&

Ar,diffajn&

caajH&

,caajHn2

&

Ov,caajHn2

&Ar,caajn&

diffajOv,prodHn .2&

caajC

caajT

caajH ,2µ

caajAr ,µ

caajOvH ,2µ

diffajgazH ,&

C

1

1

1

1

1

1

Electrochemichal

reaction

caajH ,2µ

caajOvH ,2µ

caajAr ,µ

caajT

caajOvH ,2µ

caajT

*,2 cnlajHP

*,2 cnlajOvHP

*, cnlajArP

cnlajT

*,2 cnlajOvHP

electrolyte

elajohmQ ,&

dpbajQ&

1 thermjRgazjsgaz mm && ou ,

meshlast if gaz,sm& meshlast if gaz,sT

gazjH&ou

)1(, −jgazm&

ou

consjHn ,2&

)1(ou +jcnlaext TT

environmentor

mesh (j+1)


1

1

cathodeactivelayer

anodeactivelayer

caaT

,consOn2

&

cacOì ,2 caaHì ,2

caaOvHì ,2

Ov,prodHn2

&

TFOvH2

υ

TFFne

TFH2

/1 υTF

O2/1 υ

loadiU

vÄG−

E i

aohmQ ,&

,consHn2

&

polη Rpol

RScR

ohmη

i

i

RScR

RSelR

electrolyteelohmQ ,

&

cohmQ ,&

Rdiff

diffη

Electrochemical reaction


anodeDiffusion zone j

interconnectanode j

C

0

0

0

0

ejHn ,2&

ejOvHn ,2&

ejArn ,&

cnlajHn ,2&

diffajHn ,2&

cnlajOvHn ,2&

diffajOvHn ,2&

cnlajArn ,&

difafjArn ,&

cnlaj

ejgazm ,&

ejgazH ,&

dpbajQ&

sjHn ,2&

sjArn ,&

sjOvHn ,2&

diffajgazH ,&

*

,2 cnlajHP

*

,cnlajArP

*

,2 cnlajOvHP

cnlajgazH ,&

cnlajT

sjgazm ,&

icnlaji Mx ,,ieji Mx ,,

diffajQ&

sjgazH ,&

cnlajP

diffajprodOvHn .,2&

cnlajT

BG to Simulink


4 – Modelling of a fuel cellResults

àComplete dynamic model of the fuel cell system (no similar result in the literature, only static models)

àSimulation results validated by comparison with experimental data

à Work with PSA is running for:àControl designing : how to maximize the power delivered by the

fuel cell system

àFault diagnosis


5 - Structural properties of bond graphmodels

LSS

1wb1wC

1wm

2wb

1sb 2sb

2wm

2wC

1rV 2rV

G (m, J) theta

AB

x

RSS

z

Bicycle heave and pitch

physical model


5 - Structural properties of bond graphmodels

R : I : J

0 0

1

1

I : m

TF TF

I :

1

1 0

1

C : LSS 1

0

1

1

C : RSS

I :

Se :

R :

Sf :

C :

Sf : R :

0 101

R :

C :

1wb

1wC

1wm

2wb

1sb 2sb2wm

2wC

1rV 2rV

mtF

Bicycle heave and pitch BG model


5 - Structural properties of bond graph modelsPassive model

• State equation

EdAxx +=&

= ermasstransfFd1

=

2

12

roadVroadV

d

=

=

ntsdisplaceme spring

impulses inertia

C

I

q

px

=

2

1

d

dd



• State equation

• order n of a model : number of I and C elements in integral causality when a preferred integral causality is assigned to the bond graph model

• BG-rank q of the state space matrix A : number of I and C elements in derivative causality when a preferred derivative causality is assigned to the bond graph model.

• number of structurally null modes of A-matrix : number of I and C elements which have to stay in integral causality when a preferred derivative causality is assigned to the bond graph model

EdAxx +=&



• State equation

• minimum number of actuators for the model to be controllable :– If BG-rank A = n, the model is controllable with a single actuator– If BG-rank A = n-k, for the model to be controllable, k well-located

actuators are needed

• minimum number of sensors for the model to be observable :– idem

EdAxx +=&


5 - Structural properties of bond graph modelsDesign of the measurement and control architecture for the

active system

• definition of the control objectives– what variables to be controlled? – for what performances (dynamical or frequential criteria)? – with what strategy (pole placement, disturbance rejection, …)?

• what type of control law? – state feedback?

• Is the state measurable?

– output feedback?


5 - Structural properties of bond graph modelsDesign of the measurement and control architecture for

the active system

Choice here

State feedback for pole placement and rejection of the disturbance corresponding to the mass transfer due to driver actions (braking or accelerating) on the 2 velocity variables (heave and pitch)

! the 2 variables (absolute velocities) to be controlled are not measurable

à an observer is needed

! We want to perform input/output decoupling

à 2 control inputs are needed



the active system

à 2 outputs to be controlled : not measurable (Df*)§

à measurement vector (Df)

à 2 control inputs (MSe)§

à disturbance vector

measurable to be rejected (Se)

non- measurable (Sf)

==

J

mV

y

yy

ω2

1

==

2

1

2

1

rel

relV

V

z

zz

==

2

1

2

1

actFactF

u

uu

= ermasstransfFd1

=

2

12

roadVroadV

d



the active system

Df :

R :

Df* :

I : J

0 0

1

1

I : m

TF TF

I :

1

1 0

1

C : LSS 1

0

1

1

C : RSS

I :

Se :

Df :

R :

Sf :

C :

Sf : R :

0 101

R :

C :

MSe :

1wb

1wC

1wm

2wb

1sb 2sb2wm

2wC

1rV 2rV

2aF

mV

1sV2sV

mtF

Df* : JωMSe: 1aF


Conclusion

* bond graph : language quite « strange » which needs a learning time

* Could appear difficult to implement, but what is difficult is PHYSICS

* more and more introduced in the industrial world in France (better than in the academic world!)

Documents

Bond Graph for Modelling, Analysis, Control Design, Fault ... · Bond Graph for Modelling, Analysis, Control Design, Fault Diagnosis Geneviève Dauphin-Tanguy Christophe Sueur Laboratoire