fuzzy logic in automobiles

7/27/2019 fuzzy logic in automobiles

1/28

INKT H E C O M P U T E R A P P L I C A T I O N S J O U R N A L

Constantin von Altrock

Fuzzy Logic in

Automotive Engineeringtive advantage is soon commonly used.In this article, Ipoint to case stud- ies in antilock braking systems (ABS), engine control,

and automatic gearbox control. I show how superior performance is achieved via fuzzy-logicIssue 88 November 1997 1Circuit Cellar INK


2/28

and neural-fuzzy design techniques. I also discuss development methodologies, tools, and

code speed/size requirements.

Automotive engineering is one

area where fuzzy logic has

made significant inroads.

Constantin brings us up to date

with the latest developments.

He examines fuzzy logics

impact on ABS braking, engine

control systems, transmissions,and antiskid steering.

uzzy logic is

apowerful way

toput

engineering

expertise into

products in a short

amount oftime. Its highly

beneficial in automotive

engineering, where

many system designs involve

the experience ofdesign

engineers as well as test

drivers.

fOver the past years, fuzzy

logic hasbecome is a common

design technology in Japan,

Korea, Germany, Sweden,

and France. The reasons aremanifold.

First, control systems in

cars are complex and involve

multiple parameters.

Second, the optimization ofmost systems is based on

engineering expertise rather

than mathematical models.

Good handling,

Fahrvergngen, and riding

comfort are optimization

goals that cant be defined

mathematically.

Third, automotive

engineering is competitive on

an international scale. Atechnology that proves a

competi-

Issue 88 November 1997 2

Circuit Cellar INK

2Issue 88 November 1997Circuit Cellar INK


3/28

ABS WITH FUZZY LOGIC

In 1947, Boeing

developed the first ABS for

airplanes as a mechanical

system. Today, ABS isstandard equip- ment on

most cars. A

microcontrollerand

electronic sensors

measure the speed of every

wheel and control the fluid

pressure for the brake

cylinders.

Mathematical models for

a carsbraking system exist,

but the interaction of the

braking system with the road

is far too complex to model

adequately. Hence, todays

ABS contains the engi-neering experience of years

oftesting

in different roads and

climates.

PRODUCING FUZZY ABS

Because fuzzy logic is an

efficient way to put

engineering knowledge into

a technical solution, its no

surprise that many ABS

applications are already on the

market. Currently, Nissan

and Mitsubishi ship cars with

fuzzy ABS. Honda, Mazda,Hyundai, BMW, Bosch,

Mercedes-Benz, and Peugeot

are work- ing on solutions as

well.

ABS also benefits from

fuzzy logics high

computational efficiency.

During a control loop time of

25 ms, the controllers mustfetch all sensordata, pre-

Issue 88 November 1997 3Circuit Cellar INK


4/28

Road Condition

Optimum Slack (s)

Dry 0.2Slippery or Wet

0.12Ice or Snow

0.05

Table 1The slack value for

maximum brake effect depends on

the road condition.

process it, compute the ABS

algorithm, drive the bypass

valves, and conduct the test

routines. Any additional

function thus has to be

computationally efficient.Most ABS systems use 16-

bit controllers, which can

compute a medium size

fuzzy-logic system in about

0.5 ms, using only about 2-KB

ROM space [1]. You can check

out a comparison of

computing times offuzzy-

logic systems on differentmicrocontrollers [2].

BRAKING BASICS

There are different ways in

which fuzzy logic is used in

ABS design. The

implementation of

Nippondenso [3] that I

present exhibits an

intelligent combination ofconventional techniques

with fuzzy logic.

Lets first discuss some

basics ofthebraking process.

If a wheel rotates exactly as

fast as it corresponds to the

speed of the car, the wheel has

nobraking effect at all. If the

wheel doesnt rotate at all, itisblocked.

Theblocking situation has

two dis- advantages. First, a

carwith blocking wheels is

hard to steer. Second, the

brake effect is not optimal.

The point ofoptimum

brake effect isbetween

these two extremes.The speed difference

between the car and the

wheel during braking is

called slack. Its

definition is:

However, the point of

maximumbrake effect

depends on the type ofroad.

Table 1 lists typical values.

ROAD SURFACE

Conventional ABS controlsthebypass valves of the brake

fluid so the slack equals a set

value. Most manufacturers

program this set value to a

slackof 0.1, which is a good

compro- mise for all road

conditions.

But, as Figure 1 and Table 1

show, this set value is not

optimal forevery road type. By

knowing the road type, the

braking effect can be enhanced

further.

So, how do you determine

what the road type is? Asking

the drivertopush abutton on

the dashboardbefore an

emergency brake is not

feasible.

Sensors provide one logical

alterna- tive. Many companies

have evaluated different types

ofsensors and concluded that

sensors which delivergood

road- surface identification are

too expensive or not

sufficiently robust.

However, consider sitting ina carequipped with a standard

ABS. Afterdriving at a known

speed, you could jam on the

brake so the ABS starts to

work.

Even if you didnt know

what the road surface was like,

you could make a good guess

from the cars reaction. If adrivercan estimate the road

surface


5/28

from the cars reaction, fuzzy

logic can implement the same

ideas into the ABS.

Nippondenso did exactly

this. When the ABS first

detects the wheel blocking, it

starts to control the brake-fluid valves so each wheel

rotates with a slackof0.1.

The fuzzy-logic system thenevalu-

ates the reaction of the car to

the braking and estimates

current road surface.

Considering this estimate,

the ABS corrects the set

value for the slack to

achieve the best braking

effect in the interval from s =

0.05 tos = 0.2.

The fuzzy-logic system

only uses input data

stemming from the existing

sensors of the ABS. Such

input variables are

deceleration and speed of the

car, deceleration and speed ofthe wheels, and hydraulic

pressure of the brake fluid.

These variables indirectly

indicate the current

operation point ofthe

braking and itsbehaviorover

time.

Experiments show that a

first proto- type withjust sixfuzzy-logic rules improves

performance significantly.

On a test track alternating

from snowy to wet roads, the

fuzzy ABS detected the road-

surface changes even during

braking.

A FUZZY BRAKE?

Due to the highcompetition in this area,

most manufacturers are

reluctant topublish any

details about the tech-

nologies they use. The cited

application only shows

results from an experimental

fuzzy-logic system. The

details about the finalproduct arent published.

Also, some carmakers

(especially in the U.S.) worry

about the negative con-

notation of the word fuzzy.

Since it implies imprecision

and inexactness,

manufacturers are afraid that

drivers may thinka fuzzyABS is inferior. Others are

threatened by the possibil- ity

of a suit in which a clever

lawyersuggests to a laymans

jury that a fuzzy-

logic ABS is somethinghazard-

ous.

s

=V

ca

r

V

w

he

el

V

carwher

es is

slack

(bet

ween

0 [no

braki

ng]

and 1

[bloc

king]

), Vwheelis thecars

velocity,

and V

is thewhee

lsveloc

ity.Fig

u C

DryR

o

a

d

WetR

o

a

d


6/28

In J

= 0,

the

whee

ls

speed

equals the

cars.

In the

case

ofs =

1, the

whee

l

blocks

comp

letely

.

The

curve

s

show

that

the

opti

mum

brake

effect

lies

be-

twee

n

these

two

extre

mes.

SnowyRoad

0S

00.250.50.751

Figure 1This

plot illustrates

brake effect

over the wheel

slack s for dry,

wet, and snowy

road surfaces.( is the friction

coefficient, or

measure of

brake effect.)

In

Ger

ma

ny,

on

theoth

er

han

d,

the

con

cept

s of

fuzzine

ss

and

engi

neer

ing

maste

rpiec

e do

not fit

toget

her

well

in the

publi

c

perce

ption.

Henc

e,

most

manu

factur

ers


7/28

usingfuzzylogicinABShidethefact.

segment ofassembly code in

a microcontroller. Once

implemented, who can tell

that this code contains fuzzy

logic?

Temperature of

Coolant

Vacum inAirIntake

O2Concentrationin

Exhaust

InjectionAmount

(FuzzyLogic)

Fuel Injection

When many publications

about fuzzy logic appeared for

the first time about

fiveyearsago,evenreputedscientists

(FuzzyLogic)

Determination ofIgnitionTiming

Ignition Timing ElectronicIgnition

andprofessors in the U.S.stated thatfuzzy logic shouldntbe usedforcritical applications. Theyclaimed that itproducesinherently instable systems.

KnockSensor

Angle ofCran

kshaft

(FuzzyLogic)

Ignition

This attitude is truly shameful. TheyFigure 2As you can see, the engine controller of NOK Corporation containsthree fuzzy-logic modules.

demonstrated only that they

did not understand what

fuzzy logic is about.

A fuzzy-logic system is a

time invari- ant,

deterministic, and nonlinear

sys- temnothing fuzzy

about that. Such systems are

already known and applied in

control engineering, and

conventional stability theory

covers them well [4].

In the case of a fuzzy ABS,

stability isnt even an issue.

Conventional ABS was

considered stable for any

slack set value in the

interval from 0.05 to 0.2.

Hence, a fuzzy-logic road-

surface esti- mator that tunes

this value to the opti- mumcannot make the ABS

instable.

Lets move on to see how

fuzzy logic easily

implements human

experience

in an embedded engine-control system.

ENGINE CONTROL

The control of car and truck

engines isbecoming

increasingly more complex

with more stringent emission

standards and constant effort to

gain higher fuel efficiency.

Twenty years ago, control

systems were mechanical (i.e.,

carbure- tor, distributor, and

breaker contact). Now,

microcontroller-based systemscontrol fuel injection and

ignition.

Since the control strategy

foran engine depends strongly

on the current operating point

(e.g., revolutions, mo-

mentum, etc.), linear control

models, (e.g., PID) are not

suitable.


8/28

Listing 1The current operation point of the engine is classified by the linguistic variable

Situation. Each linguistic term denotes a typical operation point. Because each term is

represented as a fuzzy-logic membership function, the linguistic variable can classify all other

operation points, too.

linguistic variable Situation {

Term 1: Start

Control strategy is that the cold enginetimed early, and the mix is fat;

Term 2:Idle

Control ignition timing and fuel injection dependingtemperature to ensure that the engine

Term 3: Normal drive, low or medium load

Maximize fuel efficiency by meagerknocking;

Term 4: Normal drive, high loadFat mix and early ignition to maximize performance.constraint is the permitted emission maximum;

Term 5:Coasting

On the other hand, no

mathematical model

describing the complete

behav- ior of an engine exists.

Most engine controllers use a

look-up table to repre-

sent the control strategy.

The table is generated from

the results ofextensive

testing and engineers

experience.

The generation ofsuch a

look-up table, however, isonly suitable forthree

dimensions (two inputs and

one output). Also, the

generation and inter-

pretation ofsuch tables is

difficult and considered a

black art.

Although fuzzy logic can

replace these look-up-tables,most manufacturers will not

publish any details on a

fuzzy-logic engine-control

solution.

This secretiveness is due to

the fact that the rules of the

fuzzy-logic system make the

entire engine-control

knowledge of the companycompletely transparent.

They are afraid competitors

will learn too much about

the solutionby

disassembling the fuzzy-

logic rules.

IDENTIFY DRIVING CONDITION

Nok andNissans case study

[5] gives the benefits of fuzzy

logic in engine control.

Figure 2 depicts the

compo- nents ofthis engine

controller, which contains

three fuzzy-logic modules.

The system first notes the

engines operational

condition by the linguistic

variable Situation. This

variable has the linguistic

terms in Listing 1.

The determination ofSituationis

a state estimation of theoperationpoint. Because

Situationis a linguistic

variable, more than one term

can

be valid at the same time, so

combina- tions of the

operational points canbe

expressed as definedby the

terms.

Apossible value ofSituationcould

be {0.8; 0; 1; 0; 0; 0.3}.

Linguistically, this value

represents the driving condi-

tion engine started a short

while ago,


9/28

normal drive condition at

medium orlow load, slightly

accelerating. From this

operation-point

identification, the individual

fuzzy-logic modules control

injection, fuel cutoff, and

ignition.

Like ABS, engine control

needs a very short loop time.

Some systems are as fast as 1

ms for an entire control loop.

Some manufacturers design

the system using fuzzy logic

but then translate it into a

look-up table for faster

processing.

Although a look-up table

computes faster, memory

requirements may pro- hibit

its use. A look-up table with

two inputs and one output, all8-bit resolution, already

requires 64 KB ofROM.

Restricting the resolution

ofthe input variables to 6

bits each, the look- up-table

still requires 4 KB. A table

with three inputs and one

output, all inputs

6-bit resolution, requires 14MB.

Some engineers

implemented a look- up table

with a limited resolution

and used an interpolation

algorithm. How- ever, the

interpolation needs about as

much computing time as the

fuzzy- logic system itself[2].

Another published

application offuzzy logic in

engine control is an idle

control unitby Ford Motor

Corp. [6].

Next, lets checkout

automatic- transmission

control to show how

fuzzy-logic systems can

adapt theircontrol

strategy to drivers.

ADAPTIVE AUTOMATICS

When the first three-speed

automatic transmissions

appeared on the market

about 30 years ago, the

enginepower ofmost cars

was just sufficient to keepthe car in pace with traffic.

The neces- sity ofgetting

maximum momentum from

the engine determined the

shift points for the gears.

Photo 1This model

car is used in high-

speed driving experi-

ments.

Now, when

most car engines

can delivermuch

more power

than necessary to

keep the car in pace

with traffic,

automatic

transmission

systems have up to

five speeds, and

fuel efficiency hasbecome an

important issue,

controlling shift

points is much more complex.

Five speeds and higher engine

powergive the automatic-

transmission system a much

higherdegree offreedom. Driv-

ing at 35 MPH, a three-speedautomatic transmission has to

select second gear. A five-

speed transmission with apow-

erful engine can select second

gearformaximum

acceleration, third gearfor

normal driving condition, and

fourth gear forminimal

acceleration.

ACCELERATE OR SAVE FUEL

Unfortunately, the goal for

the control strategy is in a

dilemma. Formaxi- mum fuel

efficiency, you want to select

the next highergear as early as

possible. But formaximum

performance, you switch to the

next highergearlater.If you have a standard shift,

you choose your strategy


10/28

depending on the traffic

condition. An automatic

gearbox has no understanding

of the traffic condition or the

drivers wishes.

However, intelligent

control techniques canenhance automatic trans-

missions as it is based on

experience

Photo 2The

first version of thefuzzy-logic

controller has 200

rules

in two rule

blocks. The four

left boxes

indicate input

interfaces for

sensors, the two

right boxesindicate output

interfaces for the

actuators, and

the two large

boxes in the

middle represent

fuzzy- logic rule

blocks.

and engineering knowledge

rather than mathematical

models. Fuzzy logic

thereforeproves to

efficiently implement the

technology.

In 1991, Nissanintroduced fuzzy- logic

controlled automatic five-

speed transmission systems

[7, 8]. Honda followed in

1992 [9], and GM/Saturn in

1993.

The job for the fuzzy-

logic system in these

applications is similar:

avoid nervous

shifting back and forth

on winding orhilly

roads

understand whetherthe

driver wants economical

orsporty performance

avoid unnecessary

overdrive, ifswitch- ing to

the next lowergear does

not deliver more

acceleration

Figure 3 shows a typicalsituation

on a fast, winding road. With a

standard shift, youd leave it

in fourth gear,buta five-speed automatic

transmission switches

between the fourth and fifth

gears depending on the speed

of the car.

The fuzzy-logic

transmission controller

evaluates more thanjust

the current speed of the car. It

also analyzes how the driver

accelerates andbrakes.

To detect a winding road,

the fuzzy- logic controller

looks at the number of

acceleratorpedal changes

within aperiod. Figure 4

shows the definition of

the linguistic variableAcceleratorpedal changes. The

variance ofthe accelerator

pedal changes is input to the

fuzzy-logic controller.

Some of the rules

estimating the road and

driving conditions from

these input variables are:


11/28

Road

AcceleratorPedal

The opposite case issimi- lar. If theautomatic trans-mission detects thatthe driver acceleratescarefully and takes thefoot offthe acceleratorlong before red lights,

chances are that thedriver wants high fueleffi- ciency.

acceleration, the next logical

step is skid-controlled

steering. An antiskid steering

system (ASS) reduces the

steering angle appliedby the

driver through the steering

wheel to the amount the road

can take. It optimizes the

steering action and avoids

sliding since a sliding car is

very difficult to restabilize,

especially fordrivers not accustomedG

ea

r

45454

WHY

FUZZYLOGIC?

to suchsituations.

Though anASSmakesa lot ofsense

Figure 3Afive-speedautomatictransmission

with fixedshift pointsalwaysswitchesbetweenfourth andfifth gear ona windingroad. A

driver with ashift

gearboxwould leaveit in fourthgear.

Thequestionremains,whydoyouneedfuzzylogictoimpleme

nttheseintelli-

from a

technic

alpoint

ofview,

such a

system

is

harder

to

market.

For anABS,

you canprove thatit never

performs

man

y

pedal

changes

wit

hin

a

peri

od

indi

cate

a fast

and

wind

ing

road

few

ped


12/28

a

l

c

h

a

ng

e

s

w

i

t

h

in

a

p

e

r

i

o

d

i

n

d

i

c

a

t

e

a

f

r

e

e

w

a

y

m

a

n

y

pe

d

a

l

c

h

a

ng

e

s

w

i

t

h

i

n

a

p

e

r

i

o

d

a

n

d

a

h

i

g

h

v

a

r

i

a

nc

e

o

f

p

e

d

a

lc

h

a

n

g

e

s

i

n

d

i

c

a

t

e

a

s

l

o

w

a

n

d

w

i

n

d

i

ng

ro

ad

m

e

di

u

m

v

a

r

i

an

c

e

o

f

p

e

d

al

c

h

a

n

g

e

s

i

n

d

i

c

a

t

e

s

a

f

a

s

t

a

n

d

w

i

n

d

i

n

g

ro

a

d

l

o

w

va

r

i

a

n

c

e

o

f

t

h

e

p

e

d

a

l

c

h

a

n

g

e

s

i

nd

i

c

a

t

e

s

a

f

r

e

e

w

a

y

T

he

inte

resti

ng

part

of

this

appl

ica-tion

is

that

the

fuzz

y-

logi

c

controll

er

uses the

driver

as the

sensor.

It inter-

prets

thedriver

s

reactio

n to the

road

and

driving

conditi

ons andadapts

the

cars

perfor

mance

accordi

ngly.

This

behaviorcould

be used

to define

an

intellig

ent

control

system.

The

technic

al

system

tries to

underst

and

whether

the

human

is

satisfied

with

its

perfor

mance

and

adapts

itselfto suit

the

needs

of the

human

using

it.

INTEL

LIGENTTRANSMISSIONS

An

other

exa

mple

of an

auto

mati

c

trans

missi

on

syste

m

curre

ntly

unde

r

deve

lopm

ent

in

Ger

man

yillust

rates

this

possi

bility

even

better.

If

driverswant to

acceler

ate,but

arent

satisfie

d with

their

cars

responce, they

uncons

ciously

push

the

pedal

down

even

morewintin

11.5s.

This

scenari

o

represe

nts the

subcon

scious

reactio

n of

most

drivers

to

unsatisf

ac- tory

acceler

ation.

Most

drivers


13/28

d

o

n

t

e

v

en

r

e

a

li

z

e

t

ha

t

t

h

e

y

li

k

e

th

e

c

ar

to

a

c

c

e

l

e

r

a

t

e

f

a

st

e

r.

I

f

a

n

au

t

o

m

a

t

i

c

t

r

a

n

s

m

i

s

s

i

o

n

s

y

s

t

e

m

i

s

c

a

p

a

b

l

e

o

f

d

e

t

ec

ti

n

g

t

h

i

s,

itc

a

n

m

o

v

e

t

h

e

s

h

if

t

p

o

i

n

t

s

h

i

g

h

e

r

t

o

a

chie

ve

mor

e

acce

lerat

ion.

gent

funct

ions?

My

answ

er:

while

you

can

use

other

tech

niqu

es to

impleme

nt

these

contr

ol

strat

egies

,

fuzzylogic

is

likel

y to

be the

most

effici

ent.

I

ntel

lige

nt

con

trol

stra

tegi

es

are

buil

t on

expe

rienc

e and

expe

rime

nts

rather

than

from

math

emat

ical

mod

- els.

Hence, a

lingu

istic

form

ulati

on is

more

effic

ient.

Th

ese

strat

egies

most

ly

invol

ve a

large

num

ber

of

input

s.

Most

of

the

inpu

ts areonly

relevant

forsome

spe-

cific

conditio

n.

Usingfuzzy

logic,

these

inputs

are only

consider

ed in the

relevant

rules,keeping

even

complex

control-

system

designs

transpar

ent.

Another

consider

ation is

that

intel-

ligent

control

strategie

s

implem

ented in

mass-

market

products

have to

be

implem

ented

cost

efficient

ly. In

com-

parison

to

conven

tional

solutions,

fuzzy

logic is

often

much

more

compu-

tational

andcode-

space

efficient

.

Lets

look

now at

how

fuzzylogic

enable

s the

design

of new

functi

onal-

ity for

autom

atic

steerin

g

contro

l.

ANTISKIDSTEERING

Activ

e

stability

control

systems

in cars

have a

long

history.First,

ABS

improve

d

braking

performa

nce by

reducing

theamount

ofbrake

force

applied

by the

driverto

what the

road

surface

can take.

This

system

avoids

skidding

and

sliding,

resulting

in shorter

braking

distance

s.

Second

,

traction-

control

systems,

which do

essential

ly the


14/28

sa

me

thi

ng

as

AB

S,im

pr

ov

e

ac

cel

era

tio

n.By

red

uci

ng

en

gin

e

po

we

r

ap

pli

ed

to

the

wh

eel

s

to

wh

at

the

roa

d

can

tak

e,

a

tra

ct

io

n

-

c

o

ntro

l

s

y

st

e

m

m

axi

m

iz

es

a

c

c

el

er

at

io

n

an

d

m

in

i

m

iz

e

s

tir

e

w

e

ar

.

Aft

er

sk

id

-co

ntr

ol

le

db

rak

in

ga

nd

worse

than

a

tradit

ional

braki

ngsyste

m.

For

an

ASS,

this

is

hard

toprove

.

Al

so,

it

may

be

diffi

cultto

sell

cars

that

tak

e

over

the

stee

ring

in

eme

r-

genc

y

situ

atio

ns.

Even

ABS

fac

ed

a

lon

g

per

iodof

rej

ect

ion

by

cus

to

me

rsbeca

use

theyfeltunea

syabou

t asyste

m

inhibitingtheirbrakeaction.

F

or

thes

e

reas

ons,

it

may

take

a

lon

gtim

e

befor

e

ASS

will

be

impleme

nted

in a

prod

uctio

n car.

All

resul

tssho

wn

in

this

secti

on

stem

from

theresea

rch

of

a

Ger

man

car

man

ufact

urer

[10].

Be-

caus

e

this

syste

m is

one

of the

most

complex

fuzzy-

logic

embedd

ed

systems

everdevelop

ed, it

effectiv

ely

demon-

strates

the

potentia

l of thetechnol

ogy.

THE TESTVEHICLE

Real

experim

ents

were

made ona

modifie

d Audi

sedan

and the

20

model

car

shownin Photo

1. In the

followin

g

discussi

on, I

only

present

the

results

derived

from

the

model-

car

experi

ments.

Amidm

ounted

1-hp

electri

c

motor

powers

the car,

rendering the

power-

to-

weight

ratio

of a

race

car.

Thissetup

enable

s the

researc

hers to

perfor

m

skiddi

ng and

sliding

experi

ments

in

extre

me

situati

ons at

high

speeds.

?

LowMediumHigh1

0 010

203040

AcceleratorPed

alChangesWithinaP

eri


15/28

od

F

i

g

u

re

4

H

e

r

e

,

dr

i

v

i

n

g

c

o

nd

it

i

o

n

i

s

c

la

s

s

if

i

e

d

u

si

n

g

a

l

i

n

g

u

i

s

t

i

c

v

a

r

i

a

b

l

e

.

T

h

e

v

a

r

i

a

b

l

e

l

i

n

g

u

i

s

t

i

ca

l

l

y

i

n

t

e

r

p

r

e

t

s

t

h

e

a

m

p

li

t

u

d

e

of

a

c

c

e

l

e

r

a

to

r

p

e

d

a

l

c

h

an

g

es

withi

n a

cert

ain

peri

od.


16/28

On dry surface, the

carreaches a velocity

of 20 MPH in 3.5 s,

with top speeds up to

50 MPH. The speed for

most experiments

ranges from 20 to

30 MPH. Each wheel

features individual

suspension and has a

separate shock

absorber. The carhas

diskbrakes and a lock-

able differential [10].

The cars controlleruses the

Position

Orientation

Ultrasound Beams

possible situation.

In a fuzzy-logic

system, every element

is self-explana- tory.

Linguistic variables are

close to the human

representa- tion of

continuous concepts.

Fuzzy if-then rules

combine these

concepts much the

same way humans do.

Fuzzy logic isnonlinear and

multiparametric by nature. So,

mother

boa

rd

of anote

boo

k

PC

connected

to aninterface

board

Figure 5Threeultrasoundsensorsguidethe

car inthetrack.

it

canbettercopew

it

hc

om

plex

controlproblemsthatar

ealso


17/28

drivi

ng

the

actu

ators

and

sensors.

Ac-

tuat

ors

are

pow

er

steer

ingservo

,

disk

brak

e

servo

, and

puls

e-

widt

h

mod

u-

lated

mot

or

cont

rol.

Se

nsors

are

three

ultra

soun

d

(US)

dista

nce

senso

rs

for

trac

king

guid

ance

(seeFigu

re 5)

and

infr

ared

(IR)

refle

x

sensors

in

each

whe

el

for

spee

d.

Thecont

rol

loop

time

fro

m

read

ing

in

sens

or

sign

als

to

setti

ng

the

valu

es

for

the

actua

tors

is

10

ms.To

meas

ure

the

dyna

mic

state

of

thecar

(e.g.,

skid

ding

and

slidin

g),

IR

sensors

meas

ure

the

indiv

idual

spee

d of

all

four

whe

els.

Eval

uatin

g

whe

el-

speed

diffe

renc

e

s

,

t

h

e

fu

z

z

y

-

l

o

g

ic

s

y

s

-

t

e

m

i

n

t

e

r

p

r

e

t

s

t

h

e

c

u

r

r

e

nt

s

i

t

u

a

t

io

n

.

T

h

r

e

e

f

i

x

e

d

-

m

o

un

t

e

d

U

S

s

e

n

s

o

r

s

m

e

a

s

u

r

e

t

h

e

di

s

t

a

n

c

e

t

ot

h

e

n

e

x

t

o

b

-

s

t

a

c

l

e

t

o

t

h

e

f

r

o

n

t

,

l

e

ft

,

a

n

d

ri

gh

t.

T

h

i

s

s

e

tu

p

p

e

r

m

it

s

au

t

o

n

o

m

o

u

s

o

p

e

r

a

ti

o

n

o

f

t

h

e

c

a

r

.L

o

w

-

c

o

s

t

s

e

n

s

o

r

s

w

e

r

e

i

n

-

t

e

n

t

i

o

n

a

l

l

y

u

s

e

d

in

t

hi

s

s

t

u

d

y

ra

t

h

e

r

th

a

n

CC

D

c

a

m

er

a

s

a

n

d

i

m

a

g

e-

re

c

o

g

ni-

tion

techn

iques

to

show

thatexpen

- sive

senso

rs can

be

replac

edby

a

fuzzy-logiccontr

ol

strate

gy.

Figu

re 6

shows

a

sample

experi

ment

involv

ing

the

model

car.

Theobsta

cle

isplaced

rightafter

thecurve

, sothe

US

sensors

ofthe

cardetecttheob-

stacle

too

late.

To

not hit

the

obstacle, the

carhas

to

decide

for a

very

rapid

turn.

Tooptimi

ze the

steerin

g

effect,

the

anti-

skid

control

ler

must

reduce

the

desired

steerin

g angle

to the

maxim

um the

road

can

take

,

avoi

ding

both

slidi

ngand

hitti


18/28

ng

the

obst

acle

.

MODELBASEDVS.FUZZYLOGIC

In

theory,

you can

build a

mecha

nicalmodel

for a car

and

derive

a

mathe

mati-

cal

modelwith

differe

ntial

equati

ons to

imple

ment a

model-

based

control

ler.

In

reality,

the

compl

exity

ofthis

ap-

proach

is

overw

helmi

ng,

and

the

result-

ingcontro

ller

would

be

diffic

ult to

tune.

He

re isthe

poin

t for

fuzzy

logic

:

race-

car

drivers

can

cont

rol a

car

in

extr

eme

situa

tion

s

very

well

with

out

solvi

ng

diffe

renti

al

equat

ions.

Henc

e,

there

must

be analtern

ative

way

for

anti-

skid

steeri

ng

control.

This

alterna

tive

way is

to

represe

nt the

drivingstrateg

y in

engine

ering

heurist

ics.

Althou

gh

there

are

multip

le ways

of

expres

sing

engine

ering

heuris-

tics,

fuzzy

l

o

g

i

c

ha

s

p

r

o

v

e

n

v

e

r

y

e

f

f

e

c

-

t

i

v

e

f

o

r

t

h

e

f

o

l

lY

contra

st

other

metho

dsexpres

sing

if-

then

causal

ities

(e.g.,

expert

syste

ms),

the

comp

utatio

n

fuzzy-

logic

syste

m

quanti

tative

rather

than

symb

olic.

fuzzy-

logic

system,

use

few

rules

to

press

gener

al

situations,

and

then

the

fuzzy-

logic

algo-rithm

deducesdecisionsfor

n

o

n

li

n

e

ar

a

n

d

in

v

ol

v

em

ul

ti

pl

e

p

ar

a

m-

et

e

rs

.

A

n

d

fi

n

al

ly

,

fu

zz

y

lo

gi

c

ca

n

b

e

e

f

f

i

-

c

i

e

n

t

l

y

i

m

p

l

e

m

e

nt

e

d

i

n

e

m

b

e

d

d

e

d

c

o

n

t

ro

l

a

p

pl

ic

atio

ns

.

E

ve

n

on

a

sta

n

d

ar

d

m

ic

ro

co

nt

ro

ll

er

,

a

fu

zz

y-

lo

gi

c

s

y

st

e

m

ca

n

outpe

rform

a

comp

arable

conve

n-tional

soluti

on

both

by

code

size

and

computing

speed.

DESIGNANDIMPLEMENTATION

Pho

to 2

shows

the

first

versio

n ofa

fuzzy-

logic

contro

ller

for the

car.

The

object

ive for

this

contro

ller

was

auton

o-

mou

s

guid

ance

of the

car in

thetrack

at

slo

w

spe

ed,

wh

ere

noski

ddi

ng

an

d

sli

din

g

yetocc

urs

.

In

Phot

o 2,

the

lowe

rrule

bloc

k

uses

the

dista

nces

mea

sure

dby

thethre

e US

senso

rs to

deter

mine

the

steering

angle.

The

upper

rule

block

imple

ment

s asimpl

e

speed

contr

ol by

using

the

dista

nce to

the

next

obsta

cle

meas

ured

by the

front

US

senso

r and

the

speed

of one

front

wheel

only.

Due

to the

slow


19/28

speed

s, no

skiddi

ng or

slidin

g

occurs. All

wheel

speed

s are

the

same.

Th

is

firstversi

on

of

the

fuzz

y-

logi

c

controll

er

cont

aine

d

abo

ut

200

rule

s

and

took

only

a

few

hou

rs to

impl

e-

me

nt.

T

he

sec

on

dver

sio

n of

the

fuz

zy-

logi

c

contr

oll

er

im

ple

me

nts

a

more

co

mp

lex

fuz

zy

sys

te

m

for

dy

na

mi

c

sta

bili

ty

co

ntr

ol. It

incl

udes

antil

ock

brak

ingas

well

as

tract

ion

and

antiski

dsteering

control (seePhoto

3).Thi

s600-rulefuzzy-logic

controllerhastwostages ofthefuzzyinference.Thefirst

stage,representedbythethreeleftruleblocks,estimates

the

Figure 6

In

this

examp

le

of

a

n

e

x

p

eri

m

e

nt

,

th

e

c

ar

sul

tr

a

s

o

u

n

d

s

en

s

or

s

wi

ll

d

et

e

ct

th

e

o

b

st

a

cl

e

pl

a

ce

d

t s

t

a

t

e

va

r

i

a

b

l

e

s

o

f

t

h

e

c

ar

s

d

y

n

a

m

i

c

s

i

t

u

a

ti

o

n

f

r

o

m

s

e

n

s

o

r

d

at

a

.

T

h

e

t

w

o

l

o

w

e

r

r

u

l

e

b

l

o

ck

s

e

s

t

i

m

at

e

s

k

i

d

d

i

n

g


20/28

and sliding states from

speed sensor signals,

while the upperrule

block estimates the

carsposition and

orientation in the

test track.

Note that theoutput of

the left three rule blocks

Development

System (PC)Serial Link

Real-Time

OnlineCode

Communication

Manager

OnlinePar

Changes

system was

modified on- the-

fly for

optimization.

The fuzzy-logic

code is separated

into two seg-

ments. One

contains all static

partscode that

doesnt need to be modi-

t

h

e

st

a

t

e

v

a

r

i

a

b

l

e

e

s

t

i

m

a

-

t

i

o

n

is

Pre

DC

Dynamic

C

odeB


21/28

f dmatedstateofthe

carcanth

erefor

ebe

the

positionisratherleft

,

whil

ethe

orienta-

P(

S(

thecodecon

tainingm

e

m

b

e

r

sh

i

p

f

u

n

c

t

i

on

s

o

f

t

he

l

i

n

g

u

i

s

t

i

c

v

a

rtionisstron

glytotheright,andth

ecarskidsovertheleft

Figure

7The

fuzzyT

ECH

Online

Edition

feature

s both

visualiz

ation of

runnin

g

system

and

modific

ations

on-the-fly.

in

fe

re

nce

st

ruc

t

ure,

a

nd

th

er

ule

s.

frontw

heel.

T

he

se

co

nd

sta

ge,re

pr

e

s

en

t

e

d

b

y

t

h

et

h

re

e

right

rul

e

bl

oc

ks,

us

es

thes

e

e

s

t

i

m

a

ti

o

n

s

a

s

i

np

u

t

s

t

o

de

t

e

r

m

i

n

e

t

h

e

b

e

s

t

c

o

n

t

r

o

l

a

ct

i

o

n

f

o

r

t

h

a

t

d

r

i

v

i

n

g

s

i

t

u

a

t

i

o

n

.

T

h

e

u

p

p

e

r

r

u

le

b

l

o

c

k

d

et

e

r

-

m

i

n

e

st

h

e

s

t

e

e

r

i

n

g

a

n

g

l

e

,

t

h

e

m

i

d

d

le

on

e

th

e

e

n

g

i

ne

p

o

w

e

r

to

b

e

a

p

p

li

e

d,

a

nd

thelo

w

er

o

neth

eb

rak

e

for

ce

.S

u

c

h

a

t

wo

-

s

t

a

g

e

co

n

t

r

o

l

s

t

r

a

t

e

g

y

i

s

s

i

m

il

a

r

t

ot

h

e

h

u

m

a

n

be

h

a

v

i

o

r.

It

f

i

r

s

t

a

n

a

l

y

z

e

s

t

h

e

s

it

u

ati

on

and

then

dete

r-

min

esthe

acti

on.

It

also

allo

ws

for

efficient

opti

miz

atio

n,

sinc

e the

tota

l

of

600

rule

struc

tures

in six

rule

bloc

ks

can

be

desig

ned

and

opti

mize

d

inde-

pend

ently

.

T

he

firs

t

ver

sion

of

the

co

ntr

oll

er

wa

sonl

y

abl

e to

gui

de

the

car

onau-

ton

om

ou

s

cru

ise

(se

e

Ph

oto

2).

Th

e

sec

on

d

ver

sio

n

also

succ

eed

ed

to

dy-

namicall

y

stab

ilize

the

cars

crui

se

via


22/28

ABS,tractioncontrol, andASS(see

Photo3).

Ho

wever

, this

versio

n

requir

ed a

muchlonger

desig

n time

before

the

result

s were

compl

etelysatisfa

ctory.

The

secon

d

versio

n also

uses

advan

ced

fuzzy-

logic

techno

logies

such

as

FAM

infere

nce

[11]

and

the

Gam

ma

aggre

gatio

nalopera

tor

[12].

ONLINEDEVELOPMENT

Thedevel

opm

ent of

the

fuzzy

-

logic

syste

mused

the

fuzzy

TEC

H

softw

are

prod

uct

[11].

Give

n the

graph

ical

defi-

nitio

n of

the

syste

m

structu

re (cf.

Photo

s 2 and

3), the

lingui

sticvariab

les,

and the

rule

bases,

fuzzyT

ECHs

com-

pilergenera

tes the

syste

m as C

or

assem

bly

code.

Thiscodewas

implementedon a

PC

board

moun

ted on

the

car.

Figure

7

shows

how

the

running

fuz

zy-

logi

c

T

h

e

d

y

na

m

i

c

s

e

g

me

n

t

i

s

d

ou

b

l

e

d

,

w

i

t

h

o

n

l

y

o

n

e

o

f

t

h

e

se

g

m

e

n

t

s

a

cti

v

e

at

the

sa

m

e

tim

e.

In

thi

s

sit

ua

tio

n,

th

e

pa

rs

er,

lin

ke

d

to

the

de

v

e

l

o

p

m

en

t

P

C

v

i

a

a

c

o

m

m

u

n

i

c

a

t

i

o

n

s

m

a

n

a

g

e

r

,

c

a

nT

r

u

n

n

i

ng

s

y

s

t

e

m

w

i

t

h

o

u

t

h

a

l

t

i

n

g

o

r

c

o

m

p

i

l

i

n

g

.

A

t

th

e

sa

me

ti

m

e,

th

e

e

nt

ire

in

fe

re

n

c

e

fl

o

w

in

si

d

e

t

h

e

f

u

z

z

y

-

lo

gi

c

c

o

nt

r

o

l

l

e

r

i

s

g

r

a

p

h

ic

a

l

l

y

v

i

s

u

a

l

i

z

e

d

o

n

t

h

e

P

C

,

s

i

n

c

e

th

e

c

om

-

m

u

n

ic

at

i

on

s

m

a

n

a

g

e

r

al

s

o

tr

a

n

sf

e

rs

al

l

r

e

al

-

ti

m

e

d

at

a.

Th

e

ASS

exa

mple

demonstr

ates

the

appli

cabil

ity of

fuzz

y-

logictech

nolo

gies

for a

com

plex

cont

rol

problem

foun

d

in the

auto

moti

ve

indu

stry.

The

syste

m

was a

strai

ghtfo

rwar

d

desig

n

based

on

exp

eri

me

ntal

exp

erience

wit

hou

t a

mat

he

mat

ical

model

of

the

pro

ces

s.

D

uri

ngopti

miz

atio

n,

the

con

trol

stra

teg

y

was

easy

to

opt

imi

ze

due

to

thelin

guist

ic

repr

esen

tatio

n

inherent

in

the

fuzz

y-

logic

syste

m.

Tests

and

verif

icati

on

were

expe

dited

due

to

the

contr

oller

s

trans

pare

ncy.

And,

the

poor

com

putat

ional

perf

orm

ance

of

early

fuzz


23/28

y-

logic

softw

are

soluti

ons

wasoverc

ome

via a

new

gener

ation

of

soft

ware-

impl

eme

ntat

ion

tool

s [2,

13].

Inthe

rem

ain

der

of

this

arti

cle,

Ipro

vide

an

over

view

of

other

auto

mo-tive

appli

catio

ns

wher

e

fuzzy

logic

hasbeenusedsuccessf

ully.

Photo 3

Heres thesecond version

of the fuzzy-

logic controller.

The controller

uses advanced

fuzzy-logic

design

technologies

and contains a

total of 600rules.

HVACINCARS

F

uzz

y-

logi

c

desi

gn

tech

nol

ogie

s

are

well

-

esta

blis

hed

in

heat

ing

and

aircon

ditioni

ng of

reside

nces

and

offices

.Hence

, its no

surpris

e that

many

car

manuf

acture

rs alsouse

fuzzy

logic in

th

ei

r

H

V

A

C-

s

y

st

e

m

d

e

sig

n

s.


24/28

Photo 4This graph depicts the control surface of the air conditioners

blower-speed control. Blower speed is determined by temperature error

and engine-coolant temperature.

with automatic gearbox and

ABS as testvehicle. The

fuzzy-logic controllerruns on

an 8-bit microcontroller.

The car uses a speed sensor

and a single-beam telemeter

for the distance to the next

car. The actuators com- mand

brake pressure and

accelerator. Tests show the

fuzzy-logic controllercan

handle the cruise underall

the tested conditions.

Future regulations in the

European Community (EC)

require a speed control forlimiting truck speeds on roads

in Europe. Todays speed

limiters use adaptive PID-

type controller. However, the

resulting truck behavioris

unsatis- factory, compared to

an experienced driver.

Therefore, a numberofrecent de-Whil

e most

car

manufa

cturers

workon

these

systems

, very

few

publish

their

efforts.

The

control

approac

h in

general

and

hencethe use

of

fuzzy

logic

in the

design

differ

signifi

cantly

for

each

manuf

acture

r. In

this

sectio

n, I

use an

exam

ple

thatFord

Motor

Compa

ny

develo

ped in

the U.S.

[14].

The

fundam

ental

goal of

HVAC

in cars

is to

make

vehicle

occupa

nts

comfort

able.Human


25/28

comfort, however,

is a complex

reaction,

involving physi-

cal,biological, and

psychological re-

sponses to thegiven conditions.

Theperformance

criterioncomfort

is not some

well-defined

mathematical for-

mulabut a

sometimes

inconsistentand empirically

determined goal.

Typical HVAC-

system sensors

measure cabin

temperature,

ambient

temperature, sun

heating load,

humid- ity, and

other factors.

Typical actuators

are variable speed

blowers, means

forvarying air

temperature,

ducting, and doors

to control the

direction ofair-

flow, and the ratio

of fresh to recircu-

lated air. This

multiple-input,

multiple-output

control problem

doesnt fall into

any convenient

cat- egory oftraditional

control theory.

Photo 4 shows

the control

surface of a part

of a HVAC

systemthe

blower-speed

control. Blowerspeed depends on

two input

variablesthe

temperature

error (i.e., the in-

car tem-

perature minus

the set-point

temperature)and the engine-

coolant

temperature.

Photo 5 shows

the rule base. Ifthe

temperature error is

zero, lowblower

speed is desired. If its

too hot inside (i.e.,

positive

temperature error),

high blowerspeed isneeded to cool the

cabin.

If the error is

negative,

indicating that its

too cold inside, and

the engine is cold,

little blowerspeed

is neededfordefrost. If the

error is negative

but the engine is

warm, high blower

speed is needed to

heat up the cabin.

OTHERAPPLICATIONS

This sectionbriefly introduces

someother

examples offuzzy-

logic control in

automotive

engineering. For

details, refer to the

papers cited.

Peugeot CitronofFrance devel-

oped a fuzzy-logic

system for an intel-

ligent cruise

control [15]. The

system combines

multiple functions

forau- tonomous

intelligent cruisecontrol (i.e.,

following another

vehicle,

stop and

go

procedu

res, and

emerge

ncystop).

The

system

uses

three

fuzzy-

logic

blocks

withfour

inputs,

one

output,

and 30

rules

each.

Optim

ization

and

verificati

on ofthe

rule base

used a

Citron

XM

sedan

P

ho

t

o

5

T

h

e

r

u

l

e

b

a

s

e

f

o

r

b

l

o

w

e

r-

s

p

e

e

d

c

o

n

t

r

o

l

s

h

o

w

s

h

o

w

t

h

e

t

wo

v

a

r

i

a

b

l

es

o

f

e

n

g

i

ne

t

e

m

p

e

r

a

t

u

r

e

a

n

d

t

e

mp

e


26/28

ra-

ture

error

affec

t

blow

er

speed.

signs use fuzzy-

logic control to

achieve robust

performance,

even under the

strong load

changes ofcommercial

trucks [16, 17].

A paper from

Ford Electronics

de- scribes the

design of a

traction-control

system for a

radio-controlledmodel car[18].

The fact that Ford

publishes model-

carapplications is

symptomatic of

the fear ofmany

automotive

manufacturers

to admit thatthey use fuzzy

logic

as a design

technique forreal cars.

THE FUTURE ISFUZZY

Over the past

five years, fuzzy

logic has

significantly

influenced the

design of

automotive

control systems.Since using fuzzy

logic involves a

paradigm shift in

the design of a

control system,

five years is a short

period. The move

from analog to

digital solutionshas taken a much

longertime.

The key reason

for fuzzy logics

suc- cess in

automotive

engineering lies in

the implications

of itsparadigm

shift. Previously,

engineers spent

much time

creating

mathematical

models ofme-

chanical systems.

More time went

to


27/28

real-world road tests that

tuned the fudge factors of the

control algorithms.

Ifthey succeeded, they

ended up with a control

algorithm ofmathemati- cal

formulas involving many

experimental parameters.

Modifying orlateroptimizing

such a solution is very diffi-

cult because of its lack of

transparency.

Fuzzy logic makes this design

process faster, easier, and

more transparent. It can

implement control strategiesusing elements ofeveryday

language. Every- one familiar

with the control problem can

read the fuzzy rules and

understand what the system

is doing and why.

It also works forcontrol

systems with many control

parameters. Design- ers canbuild innovative control sys-

tems that would have been

intractable using traditional

design techniques.

The future for fuzzy logic in

automotive engineering is

bright. Semicon- ductor

manufacturers are

incorporating fuzzy-logicinstruction sets in their

controllers. Motorolajust

introduced the new 68HC12

family of

16-bit micros that integrate

a com-plete instruction set

for fuzzy logic at no extra

cost.

Anothernew development

is the upcoming IEC 1131-7

fuzzy-logic standard [19].

This international

standard defines

consistent fuzzy-logic

development and

documentation

procedures.

With these twodevelopments, de-

signing with fuzzy logic

becomes a much simpler

task.

Constantin von Altrock

began re- search onfuzzy

logic with Hewlett-

Packardin 1984. In 1989,hefoundedandstill

manages the Fuzzy

Technolo-giesDivision of

Inform Software

Corp., a market leaderin

fuzzy-logic development

tools and turn-key appli-

cations. You may reach

Constantin [email protected].

REFERENCES

[1] Intel, Fuzzy Anti-

Lock Braking

System,

developer.intel.com/

design/MCS96/DESIG

NEX/2351. htm, 1996.[2] Benchmark

Suites forFuzzy

Logic,

www.fuzzytech.co

m/e_dwnld.htm,

1997.

[3] N. Matsumoto et al.,

Expert antiskid system,

IEEEIECON87,

810816, 1987.

[4] C. von Altrock,FuzzyLogic

andNeuroFuzzy

Applications Ex-plained,Prentice Hall, Englewood

Cliffs,NJ, 1995.

[5] H. Kawai et al., Engine

control system,Proc. of the

Intl Conf. on FuzzyLogic and

NeuralNetworks, Iizuka,

Japan, 929937, 1990.

[6] L. Feldkamp and G.

Puskorius, Trainable fuzzyand neural-fuzzy systems for

idle-speed control,

2nd IEEE Intl. Conf. onFuzzy

Systems, 4551, 1993.

[7] H. Takahashi, K. Ikeura, and

T. Yamamori, 5-speed

automatic transmission

installed fuzzy reason- ing,

IFES91FuzzyEngineering

toward Human Friendly

Systems,

11361137, 1991.

[8] H. Ikeda et al., An

intelligent automatic

transmission control using

a one-chip fuzzy inference

engine, Proc. of the Intl.

Fuzzy Systems and

Intelligent Control Conf. in

Louisville, 4450, 1992.

[9] P. Sakaguchi et al.,

Application of fuzzy logic to

shift scheduling method for

automatic transmission,

2nd IEEE Intl. Conf. on

Fuzzy Systems, 5258, 1993.

[10] C. von Altrock, B. Krause,and H.-J. Zimmermann,
mailto:[email protected]://www.fuzzytech.com/http://www.fuzzytech.com/http://www.fuzzytech.com/http://www.fuzzytech.com/mailto:[email protected]


28/28

Advanced fuzzy logic

control of a model carin

extreme situations,Fuzzy

Sets and Systems, 48:1, 41

52, 1992.

[11] INFORM GmbH/Inform

Soft- ware Corp.,fuzzyTECHand

NeuroFuzzy Module 5.0

UsersManual, Chicago,

IL, 1997.

[12] H.-J. Zimmermann and U.

Thole, On the suitability of

minimum andproduct

operators for the inter-

section of fuzzy sets,FuzzySets and Systems, 2, 173

186, 1979.

[13] C. von Altrockand B.

Krause, On-Line-

Development Tools forFuzzy

Knowledge-Base Systems of

Higher Order, 2nd Intl

Conf. on FuzzyLogic and

Neural Networks

Proceedings, Iizuka, Japan,

1992.

[14] L.I. Davis et al., Fuzzy

Logic forVehicle Climate

Control, 3rdIEEE Intl.

Conf. onFuzzy Sys- tems,

530534, 1994.

[15] J.-P. Aurrand-Lions, M. des

Saint

Blancard, and P. Jarri,

Autonomous

Intelligent Cruise

Control with Fuzzy

Logic,EUFIT931st

Eur. Congress onFuzzy

andIntelligent

Technologies, Aachen,

17, 1993.

[16] V.M. Thurm, P.

Schaefer, and W.

Schielen, Fuzzy

Control ofa Speed

Limiter, ISATA Conf.,

1993.

[17]www.fuzzytech.com/e_a_

spe.htm.[18] R. Russ,

Designing a Fuzzy

Logic Traction

Control System,

Proc. of the

Embedded Systems

Conf., 2, 183196,

1994.[19]www.fuzzytech.com/e_iec.htm.

SOURCES

fuzzyTECHDevelopment System

Inform Software Corp.

2001Midwest Rd.

Oak Brook,

IL 60523

(630) 268-

7550

Fax: (630)

268-7554

www.fuzzyt

Motorola MCU Information

P.O. Box 13026

Austin, TX 78711 (512)

328-2268, x985

www.mcu.motsps.com

www.fuzzytech.com/moto

rola.htm

Circuit Cellar INK, the ComputerApplications Journal. Reprinted by

permission. For subscription

information, call (860) 875-2199 or

subscribe circellar.com
http://www.fuzzytech.com/e_a_spe.htmhttp://www.fuzzytech.com/e_a_spe.htmhttp://www.fuzzytech.com/e_iec.htmhttp://www.fuzzytech.com/e_iec.htmhttp://www.fuzzytech.com/http://www.mcu.motsps.com/http://www.fuzzytech.com/motorola.htmhttp://www.fuzzytech.com/motorola.htmhttp://www.fuzzytech.com/e_a_spe.htmhttp://www.fuzzytech.com/e_a_spe.htmhttp://www.fuzzytech.com/e_iec.htmhttp://www.fuzzytech.com/e_iec.htmhttp://www.fuzzytech.com/http://www.mcu.motsps.com/http://www.fuzzytech.com/motorola.htmhttp://www.fuzzytech.com/motorola.htm

fuzzy logic in automobiles

Documents