Self-Tuning Control Strategy forAntilock Braking Systems

8/7/2019 Self-Tuning Control Strategy forAntilock Braking Systems

1/21

Self-Tuning Control Strategy forAntilock Braking Systems

Riccardo MORSELLI

Roberto ZANASINicola SPONGHI

Computer Science Engineering Department (DII)

University of Modena and Reggio Emilia, ITALY


2/21

Outline

Introduction on ABS and emergency braking

Assumptions

Basic operating principle

6-State control algorithm

Relaxation of some assumptions

Simulation experiments and Conclusions

MORSELLI, Zanasi, Sponghi Self-Tuning Control Strategy for ABS


3/21

IntroductionTire Behaviour and Emergency Braking

The longitudinal and lateral

tire forces Fx and Fy are a

function of the tire slipl

Fx

l

lopt

Fy

l

Braking

Panic braking: locked wheels (l =-1)

and suboptimal braking forces, thus

lengthening of the travelled distance

reduced steering effectiveness

Nz

vx

wRe

w

wJFx

x

xe

v

vR =

FyFx

vx



4/21

IntroductionABS Functioning Principle and Issues

Fx

l

lopt

Fy

l

Braking

By properly operating the braking system,during an emergency braking,the ABS control should be able to make the tire

to work where the longitudinal and lateral tire

forces Fx and Fy are around their maximum:

reduced travelled distance

high steering effectiveness

Main issues:

high parameters uncertainties

low cost (low performance) actuators

low cost and limited sensors

safe vehicle behaviour when ABS is on

...

Self-Tuning Control Strategy for ABSMORSELLI, Zanasi, Sponghi


5/21

Brief Review of Previous Works AboutAntilock Braking Systems

There are several papers about ABS (it was first developed in the 70s)and the manufacturers of ABS systems already have a deep experience.

The proposed ABS controls can be roughly classified by evaluating:

1. Sensors (what is supposed to be known or measured?)

2. Actuators (is the actuators dynamics taken into account?)

3. Theory (is the control strategy proved?)

To the best of our knowledge there are NO papers with:

1. real and cheap sensors (i.e. wheels speed/acceleration only)

2. dynamics of the hydraulic actuators taken into account

3. proved control strategy (not empirical)

This paper proposes and prove a new ABS control strategy based only onthe wheel speed measure and that considers the actuators dynamics.



6/21

Assumptions

1. Standard ABS braking system with ON-OFF valves:

a) few control actions: INCREASE, HOLD, DECREASE pressure P

b) valve opening/closing time limited above by Tdthus any control action is ensured within the time Td

c) during the HOLD phases the braking pressure P is constant

2. The curve Fx(l) has a constant shape (not time/speed dependent,this assumption is relaxed later) with unique minimum.

3. The wheel angular speed is measured,the wheel angular acceleration is measured or estimated.

tyrewheelcylinder

brakediskpump

mastercylinder

builtvalve

dampvalve

vacuum

booster

brakepedal

Reservoir

PFx

l

loptBraking



7/21

Basic Operating Principle

The control strategy is a minimum seek algorithm:

1) Find if the operating point of thetire is in the stable or in theunstable region.

2) Operate the actuators to switch fromone region to the other.

The curve Fx(l) has a unique minimum

Fx

l

lopt

Braking

Stable

region

Unstable

region

Limit

cycle

A sort of limit cycle arises

around the minimum ofFx(l)



8/21

Where is the operating point of the tire?First 2 Properties

Nz

vx

wRe

w

wJFx

x

xe

v

vR =

FyFx

vx

Computing the tireslip time derivative:

2

x

xx

ev

vvR

&&&

=

By measuring the wheel accelerationit is possible to infer the sign of thetime derivative of the slip ratio.

the following two properties can be proved:

1)

2)

are known constants.

0then0if > &&& p

0then0if


9/21

Where is the operating point of the tire?Last 2 Properties

)(xebrkw

FRPKJ =&

The dynamics of the tire is:(Kbrk is the brake coefficient, P is the braking pressure)

Nz

vx

w Re

w wJ

Fx

The time derivative of the above equation is:

&&&&

d

dFRPKJ x

ebrkw

)(=

(Kbrk

andFx(

l

)are not time dependent,

this assumption is removed later)

the following two properties can be proved:

ifP is constant and

3)

4)

0then0andopt


10/21

Schematic Representation of theWorking Cycle: the P-l plot

From the dynamics of the tire it is possible to compute the pressure Pas a function of the slip and of the wheel acceleration:

)(xebrkw

FRPKJ =&

brk

xew

K

FRJP

)(),(

=

&&

For a fixed value of the wheelacceleration, the shape

of the curve P(l

) is the sameas the shape of -Fx(l)and the 4 properties statedbefore can be easily

represented.

P

llopt-1

0=&

N &&

0Region &

),(P

P &

),( NP &



11/21

Schematic Representation of theWorking Cycle: Properties of the P-l plot

P

llopt-1

0=&

N &&

0Region &

),(P

P &

),( NP &curve P(l) with constant

wheel acceleration

Property 2:regionwith decreasing slip

The curves with constantpressure are horizontal lines

It exist a value for thewheel acceleration thatensures a constant slip

Property 1:regionwith increasing slip


S lf T i C l S f


12/21

Self-Tuning Control Strategy forAntilock Braking Systems: States 1-2

The proposed control strategy is based on a 6-state algorithm.

1Transition :

the wheel accelerationis low enough, the slip isdecreasing (prop. 2), theHOLD command is given.

n && > &&& p

INC

HOLD

210


13/21


Transition : ifthe operating point isin the unstable region(property 4), theDECREASE commandis given to switch to

the stable region.

3 0

P

llopt-1

0=&

0> &&& p

HOLD

DEC

3

4

n && =

p && =

The proper computation of this condition in adiscrete time control system is discussed soon.


S lf T i C t l St t f


14/21


Transition :

the time Tdhas elapsedthe pressure P can beconsidered constant.The HOLD command is

maintained

5

P

llopt-1

0=&

0> &&& p

HOLD

5

INC

6

n && =

p && =

Transition : ifthe operating point isin the stable region

(property 3), theINCREASE commandis given to switch tothe unstable region.

6 0


15/21

Self-Tuning Control Strategy andWheel Acceleration Time Derivative

Properties 3 and 4 involve the sign of the time derivative of the

wheel acceleration:

ifP is constant and

3)

4)

0then0andopt


16/21

Self-Tuning Control Strategy:Parameters Variations and Robustness (1/2)


P

llopt-1

3

6

What does it happen when Kbrkand Fx(l) are time variant? Two new termsappears in the equation of the time derivative of the wheel acceleration:

dt

tdFR

d

tdFRP

dt

tdKPtKJ x

e

x

e

brk

brkw

),(),()()(

= &&&&

Prop. 1 and 2 are not affected

The condition ofprop. 3 and 4 does not exactlyensure the switch betweenthe stable/unstable regions.

However if the two new termsare slowly time varying, theireffect on transitions 3 and 6(based on prop. 3 and 4) is atranslation of the limit cycle.

The same happens if

is different from .

0


17/21

Self-Tuning Control Strategy:Parameters Variations and Robustness (2/2)


What does it happen in case of sudden parameter variations?

The operating pointis subject to a jump.

Independently from thecurrent state of the algorithm,1 or 2 transitions are enough

to detect where is the newoperating point and recovery.The detection and the recoveryare embedded in the algorithm.

As soon as the parametersbecome slowly varying again,the operating points approaches

the new correct limit cycle.

P

llopt-1


18/21

Simulation Results 2/3


19/21

Simulation Results 2/3Mid Quality Actuators and Sensors

Self-Tuning Control Strategy for ABS

Wheel slipOptimal slip

Braking forceForce @ Locked wheel

Tire curves (extreme)

Operating pointsOptimal operating points

MORSELLI, Zanasi, Sponghi

Simulation Results 3/3


20/21

Simulation Results 3/3Low Quality Actuators and Sensors

Vehicle speedWheel speed

Optimal wheel speed

Braking forceForce @ Locked wheel

Wheel slipOptimal slip



21/21

Conclusions

The proposed control strategy is based on someassumptions rather close to the real implementation.

The algorithm is based on few proved properties.

The remaining key issue is the computation and thedetection of the condition .

Thanks to its simplicity and its adaptability, theproposed control can be used as a benchmarkto test different control strategies.

0

Documents

Self-Tuning Control Strategy forAntilock Braking Systems