lpv methods applied to vehicle dynamcis controlo.sename/docs/lpv_vdc.pdf · why vehicle dynamics...

LPV methods applied to vehicle dynamcis control

Olivier Sename

Grenoble INP / Gipsa-lab

Master Course - January 2021

Olivier Sename (Grenoble INP / Gipsa-lab) LPV VDC Master Course - January 2021 1/102

Outline

1. Why Vehicle Dynamics Control is important and interesting?2. Models3. Lateral control of Autonomous vehicles

IntroductionLPV Control problemExperimental validation

4. Towards global chassis control5. Active safety using coordinated steering/braking control

Active safetyObjectiveBasics on vehicle dynamicsPartial non linear Vehicle modelLateral stability controlSimulations

6. LPV FTC for Vehicle Dynamics ControlTowards global chassis controlThe LPV FTC VDC... approachValidation: LPV control vs professional driverValidation: simulation of the fault free caseValidation: FTC case

7. Conclusions and future work


Why Vehicle Dynamics Control is important and interesting?

Outline









Road safety: an international stake

• Worldwide, 1.24 million people of road traffic deaths per year (+ 50 million of injuries) a.• For people aged 5-29 years, road traffic injuries is the leading cause of death.• Various causes: speed, alcohol, drugs, non safe driving,...

aWorld health organization 2015



Road safety: an international stake

• Worldwide, 1.24 million people of road traffic deaths per year (+ 50 million of injuries) a.• For people aged 5-29 years, road traffic injuries is the leading cause of death.• Various causes: speed, alcohol, drugs, non safe driving,...

aWorld health organization 2015

Among the 5 pillars towards road safety

Safer vehicles: Electronic Stability Control is part of the minimum standards for vehicleconstruction (ex European and Latin New Car Assessment Programs - NCAP)



Smart and autonomous vehicles: connected, safer, and comfortable


Important stakes

• reduce road fatalities, traffic jams, CO2• allow everyone to travel regarless of its abilities• enhance in-car passenger experiences

Automated vehicles towards self-driving cars

• Driver supervision: ESP, CACC, Lane Keeping• Unsupervised: Traffic Jam Chauffeur, Valet

parking, Highway pilot with platooning...

Figure: Renault’s goal: make riding in cars it more pleasant,less stressful and more productive c© Groupe Renault 2019


Smart and autonomous vehicles: connected, safer, and comfortable


Important stakes

• reduce road fatalities, traffic jams, CO2• allow everyone to travel regarless of its abilities• enhance in-car passenger experiences

Automated vehicles towards self-driving cars

• Driver supervision: ESP, CACC, Lane Keeping• Unsupervised: Traffic Jam Chauffeur, Valet

parking, Highway pilot with platooning...

Figure: Renault’s goal: make riding in cars it more pleasant,less stressful and more productive c© Groupe Renault 2019

Future cars: many technical challenges

• deal with many sensors/actuators : middlerange cars with around 1000 sensors and 100small actuators

• increased software/hardware complexity: howto synchronize & monitor all the intelligentorgans for performance and reliability?


Course content

This course has been mainly written thanks to:• the Post-doctoral work of [Moustapha Doumiati (2010)]

• The PhD works from Hussam Atoui and Dimitris Kapsalis• the PhD dissertations of [Poussot-Vassal(2008), Soheib Fergani (2014)].• interesting books cited below


Models

Outline








Models

Suspension system

Objective

• Link between unsprung and sprung masses

• Involves vertical (zs,zus) dynamics


Models

Suspension system

Objective

• Link between unsprung (mus) and sprung (ms) masses


Passive suspension system


{ms,zs}

{mus,zus}

Models

Suspension system

Objective



Semi-active suspension system −−−→dissipates energy through an adjustable damping coefficient


{ms,zs}

{mus,zus}

Models

Suspension system

Objective



Active suspension system −−−−−−−−→dissipate and generate energy working as an active actuator


{ms,zs}

{mus,zus}

Models

Vehicle model - dynamical equations

Full vertical model

• Mainly influenced by the vehicle suspension systems.• Describes the comfort and the roadholding performances.


zs = −(Fsz f l +Fsz f r +Fszrl +Fszrr

)/ms

zusi j =(Fszi j −Ftzi j

)/musi j

θ =((Fszrl −Fszrr )tr +(Fsz f l −Fsz f r )t f

)/Ix

φ =((Fszrr +Fszrl )lr− (Fsz f r +Fsz f l )l f

)/Iy

Models

Wheel & Braking system

Objective

• Link between wheel and road• Influences safety performances• Involves longitudinal (v) rotational (ω) and slipping (λ = v−Rω

max(v,Rω) ) dynamics


Models

Wheel & Braking system

Objective

• Link between wheel and road (zr, µ)• Influences safety performances• Involves longitudinal (v) rotational (ω) and slipping (λ = v−Rω

max(v,Rω) ) dynamics

Extended quarter vehicle model


0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.2

0.4

0.6

0.8

1

λ

Ftx

/Fn

Normalized longitudinal tire force

Cobblestone

Dry

Wet

Icy

Models


Full vertical model

• Mainly influenced by the vehicle suspension systems .• Describes the comfort and the roadholding performances .



)/ms


)/musi j


)/Ix

φ =((Fszrr +Fszrl )lr− (Fsz f r +Fsz f l )l f

)/Iy

Models


Full vertical and longitudinal model

• Mainly influenced by the vehicle suspension systems and the braking system.• Describes the comfort and the roadholding performances and the the stability and security

issues.


xs =((Ftx f r +Ftx f l )+(Ftxrr +Ftxrl )

)/m


)/ms


)/musi j


)/Ix

φ =((Fszrr +Fszrl )lr− (Fsz f r +Fsz f l )l f +mhxs

)/Iy

λi j =vi j−Ri jωi j

max(vi j ,Ri jωi j )

ωi j = (−RFtxi j (µ,λ ,Fn)+Tbi j )/Iw

Models

Wheel & Steering system

Objective

• Wheel / road contact• Influences safety performances• Involves lateral (ys), side slip angle (β ) and yaw (ψ) dynamics


Models

Wheel & Steering system

Objective

• Wheel / road contact• Influences safety performances• Involves lateral (ys), side slip angle (β ) and yaw (ψ) dynamics

Bicycle model


]*

Fty f Ftx f

-ψ

-

6

xs

ys

1−→v

βK

Models


Full vertical and longitudinal model


xs =((Ftx f r +Ftx f l )+(Ftxrr +Ftxrl )

)/m


)/ms


)/musi j


)/Ix

φ =((Fszrr +Fszrl )lr− (Fsz f r +Fsz f l )l f +mhxs

)/Iy

λi j =vi j−Ri jωi j

max(vi j ,Ri jωi j )


Models


Full model• A very complex model with dynamical correlations.

• Subject to several external disturbances.


xs =((Ftx f r +Ftx f l )cos(δ )+(Ftxrr +Ftxrl )−(Fty f r +Fty f l )sin(δ )+mψ ys

)/m

ys =((Fty f r +Fty f l )cos(δ )+(Ftyrr +Ftyrl )+(Ftx f r +Ftx f l )sin(δ )−mψ xs

)/m


)/ms


)/musi j

θ =((Fszrl −Fszrr )tr +(Fsz f l −Fsz f r )t f−mhys +(Iy− Iz)ψφ

)/Ix

φ =((Fszrr +Fszrl )lr− (Fsz f r +Fsz f l )l f +mhxs+(Iz− Ix)ψθ

)/Iy

ψ =((Fty f r +Fty f l )l f cos(δ )− (Ftyrr +Ftyrl )lr +(Ftx f r +Ftx f l )l f sin(δ )+(Ftxrr −Ftxrl )tr +(Ftx f r −Ftx f l )t f cos(δ )− (Ftx f r −Ftx f l )t f sin(δ )+(Ix− Iy)θ φ

)/Iz

λi j =vi j−Ri jωi j cosβi j

max(vi j ,Ri jωi j cosβi j )


βi j = arctan( xi j

yi j

)

Models


Full model• A very complex model with dynamical correlations.

• Subject to several external disturbances.


xs =((Ftx f r +Ftx f l )cos(δ )+(Ftxrr +Ftxrl )−(Fty f r +Fty f l )sin(δ )+mψ ys−Fdx

)/m

ys =((Fty f r +Fty f l )cos(δ )+(Ftyrr +Ftyrl )+(Ftx f r +Ftx f l )sin(δ )−mψ xs−Fdy

)/m

zs = −(Fsz f l +Fsz f r +Fszrl +Fszrr+Fdz

)/ms


)/musi j

θ =((Fszrl −Fszrr )tr +(Fsz f l −Fsz f r )t f−mhys +(Iy− Iz)ψφ+Mdx

)/Ix

φ =((Fszrr +Fszrl )lr− (Fsz f r +Fsz f l )l f +mhxs+(Iz− Ix)ψθ+Mdy

)/Iy

ψ =((Fty f r +Fty f l )l f cos(δ )− (Ftyrr +Ftyrl )lr +(Ftx f r +Ftx f l )l f sin(δ )+(Ftxrr −Ftxrl )tr +(Ftx f r −Ftx f l )t f cos(δ )− (Ftx f r −Ftx f l )t f sin(δ )+(Ix− Iy)θ φ+Mdz

)/Iz

λi j =vi j−Ri jωi j cosβi j

max(vi j ,Ri jωi j cosβi j )


βi j = arctan( xi j

yi j

)

Models

Vehicle model - synopsis

Chassis

Suspensions

Wheels

-

-

-

-

Fszi j

Ftx,y,z

-

-

xsyszs

θ

φ

ψ

q?

?

-

6

[zs,zs

zus,zus

]

xs, ysψ,v,

Fsz,zus

- λi j

βi jωi j

(vehicle dynamics)

(tire, wheel dynamics)

?

6


Models


Chassis

Suspensions

Wheels

-

-

-

-

Fszi j

Ftx,y,z

-

-

xsyszs

θ

φ

ψ

q

Fdx,y,z & Mdx,y,z

?

?

-

6[µi j,zri j ]

[zs,zs

zus,zus

]

xs, ysψ,v,

Fsz,zus

(external disturbances)

- λi j

βi jωi j

(vehicle dynamics)

(road characteristics)(tire, wheel dynamics)

?

6


Models


Chassis

Suspensions

Wheels

-

-

-

-

Fszi j

Ftx,y,z

-

-

xsyszs

θ

φ

ψ

q

Fdx,y,z & Mdx,y,z

?

?

ui j

[Tbi j ,δ ]

-δ

6[µi j,zri j ]

[zs,zs

zus,zus

]

xs, ysψ,v,

Fsz,zus

(external disturbances)

(suspensions control)

(braking & steering control)

- λi j

βi jωi j

(vehicle dynamics)

(road characteristics)(tire, wheel dynamics)

?

6


Lateral control of Autonomous vehicles


Lateral control of Autonomous vehicles

i

Outline






7. Conclusions and future workOlivier Sename (Grenoble INP / Gipsa-lab) LPV VDC Master Course - January 2021 15/102

Lateral control of Autonomous vehicles Introduction

Control of autonomous vehicles

Mainly includes path planning, longitudinal control, lateral control

Steering control is a ’classical control’ problem

• many contribution for ADAS (MPC, H∞, Sliding mode.....) Ackermann, Rajamani, Tseng,Mammar...

• recent studies for autonomous vehicles (Lane keeping, lane changing..) Gerdes, Borelli, Puig,Sentouh, Milanes

• Key issues: handle low/high speeds, ensures small lateral errors, accounts for varyinglook-ahead distance,

Collaboration: Renault : 2 co-supervised PhD thesis, Real car & trajectory

-400 -200 0 200 400 600 800 1000 1200X (m)

2700

2800

2900

3000

3100

3200

3300Y

(m

)


Lateral control of Autonomous vehicles Introduction

LPV modelling


LPV simplified bicycle model : 3 approaches

polytopic: ρ1 = vx, ρ2 = 1/vx

grid-based 40 grid points for ρ = vx ∈ [3,40]m/s

Linear Fractional Tranfsformation

2 wheels bicycle model

x(t) =[

vyψ

]=

[lateral acceleration

yaw rate

]

G(vx)

{x(t) = A(vx)x(t)+Bu(t)

y(t) =Cx(t)+Du(t)

A(vx) =

−Cr+C fmvx

− l f C f−lrCrmvx

− vx

− l f C f−lrCrIvx

− l2f C f +l2

r Cr

Ivx

Lateral control of Autonomous vehicles LPV Control problem

LPV Control problem


Control design scheme

We : tracking performances, Wu actuatorlimitationsAnalysis of the sensitivity FunctionsS =

wre f−wwre f

10-4 10-3 10-2 10-1 100 101 102-80

-60

-40

-20

0

Frequency (rad/s)

Sin

gu

lar

Val

ues

(d

B)

Control implementaiton scheme:experimental validation

Speed profile measured from a real test(m/s)

0 20 40 60 80 100Time (s)

0

5

10

15

20

Lo

ng

itu

din

al V

elo

city

vx (

m/s

)

Lateral control of Autonomous vehicles Experimental validation

Experimental comparison


Experimental lateral error of the LTI and LPVcontrollers (m)

0 20 40 60 80 100Time (s)

-0.4

-0.2

0

0.2

0.4

Lat

eral

Err

or

(m)

PolytopicLTIGriddingLFT

Table: RMS of the lateral error for experimentalcomparison

Polytopic LTI Gridding LFTRMS 0.1473 0.1105 0.1025 0.1096

All controllers have good peformances interm of minimization of the lateral error

Experimental steering wheel angle of the LTIand LPV controllers (rad)

0 20 40 60 80 100Time (s)

-0.1

-0.05

0

0.05

0.1

0.15

Ste

erin

g W

hee

l An

gle

(ra

d) Polytopic

LTIGriddingLFT

Table: RMS of the steering wheel rate forexperimental comparison

Polytopic LTI Gridding LFTRMS 0.0263 0.0149 0.0107 0.0129

The grid-based and LFT controllers providesmooth steering control. The polytopic andthe LTI controllers are sensitive to noises,especially at high speeds (when t ≤ 60 s)

Towards global chassis control

Outline









Towards global chassis control approaches (GCC)

Some facts

• In most vehicle control design approaches, the vehicle-dynamics control sub-systems(suspension control, steering control, stability control, traction control and, more recently,kinetic-energy management) are traditionally designed and implemented as independent (orweakly interleaved) systems.

• The global communication and collaboration between these systems are done with empiricalrules and may lead to unappropriate or conflicting control objectives.

• So, it is important to develop new methodologies (centralized control strategies) that force thesub-systems to cooperate in some appropriate "optimal" way.

Global chassis control

• This approach combines several (at least 2) vehicle sub-systems in order to improve thegeneral behavior of the vehicle ; in particular, the GCC methodology is developed to improvecomfort and safety properties, according to the vehicle situation, taking into account theactuators constraints and the knowledge (if any) of the environment of the vehicle.

• The objective is then to make the sub-systems collaborate towards the same goals, accordingto the vehicle situation (constraints, environment, ...) in order to fully exploit the potentialbenefits coming from their interconnection.




The GCC strategies are de-veloped in 2 steps:• The monitoring

approach→collaborative basedstrategy.

• Developpingcoordinated controlstrategies→ achieveclose loop performanceand actuatorscoordination.


Steering controller

Braking controller

Suspension controller

Coordination strategyMonitoring system

Renault Mégane Coupé



The GCC strategies are de-veloped in 2 steps:• The monitoring

approach→collaborative basedstrategy.

• Developpingcoordinated controlstrategies→ achieveclose loop performanceand actuatorscoordination.


Steering controller

Braking controller

Suspension controller

Coordination strategyMonitoring system

Renault Mégane Coupé

Main objective:

• Improve the overall dynamics of the carand the vehicle safety in critical drivingsituations.


Towards Global chassis control approaches

Two main approaches, one considering the vehicle as a MIMO system, the other developing a"super controller" for the local actuators. Some references : Lu and DePoyster (2002), Shibahata(2005), Chou and d’Andréa Novel (2005), Andreasson and Bunte (2006), Falcone et al. (2007a),Falcone et al. (2007b), Gáspár et al. (2008), Fergani and Sename (2016)...

Vehicle considered as a MIMO system

• This approach consists in considering the vehicle as a global MIMO system and in designinga controller that solves all the dynamical problems by directly controlling the various actuatorswith the available measurements. No local controller is considered (no inner loop). See, forinstance Lu and DePoyster (2002), Chou and d’Andréa Novel (2005), Andreasson and Bunte(2006), Gáspár et al. (2008), Fergani et al (2016).

High level reference super controller

• The second approach consists in designing a controller which aims at providing somehow,the reference signals to local controllers, which have been previously designed to solve alocal subsystem problem (e.g. ABS). Thus, this controller, more than a controller, "monitors"the local controllers. Therefore, such a controller solves the global vehicle dynamicalproblems, playing the role of "super controller". See also Falcone et al. (2007a).



A MIMO case: Suspension and braking

Characteristic of the solution

Build a multivariable global chassis controller Shibahata (2004), (Poussot et al. 2011) :• Improve comfort in normal cruise situations• Improve safety in emergency situations (safety prevent comfort)• Supervise actuators and resources• The proposed design relies in the introduction of two parameters to handle the performance

compromise, actuator efficiency and well-coordinated action.• The suspension performance moves from comfort to road holding characteristics when the

braking monitor identifies a normal or critical longitudinal slip ratio.• Robust control theory approach (LPV/H∞)⇒ MIMO internal stability & no switching




Some examples

• braking/suspension : non linear approach (Chou & d’Andréa Novel), LPV for heavy vehicles(Gaspar, Szabo & Bokor), for cars (Poussot et al.)

• braking / steering : optimal control [Yang et al.], predictive [Di Cairano & Tseng, controlallocation [Tjonnas & Johansen], or LPV [Doumiati et al, 2013]

• braking /suspension/ steering : [Fergani, Sename, Dugard]


LPV interest: on-line Adaption of the vehicle performances

• to various road conditions/types (measured, estimated)• to the driver actions• to the dangers identified thanks to some measurements of

the vehicle dynamical behavior• to actuators/sensors malfunctions or failures



In this presentation, 2 examples are provided for the topic:

F Active safety using coordinated steering/braking control.

F LPV FTC for Vehicle Dynamics Control.


Active safety using coordinated steering/braking control

Outline








Active safety using coordinated steering/braking control Active safety

Outline

1. Why Vehicle Dynamics Control is important and interesting?

2. Models

3. Lateral control of Autonomous vehiclesIntroductionLPV Control problemExperimental validation

4. Towards global chassis control

5. Active safety using coordinated steering/braking controlActive safetyObjectiveBasics on vehicle dynamicsPartial non linear Vehicle modelLateral stability controlSimulations




Active safety using coordinated steering/braking control Active safety

Vehicle safety systems:• Prevent unintended behavior• Help drivers maintaining the vehicle control• Current production systems include:

• Anti-lock Braking Systems (ABS): Prevent wheel lock during braking• Electronic Stability Control (ESC): Enhances lateral vehicle stability

• Braking based technique• 4 Wheel steering (4WS): Enhances steerability

• Adding additional steering angle

General structure:

Vehicle

Sensors

Active safety systems:

measures Act on Actuators (suspensions, brakes, steer) Alert the driver

Any vehicle control system needs accurate information about the vehicle dynamics, and the moreaccurate information it gets, the more it can perform


Active safety using coordinated steering/braking control Objective

Outline


2. Models








The presentation of today focuses on:

• Yaw stability by active control• Prevents vehicle from skidding and spinning

out• Improves of the turning (yaw) rate response• Improves lateral vehicle dynamics• Involves Braking and Steering actuators

Desired trajectory

Undesired motion

Figure: The objective is to restore the yaw rate asmuch as possible to the nominal motion expected bythe driver



Problematic

Problem tackled: vehicle critical situations

• Lateral and yaw stability of ground vehicles & braking actuator limitations• Widely treated in literature [Ackermann, Falcone, Villagra, Bunte, Chou, Canale] (mainly

steering or braking, but a few use both)

Contributions

• Use Rear braking & Steering actuators to enhance vehicle stability properties• Extension of [Poussot-Vassal et al., CDC2008 & ECC2009] results• Propose a simple H∞ tuning using [Bünte et al., IEEE TCST, 2004] results• LPV Controller structure exploiting system properties to handle braking constraints• Nonlinear frequency validations


Active safety using coordinated steering/braking control Basics on vehicle dynamics

Outline


2. Models








Lateral motion of a vehicle

• Motion of a vehicle is governed bytire forces

• Tire forces result from deformationin contact patch

• Lateral tire force, Fy, is function of:1 Tire slip (α)2 Vertical load applied on the tire (Fz)3 Friction coefficient (µ)

V (tire velocity)

α

Fy (lateral tire force)

(tire sideslip angle)

Side view

Contact patch Ground

Fy

α Bottom view



0 5 10 15 20 0

1000

2000

3000

4000

5000

6000

Sideslip angle (°)

Late

ral f

orce

(N)

µFz

Linear

1

C

Saturation Loss of control

α

Maximum tire grip

0 5 10 15 20

Linear model

Dugoff model Pacejka model 0.5

1

1.5

2

2.5

3

3.5

4

Late

ral f

orce

(kN

)

Measure

Sideslip angle (°)

Vehicle response

• Normally, we operate in LINEAR region• Predictable vehicle response

• During slick road conditions, emergency maneuvers, or aggressive driving• Enter NONLINEAR tire region• Response unanticipated by driver



Why we lose the vehicle control?

Imagine making an aggressive turn. . .• If front tires lose grip first, plow out of turn

(limit understeer)• May go into oscillatory response• Driver loses ability to influence vehicle

motion• If rear tires saturate, rear end kicks out

(limit oversteer)• May go into a unstable spin• Driver loses control

• Both can result in loss of control

Desired trajectory

Desired trajectory

Unstable motion due to nonlinear tire characteristics


Active safety using coordinated steering/braking control Partial non linear Vehicle model

Outline


2. Models








Planar bicycle model (Dugoff et al.(1970))

Main dynamics under interest, toward control scheme . . .• Equation of lateral motion:

mv(

β − ψ

)= Fy f +Fyr (1)

• Equation of yaw motion:Izψ = l f Fy f − lrFyr, (2)

V

lr

lf

Fyr

Fyf

Ψ .

vy

δ



Linear Synthesis model

The 2-DOF linear bicycle model described in Section 2 is used for the control synthesis. Althoughthe bicycle model is relatively simple, it captures the important features of the lateral vehicledynamics. Taking into account the controller structure and objectives, this model is extended toinclude:• the direct yaw moment input M∗z ,• a lateral disturbance force Fdy and a disturbance moment Mdz. Fdy affects directly the sideslip

motion, while Mdz influences directly the yaw motion.

[ψ

β

]=

− l2f C f +l2

r Cr

IzvlrCr−l f C f

Iz

1+lrCr−l f C f

mv2 −C f +Crmv

[ ψ

β

]+

[ l f C fIz

C fmv

]δ∗+[ 1

Iz0

]M∗z +

[ 1Iz1

mv

][MdzFdy

](3)


Active safety using coordinated steering/braking control Lateral stability control

Outline


2. Models








Steering vs. Braking

Steering control: (Rajamani(2006), Guven et al.(2007))• Adds steering angle to improve the lateral vehicle dynamics• Regulates tire slip angles and thus, the lateral tire force• Drawback:

• Becomes less effective near saturation

DYC (Direct Yaw Control) - Braking control: (Park(2001), Boada et al.(2005))• Regulates the tire longitudinal forces• Maintains the vehicle stability in all driving situations• Drawbacks:

• Wears out the tires• Causes the vehicle speed to slow down against the driver demand



The idea is to design a controller that:• Improves vehicle steerability and stability

• Makes the yaw rate tacking the desired value (response of a bicycle model with linear tires)• Makes the slip angle small

• Coordinates Steering/braking control• Minimizes the influence of brake intervention on the longitudinal vehicle dynamics

• Rejects yaw moment disturbances

Methodology:H∞ synthesis extended to LPV system:• H∞ synthesis: frequency based performance criteria• LPV : One type of a gain scheduled controller

See paper Doumiati et al (2013)



Overall control scheme diagram

Vehicle simulation

model

Sideslip

dynamics

Driver

command

Reference model

(bicycle model) +

Bounding limits

External yaw

disturbances

VDSC controller

EMB

AS

Yaw rate (measure)

+

_

Steering angle (δd)

Tbr *

δ *

Vehicle velocity

+

+

δd

Monitor

Yaw rate target

AS: Steer-by-wire systemEMB: Brake-by-wire Electro Mechanical system




Vehicle simulation

model

Sideslip

dynamics

Driver

command

Reference model

(bicycle model) +

Bounding limits

External yaw

disturbances

VDSC controller

EMB

AS

Yaw rate (measure)

+

_


Tbr* br

δ*

Vehicle velocity

+

+

δd

MonitorMM iit

Yaw rate target

AS: Steer-by-wire systemEMB: Brake-by-wire Electro Mechanical system



Reference model

The basic idea is to assist the vehicle handling to be close to a linear vehicle handlingcharacteristic that is familiar to the driver• Bicycle linear model, Fy =Cα α (low sideslip angle)• ψ ≤ µ×g/Vx

• Ensures small slip dynamics (β , β )• Attenuates the lateral acceleration




Vehicle simulation

model

Sideslip

dynamics

Driver

command

Reference model

(bicycle model) +

Bounding limits

External yaw

disturbances

VDSC controller

EMB

AS

Yaw rate (measure)

+

_


Tbr *

δ *

Vehicle velocity

+

+

δd

MonitorMM iit

Yaw rate target



VDSC Controller architecture

Upper controller

Lower controller

Commanded steering angle

Desired yaw moment

Applying brake torque to the appropriate wheel

Objective: Lateral stability control

Yaw rate Steering angle SideSlip angle

and/or

Measurements/estimation Level 1

Level 2



VDSC-upper controller: LPV/H∞ control

Vehicle model

Fdy

S(ρ) LPV/H∞

+ _

Ψ

Ψd

W1

W2

W3 (ρ)

W4

M *

δ*

z1

z2

z3

z4

.

.

β

∑

e Ψ .

z

Generalized plant (tracking problem)

Vehicle model is LTI:• Linear bicycle model• Synthesized considering a dry road

ρ scheduling parameter:• ρ(t) is time dependent and known

function• ρ bounded: ρ ∈

[ρ,ρ

]

w(t) =[ψd ,Fdy

]exogenous input

u(t) =[δ∗ ,M∗z

]control input

y(t) =[eψ

]measurement

z(t) =[W1z1 ,W2z2 ,W3z3 ,W4z4

]controlled output



VDSC design (cont’d)

• z1 : sideslip angle signal, β : W1 = 2. to reduce the body sideslip angle

• z2 yaw rate error signal: W2 =s/M+w0s+w0A , where M = 2 for a good robustness margin, A = 0.1 so

that the tracking error is less than 10%, and the required bandwidth w0 = 70 rad/s.• z3 braking control signal, M∗z ,according to a scheduling parameter ρ:

W3 = ρs/(2π f2)+1

s/(α2π f2)+1, (4)

where f2 = 10 Hz is the braking actuator cut-off frequency and α = 100.ρ ∈

{ρ ≤ ρ ≤ ρ

}(with ρ = 10−4 and ρ = 10−2).

• z4, the steering control signal attenuation ( f3 = 1Hz, f4 = 10Hz):

Wδ = Gδ 0(s/2π f3 +1)(s/2π f4 +1)

(s/α2π f4 +1)2

Gδ 0 =(∆ f /α2π f4 +1)2

(∆ f /2π f3 +1)(∆ f /2π f4 +1)and ∆ f = 2π( f4 + f3)/2

(5)

This filter is designed is order to allow the steering system to act only in [ f3, f4]Hz. At ∆ f /2,the filter gain is unitary [Bunte et al. 2004, TCST].




Controller solution: LPV/H∞

• Mixed-Sensitivity problem• Minimizes the H∞ norm from w to z• γ∞ = 0.89 (Yalmip/Sedumi solver)

W3(ρ):

• ρ = 0.1→ braking is ON• ρ = 10→ braking is OFF

Steering control

Frequency (rad/sec)

10 −1 10 0 10 1 10 2 − 50

0

50

100

Mag

nitu

de (d

B)

Brake control

Frequency (rad/sec)

10 − 1 10 0 10 1 10 2 − 5

0

5

10

Mag

nitu

de (d

B)

ρ = ρ ρ = ρ

Figure: Bode diagrams of the controller outputs δ ∗ andM∗z




Sensitivity functions:

10 −2 10 0 10 2 − 120

− 100

− 80

− 60

− 40

− 20

0

Mag

nitu

de (d

B)

Ψ

Frequency (Hz) 10 − 2 10 0 10 2 − 180

− 160

− 140

− 120

− 100

− 80

− 60

− 40

− 20

0

Mag

nitu

de (d

B)

Frequency (Hz) 10 − 2 10 0 10 2 − 250

− 200

− 150

− 100

− 50

0

Mag

nitu

de (d

B)

Frequency (Hz)

1/W1 1/W1 1/W1

LPV

LPV

LPV

β/ β/Fdy β/Mdz

. d

Figure: Closed loop transfer functions between β and exogenous inputs

• Attenuation of the side slip angle• Rejection of the yaw disturbance





10 −2 10 0 10 2 − 25

− 20

− 15

− 10

− 5

0

5

10

Mag

nitu

de (d

B)

Frequency (Hz) 10 − 2 10 0 10 2 − 250

− 200

− 150

− 100

− 50

0

50

Mag

nitu

de (d

B)

Frequency (Hz) 10 − 2 10 0 10 2 − 140

− 120

− 100

− 80

− 60

− 40

− 20

0

20

Mag

nitu

de (d

B)

Frequency (Hz)

1/W2 1/W2 1/W2

LPV LPV

LPV

e ψ . e ψ

. e ψ . ψ / . / F / M dy dz d

Figure: Closed loop transfer functions between eψ and exogenous inputs

• Attenuation of the yaw rate error• Rejection of the yaw disturbance



VDSC-upper controller: LPV/H∞ control design


10 −2 10 0 10 2 − 80

− 60

− 40

− 20

0

20

40

60

80

100

Mag

nitu

de (d

B)

Frequency (Hz) 10 − 2 10 0 10 2 − 300

− 250

− 200

− 150

− 100

− 50

0

50

100

Mag

nitu

de (d

B)

Frequency (Hz) 10 − 2 10 0 10 2 − 200

− 150

− 100

− 50

0

50

100

Mag

nitu

de (d

B)

Frequency (Hz)

1/W3 (ρ) 1/W3 (ρ) 1/W3 (ρ)

1/W3 (ρ) 1/W3 (ρ) 1/W3 (ρ)

ρ = ρ

ρ = ρ

ρ = ρ

ρ = ρ

ρ = ρ

ρ = ρ

M*/ Ψ M*/ Fdy M*/ Mdz .

d z z z

Figure: Closed loop transfer functions between M∗ and exogenous inputs

ρ = 0.1→ braking is activated, ρ = 10→ braking is penalized



VDSC-upper controller: LPV/H∞ control design


10 −2 10 0 10 2 − 40

− 30

− 20

− 10

0

10

20

30

40

50

10 − 2 10 0 10 2 − 250

− 200

− 150

− 100

− 50

0

50

10 − 2 10 0 10 2 − 200

− 150

− 100

− 50

0

50

Ψ

Mag

nitu

de (d

B)

Mag

nitu

de (d

B)

Frequency (Hz)

1/W4

1/W4

δ / δ /Fdy δ /Mdz

.

Frequency (Hz) Frequency (Hz)

Mag

nitu

de (d

B)

d * * *

1/W4

LPV LPV

ρ = ρ

ρ = ρ

Figure: Closed loop transfer functions between δ ∗ and exogenous inputs

• Steering is activated on a specified range of frequency• W4: Activates steering in a frequency domain where the driver cannot act (Guven et al.(2007))




Vehicle simulation

model

Friction estimator

Sideslip

dynamics

Driver

command

Reference model

(bicycle model) +

Bounding limits

External yaw

disturbances

VDSC controller

EMB

AS

Yaw rate (measure)

+

_


Tbr* br

δ*

Vehicle velocity

+

+

δd

Monitor

Yaw rate target



Coordination between Steering and braking

• β − β phase plane is used as measure of the vehicle operating points

• Stability boundaries for controller design: χ =∣∣∣ 1

24 β + 424 β

∣∣∣< 1

(Yang et al.(2009), He et al.(2006))

−40 −30 −20 −10 0 10 20 30 40

−100

−80

−60

−40

−20

0

20

40

60

80

100

Sideslip angle (°)

Side

slip

ang

ular

vel

ocity

(°/s

)

Control boundaries

Stable region

Unstable region

Unstable region

AS control

DYC+AS control

DYC+AS control

This criterion, χ, allows accurate diagnosis of the vehicle stability.



Monitor

ρ

ρ

λ

_

_

Steering Steering + full Braking

λ λ _ _

(Stability index)

Intermediate behavior

Sche

dulin

g p

aram

eter

ρ(χ) :=

ρ if χ ≤ χ (steering control - Steerability control task)χ−χ

χ−χρ +

χ−χ

χ−χρ if χ < χ < χ (steering+braking)

ρ if χ ≥ χ (steering+full braking - Stability control task)

(6)

where χ = 0.8 and χ = 1 (χ is user defined)



Sideslip angle estimation

Available measurements (from ESC or reasonable cost sensors):• Yaw rate, ψ

• Steering wheel angle, δ

• Wheel speeds, wi j

• Lateral acceleration, ay

• β can be evaluated through available sensors:

β =ay

vx− ψ, (7)

β?? → Existing Methods:• Integration of β

• Kinematic equations (eq. ay,ax)• Model-based observer (Vehicle model + Estimation technique)



Sideslip angle estimation

This study:• Planar bicycle model (with constant velocity):{

β = (Fy f +Fyr)/(mv)+ ψ

ψ =[l f Fy f − lrFyr +M∗z

]/Iz

(8)

• Dugoff’s tire model:

Fy =−Cα × tan(α)× f (α,Fz,Cα ), where f(.) is nonlinear (9)

• Nonlinear filtering: Extended Kalman Filter

State-space representation:• X = [β , ψ]T

• U =[M∗z , δ , Fz

]T .• δ = δ ∗+δd .

• Y = [ψ]T

M z *

δ*+δd

Fz

Vehicle system

Bicycle nonlinear model

β

ψ .

EKF

Observer



VDSC Controller architecture

Upper controller

Lower controller

Commanded steering angle

Desired yaw moment

Applying brake torque to the appropriate wheel

Objective: Yaw stabilitycontrol

Yaw rateSteering angle Sideslip angle

and/or

Measurements/estimationLevel 1

Level 2



VDSC-lower controller algorithm

The stabilizing moment M∗z provided by the controller is converted into braking torque and appliedto the appropriate wheels

Rules

• Braking 1 wheel: from an optimal point of view, it is recommended to use only one wheel togenerate the control moment (Park(2001))

• Only rear wheels are involved to avoid overlapping with the steering control

Decision rule:

Oversteer Understeer

Brake outer rear wheel Brake inner rear wheel

Driving situations


Active safety using coordinated steering/braking control Simulations

Outline


2. Models








Simulation results and results

• Matlab/Simulink software• Vehicle Automotive toolbox

• Full nonlinear vehicle model• Validated in a real car "Renault Mégane Coupé"

Two tests:

1 Double-lane-change maneuver at 100 km/h on a dry road (µ = 0.9)2 Steering maneuver at 80 km/h on a slippery wet road (µ = 0.5)



Test 1: Results [dry road µ = 0.9, V = 100 km/h]

0 0. 5 1 1. 5 2 2. 5 3

−30

−20

−10

0

10

20

30

Yaw rate [deg/s]

t [s ]

Uncontrolled

controlled

Reference

0 0. 5 1 1. 5 2 2. 5 3

−4

−3

−2

−1

0

1

2

3

4

β [deg]

t [s ]

Uncontrolled

Controlled

Vehicle dynamic responses with and without controller




−4 −3 −2 −1 0 1 2 3 4

−30

−20

−10

0

10

20

30

δ [deg]

Ψ [d

eg/s

]

. Reference

Uncontrolled

controlled

Figure: Response of the yaw rates versus steeringwheel angle

0 10 20 30 40 50 60 70 80

−0. 5

0

0. 5

1

1. 5

2

2. 5

3

x − Distance [m]

y − Di

stan

ce [m

]

Top view of the vehicle

Uncotrolled vehicle

Controlled vehicle

Figure: Trajectories of the controlled anduncontrolled vehicles




0 0.5 1 1.5 2 2.5

0.20.40.60.8

1

λ

Stability index

0 0.5 1 1.5 2 2.5 3

−200

0

200

400

Time [s]

M* z [N

m]

Corrective yaw moment

0.5 1 1.5 2 2.5 30

5

10

ρ

ρ−parameter variations

Figure: M∗z and ρ variations according to χ for thedouble lane-change maneuver

0 0.5 1 1.5 2 2.5 30

20

40

60

80

Time [s]

Tb le

ft [N

m]

Brake torque0 0.5 1 1.5 2 2.5 3

0

20

40

60

Tb r

ight

[Nm

]

Brake torque

0 0.5 1 1.5 2 2.5 3−4

−2

0

2

δ [d

eg]

Additive steer angle

Figure: Control signals generated by the controller



Test 2: Results [wet road µ = 0.5, V = 80 km/h]

0 0. 5 1 1. 5 2 2. 5 3

−25

−20

−15

−10

−5

0

5

10

15

20

25

Time [s]

Ψ ’ [

deg/

s]

Yaw rate

.

Uncontrolled

Controlled

Reference

0 0. 5 1 1. 5 2 2. 5 3

−3

−2

−1

0

1

2

3

Time [s]

β [d

eg]

Sideslip angle

Uncontrolled

controlled

Vehicle dynamic responses with and without controller




−4 −3 −2 −1 0 1 2 3 4

−25

−20

−15

−10

−5

0

5

10

15

20

25

δ [deg]

ψ’ [

deg/

s]

Figure: Response of the yaw rates versus steeringwheel angle

0 10 20 30 40 50 60

0

0. 5

1

1. 5

2

2. 5

3

x−Distance [m]

y−Di

stan

ce [m

]

Top view of the vehicle

Uncotrolled vehicle

Controlled vehicle

Figure: Trajectories of the controlled anduncontrolled vehicles




0 0.5 1 1.5 2 2.5 3

0.20.40.60.8

λ

Stability index

0 0.5 1 1.5 2 2.5 3−100

−50

0

50

Time [s]

M* z [N

m]

Corrective yaw moment

0 0.5 1 1.5 2 2.5 3

5

10

ρ

ρ−parameter variations

Figure: M∗z and ρ variations according to χ for the steering maneuver


LPV FTC for Vehicle Dynamics Control

Outline








LPV FTC for Vehicle Dynamics Control Towards global chassis control

Outline


2. Models









Some facts

• Vehicle-dynamics sub-systems control (suspension, steering, stability, traction ....) aretraditionally designed and implemented as independent (or weakly interleaved) systems.

• Global collaboration between these systems is done through empirical rules and may lead toinappropriate or conflicting control objectives.

What is GCC ?

• combine several (at least 2) subsystems in order to improve the vehicle global behaviorShibahata (2004)

• tends to make collaborate the different subsystems in view of the same objectives, accordingto the situation (constraints, environment, ...)

• is develop to improve comfort and safety, according to the driving situation, accounting foractuator constraints and to the eventual knowledge of the vehicle environment



Active safety using LPV FTC VDC coordinated control


Key points

Yaw is one of the most complex dynamics to handle on aground vehicle. FTC LPV control:• Prevents vehicle from skidding and spinning out• Improves lateral vehicle dynamics face to critical

situations• Handle Braking and suspension actuator

malfunctions and Steering activation

Desired trajectory

Undesired motion

The LPV FTC strategy

Monitoring Parameters• Braking efficiency : torque

transmission• Steering activation during

emergency situation (low slip)• LTR: roll induced load transfer

by damper malfunctions

Control Issues• Lateral coordinated steering/braking control:

parameter dependent weighting functions for brakingtorque limitation and activation of the steering action

• Full car vertical suspension control: fixed controlstructure for suspension force distribution, parameterdependent weighting functions for roll attenuation incritical situations and comfort improvement in normalones.


Global chassis control implementation scheme

zr

δd

uij Tbrj

Non Linear Full Vehicle Model

Road profil

Steer input

Suspension Controller Steering Controller Braking Controller

uij δ+ Tbrj

Load TransferDistribution

ρlij

Monitor 1

Steering+ Braking

ρbSupervision strategy

LPV/Hinf

Controllers

Driving scenario

Monitor 2

ρlij

ρs

ρs ρb ρb

δ+


LPV FTC for Vehicle Dynamics Control The LPV FTC VDC... approach

Outline


2. Models








Coordinated steering/braking control


+

-

ψref(v)

Weψref

GCC(ρb, ρs)

WTbrj (ρb)

Wδ0(ρs)

Bicycle

Wvy

ψ

z1

z2

z3

z4

Tbrj , δ0eψref

Vehicle model : Single track model(dry road).

Inputs/Ouputs:

w(t) = [ψre f (v)(t),Mdz(t)]u(t) = [δ+(t),T+

brl(t),T+

brr(t)]

y(t) = eψ (t)z(t) = [z1(t),z2(t),z3(t)]

Weighting functions for performance requirements

Weψand Wvy are 1st order systems.

Weighting functions for actuator coordination

• Wδ (ρs) = (1−ρs)× 4th order• WTbr j

(ρb) = (1−ρb)× 1st order→ braking (and steering) penalized if ρ = ρ

→ braking (and steering) allowed if ρ = ρ

When a high slip ratio is detected (critical situation) , the tire may lock, so ρb→ 0 and thegain of the weighting function is set to be high.This allows to release the braking action leading to a natural stabilisation of the slipdynamic.


The suspension control configuration


ΣgvWu

Ks(ρl)uH∞ij

z1

z2

zdefij

z3

Wzs(ρs)

Wθ(1− ρs)

A new partly fixed control structure: manage the suspension control distribution in case ofdamper malfunction

Ks(ρs,ρl) :=

xc(t) = Ac(ρs,ρl)xc(t)+Bc(ρs,ρl)y(t)uH∞

f l (t)uH∞

f r (t)uH∞

rl (t)uH∞

rr (t)

=

1−ρl 0 0 00 ρl 0 00 0 1−ρl 00 0 0 ρl

C0c (ρs)xc(t)

ρl allows to generate the adequate suspension forces in the 4 corners of the vehicledepending on the load transfer (left� right) caused by the performed driving scenario.

LPV FTC for Vehicle Dynamics Control Validation: LPV control vs professional driver

Outline









Validation: LPV control vs professional driver

Vehicle Automotive ’GIPSA-lab’ toolbox

• Full nonlinear vehicle model• Validated in a real car "Renault Mégane" Special thanks to MIPS laboratory, Mulhouse,

France (Prof. M. Basset): ]see C. Poussot-Vassal PhD. thesis

20 25 30 35 40 45 50 55 60−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8Yaw rate [rad/s2]

Measurementsimulation

• The stabilizing torques T ∗b provided by the controller is then handled by a local ABS strategyTanelli et al. (2008)



Scenario and scheduling parameters


−800 −600 −400 −200 0 200 400 600−300

−250

−200

−150

−100

−50

0

X [m]

Y [

m]

Track trajectory Experimental Moose performed by aprofessional driver on the Renault Mégane at90km.h−1 (to assess the efficiency forobstacles avoidance). The circuit includes aleft bend and then an obstacle avoidance inemergency situations to determine how wella vehicle evades a suddenly appearingobstacle.

20 25 30 35 40 45 50 55 600

0.2

0.4

0.6

0.8

1

t [S]

Mag

nitu

de

Rb

20 25 30 35 40 45 50 55 600

0.2

0.4

0.6

0.8

1

t [S]

Mag

nitu

de

Rs


Vehicle dynamical variables


20 25 30 35 40 45 50 55 60−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

t [S]

ψdt

Yaw rate [rad/s2]

Measurement passive vehicleLPV VDC

20 25 30 35 40 45 50 55 60

−10

−5

0

5

10

t [S]

Ay

Lateral acceleration [m/s2]


20 25 30 35 40 45 50 55 60−5

0

5

10

15

20

25

30

t [S]

Vx

Longitudinal velocity [m/s]


20 25 30 35 40 45 50 55 60−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

t [S]

θdt

Roll velocity [rad/s]



Steering control input


20 25 30 35 40 45 50 55 60−150

−100

−50

0

50

100

150

t [S]

Ang

le (

Deg

°)

Steering wheel mesurement

20 25 30 35 40 45 50 55 60−3

−2

−1

0

1

2

3

t [S]

Ang

le (

Deg

°)

Additive steering angle from the controller

1 Improved vehicle dynamical behaviorsubject to critical driving situations

2 Coordinated and hierarchical use ofthree types of actuators, depending onthe driving situations

3 LPV vs LTI: limitation of the brakingactuation in critical situations to avoidwheel locking and skidding, and itscoordination with active steering andsemi-active suspension controllers,leading to vehicle stability and roadhandling improvements.

4 Convincing simulation results, obtainedfrom experimental input data andperformed with a validated complexnonlinear vehicle model

LPV FTC for Vehicle Dynamics Control Validation: simulation of the fault free case

Outline









1st Scenario: vehicle at 100 km/h on a WET road


1 from t = 0.5s to t = 1s: 5cm Road bumpon the left wheels ,

2 from t = 2s to t = 6s: Doublelane-change maneuver

3 from t = 2.5s to t = 3s: a lateral windoccurs at vehicle’s front, generating anundesirable yaw moment,

4 from t = 3s to t = 3.5s: 5cm Road bumpon the left wheels, during the maneuver

Rb = braking efficiency Rs: activation of the steering actuator &coordination with adaptive suspension control


System analysis



Actuator analysis: braking system



Actuator analysis: steering and suspension systems

£


-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1-8000

-6000

-4000

-2000

0

2000

4000

6000

8000

Time [s]

Fd

am

pe

r

Semi-ActiveCmin=881Cmax=7282

Figure: Damper force/deflection

LPV FTC for Vehicle Dynamics Control Validation: FTC case

Outline


2. Models








Validation: FTC caseSimulation results

• Vehicle Automotive ’GIPSA-lab’ toolbox• Full nonlinear vehicle model• Validated in a real car "Renault Mégane Coupé" coll. MIAM lab [Basset, Pouly and Lamy]

see C. Poussot-Vassal PhD. thesis

The stabilizing torques T ∗b provided by the controller is then handled by a local ABS strategyTanelli et al. (2008)

Simulation scenario


Double lane-change maneuver at 100 km/hon a WET road (from t = 2s to t = 6s)

0 1 2 3 4 5 6−20

−15

−10

−5

0

5

10

15

20

t [s]

δ d[D

eg]

Driver Steering Angle

• Faulty left rear braking actuator:saturation = 75N

• 5cm Road bump from t = 0.5s tot = 1.5s and from t = 4s to t = 5s)

• Faulty front left damper: force limitationof 70%

• Lateral wind occurs at vehicle’s frontgenerating an undesirable yaw moment(from t = 2.5s to t = 3s).


Monitoring parameters


0 1 2 3 4 5 60

0.2

0.4

0.6

0.8

1

t [s]

ρ b

Braking scheduling parameter

0 1 2 3 4 5 60

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t [s]

ρ s

Performance scheduling parameter

0 1 2 3 4 5 6−0,1

0

0,1

0,2

0,3

0,4

0,5

0,6

t [s]

ρ l

Suspension scheduling parameter

• ρb handles the braking efficiency• ρs: activation of the steering actuator• ρl (LTR): Coordination of suspension

control and on-line modification of thesuspension performances

ρb

ρs

ρl


Braking/Steering actuators - stability analysis

0 1 2 3 4 5 60

200

400

600

800

t [s]

Tb

left

[Nm

]

Rear Left Braking Torque

0 1 2 3 4 5 60

200

400

600

800

t [s]

Tb

right

[Nm

]

Rear right Braking Torque

0 1 2 3 4 5 6−6

−4

−2

0

2

4

t [s]

δ[d

eg]

Additive Steering Angle

−6 −4 −2 0 2 4 6

−40

−20

0

20

40

β [deg]

β’[d

eg/s

]

Stability Region

FTC LPV

Stability boundries Uncontrolled


Fault Tolerant Yaw control through an efficient coordination of braking/steering actuators.


Suspension control distribution

0 1 2 3 4 5 6−500

0

500

Fs

rr

Suspension Forces

0 1 2 3 4 5 6−200

0

200

Fs

fl

0 1 2 3 4 5 6−500

0

500

Fs

fr

0 1 2 3 4 5 6−500

0

500

t [S]

Fs

rl

Faulty dampers

Faulty damper

0 1 2 3 4 5 6−2

−1.5

−1

−0.5

0

0.5

1

t [s]

θ[d

eg

]

Roll displacement

1 20

1000

2000

3000

4000

5000

6000

7000

8000

9000

Front left damper

Front left damper

Rear right damper

Rear right damper

Rear left left damper

Rear left left damper

Front right damper

Front right damper

With Damper Fault Without Damper Fault


Fixed structure LPV control for suspension force coordination in case of damper malfunction

Conclusions and future work

Outline









Conclusions

About today’s presentation:

An approach to the vehicle yaw stabilizing problem. . .• Objective: Enhance vehicle steerability and stability

• Steerability is enhanced in normal driving condition.• Braking is involved only when the vehicle tends to instability.

• Flexible design: Integration of different scheduled sub-controllers• Scheduling parameters: Estimation of the sideslip angle• Real-time implementation: General structure does not involve online optimization• Real time performance adaption: Control adaption based road profile reconstruction• Fault detection, isolation and tolerante control system failures must be handled



Future work

• Implementation of the new developed controllers onboard.• Development of more intelligent vehicle control strategies based on cloud data sharing.• Development of a guarantee estimation strategies for the monitoring approaches trough

interval analysis.• Use of novel active diagnosis strategies to enhance the vehicle control.• Investigation of the human factor (arm and reaction) properties during the driving maneuvers

(steering, braking).



Thank you for your attention


Bibliography

References

• Dugoff et al. (1970) : H. Dugoff, P.S. Francher, and L. Segel. "An analysis of tire traction properties andtheir influence on vehicle dynamic performance". SAE transactions, volume 79, pages 341–366, 1970.

• Karnopp et al. (1974) : Karnopp, D.; Crosby, M. & Harwood, R. "Vibration Control Using Semi-Active ForceGenerators", Journal of Engineering for Industry, 1974, 96, 619-626.

• Oustaloup et al. (1996) : Oustaloup, A.; Moreau, X. & Nouillant, M. The CRONE Suspension ControlEngineering Practice, 1996, 4, 1101-1108

• Scherer et al. (1997) : C. Scherer, P. Gahinet, and M. Chilali. "Multiobjective output-feedback control viaLMI optimization". IEEE Transaction on Automatic Control, volume 40, pages 896–911, 1997.

• Valasek et al. (1998) : Valasek, M.; Kortum, W.; Sika, Z.; Magdolen, L. & Vaculin, O. "Development ofsemi-active road-friendly truck suspensions", Control Engineering Practice, 1998, 6, 735-744

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Bibliography

Sincères remerciements à ...


Soheib Fergani

Charles Poussot

Moustapha Doumiati

Hussam Atoui

Dimitrios Kapsalis et bien sûr à moncollègue Dr. Luc Dugard

Merci pour votreattention

lpv methods applied to vehicle dynamcis controlo.sename/docs/lpv_vdc.pdf · why vehicle dynamics...

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