ME

58

1/ E

CE

573 F

uzzy Logic C

ontrol Systems

Fall 2007

Instructor: D

r. Dean E

dwards

Office:

BE

L 319

Office H

ours: M

,W -

3:30 p.m. to 5:00 p.m

.

Course H

ours: M

WF

, 10:30 a.m. to 11:20 a.m

. in JEB

026

Resource B

ook: "F

uzzy Logic" by John Y

en and Reza L

angari, Prentice H

all.

Reference B

ooks: "A

n Introduction to Fuzzy C

ontrol," by Driankou, et.a1., S

pringer-Verlag.

"Modem

Control S

ystems," by R

ichard C. D

orf, Addison W

esley, 10th

Edition.

"Neural N

etworks and F

uzzy System

s," by Bart K

osko, Prentice H

all.

"Fuzzy C

ontrol System

s," by A. K

audel and G. L

angholz, CR

C P

ress.

Softw

are: M

atlab

Prerequisites:

ME

481, EE

470 or permission.

Grading:

Grade w

ill be based on a semester project.

U o

fl V

ideo H

W A

ssigned (Notebook)

10%

15%

Proposal (P

roblem D

efinition) 15%

15%

D

raft Report

15%

20%

Presentation

20%

Final Report

40%

50%

Total

100%

100%

Course O

bjective: T

o familiarize students w

ith fuzzy logic control systems so that they can

analyze, model, and design these system

s.

/

ME

58

1/ E

CE

573 F

uzzy Logic C

ontrol Systems

Course O

utline

Chapter 1

Introduction

Notes

Review

of C

lassical Control System

s

Chapter 2

Basic C

oncepts of F

uzzy Logic

Notes

Linear E

quivalent Fuzzy L

ogic Control S

ystem (L

EF

LC

)

Chapter 3

Fuzzy S

ets

Chapter 4

Fuzzy R

elations, Fuzzy G

raphs, and Fuzzy A

rithmetic

Chapter 5

Fuzzy If-T

hen Rules

Project P

roposal

Chapter 6

Fuzzy Im

plications and Approxim

ate Reasoning

Chapter 7

Fuzzy L

ogic and Probability T

heory

Chapter 8

Fuzzy L

ogic in Control E

ngineering

Draft P

roject Report

Chapter 14

Fuzzy M

odel Identification

Chapter 9

Hierarchical Intelligent C

ontrol

Chapter 10

Analytical Issues in F

uzzy Logic C

ontrol

Project P

resentations

Final P

roject Report

.,

-I

580 F

uzzy Control System

s

A F

UZ

ZY

LO

GIC

CO

NT

RO

LL

ER

F

OR

A R

IGID

DISK

DR

IVE

Shuichi Y

oshida Inform

ation Equipm

ent Research L

aboratory M

atsushita Electric Industrial C

o., Ltd.

Osaka, 571 Japan

1. IN

TR

OD

UC

TIO

N

With

the recent

trends tow

ard more

powerful

personal co

mp

uters

and w

orkstations has emerged a dem

and for magnetic rigid disk drives (R

DD

) and other peripheral storage devices w

hich are smaller in

size and provide greater storage capacities w

ith increased rates of data transfer to host com

puters. (See F

ig. 1.) T

he time for data transfer is determ

ined by the seek time required by the head

reading the data. This is the tim

e to move from

one data cylinder to the target cylinder. T

he seek time is lim

ited by the performance of the actuator m

oving the head as well as

by the control method.

This chapter show

s how to reduce seek tim

e, through a bang-bang controller em

ploying fuzzy logic together with a m

ethod for correcting for changes in actuator coil resistance and actuator force unevenness[l ,2,3].

Fig. 1

External V

iew of a R

igid Disk D

rive

9 C

OM

PA

RIS

ON

OF

FU

ZZ

Y

AN

D N

EU

RA

L

TR

UC

K B

AC

KE

R-U

PP

ER

C

ON

TR

OL

SY

ST

EM

S

Seon~~Gol'rKon

g and Bart K

osko

FU

ZZ

Y A

ND

NE

UR

AL

CO

NT

RO

L S

YS

TE

MS

In this chapter we develop fuzzy and neural system

s to back up a simulated

truck, and truck-and-trailer, to a loading dock in a planar parking lot. W

e use dif­ferential com

petitive learning and the product-space clustering technique, discussed in C

hap

ter 8, to adaptively generate fuzzy-associative-mem

ory (FA

M) rules from

training data taken from

the fuzzy and neural simulations.

We developed the neural truck system

s on the design recently proposed by N

guyen and Widrow

[1989]. W

e trained the neural truck systems w

ith the back­propagation learning algorithm

, discussed in Chapter 5.

In principle product-space clustering can convert any neural black-box system

into a representative set of FA

M

rules.

339

340 C

OM

PA

RIS

ON

OF

FU

ZZ

Y A

ND

NE

UR

AL C

ON

TR

OL S

YS

TE

MS

C

HA

P. 9

loading dock (xf · Yf)

I

rear

front

FIG

UR

E 9.1

Diagram

of simulated truck and loading zone.

BA

CK

ING

UP

A T

RU

CK

Figure 9.1 show

s the simulated truck and loading zone. T

he truck corresponds to the cab part o

f the neural truck in the Nguyen-W

idrow neural truck backer-upper

system.

The three state variables ¢

, x, and y exactly determine the truck position.

¢ specifies the angle o

f the truck with the horizontal.

The coordinate pair (x, y)

specifies the position of the rear center o

f the truck in the plane. T

he goal w

as to make the truck arrive at the loading dock at a right angle

(¢f =

90°) and to align the position (x, y)

of the truck w

ith the desired loading d

ock

(x

f. Yf).

We considered only backing up.

The truck m

oved backward by

some fixed distance at every stage.

The loading zone corresponded to the plane

[0. 100] x [0.

100], and (Xf.

Yf) equaled (50, 100).

At every stage the fuzzy and neural controllers should produce the steering

angle e that backs up the truck to the loading dock from any initial position and

from any angle in the loading zone.

Fu

zzy Tru

ck Backer-U

pp

er System

We

first specified each controller's

input and output variables.

The

input variables w

ere the truck angle ¢ and the x-position coordinate x. Th

e output variable w

as the steering-angle signal e. W

e assumed enough clearance betw

een the truck and the loading dock so w

e could ignore the y-position coordinate. T

he variable ranges w

ere as follows:

0~x~100

-90

~ ¢

~ 270

-30

:; e:; 30 P

ositive values of e

represented clockwise rotations o

f the steering wheel.

Negative

values represented counterclockwise rotations.

We discretized all values to reduce

BA

CK

ING

UP

A T

RU

CK

(a)

(b) (c)

FIG

UR

E 9.6

Sam

ple truck trajectories of the fuzzy controller for initial positions (x, y, C/»: (a) (20, 20, 30), (b) (30, 10, 220), and (c) (30, 40, -1

0).

examples o

f the fuzzy-controlled truck trajectories from different initial positions.

The fuzzy control system

did not use ("fire") all FAM

rules at each iteration. Equjva­

lently most output consequent sets are em

pty. In most cases the system

used only one or tw

o FA

M rules at each it~ration. T

he system used at m

ost 4 FAM

rules at once.

345

353 B

AC

KIN

G U

P A

TR

UC

K

(a) Docking E

rror

Back-up T

rial -

DC

L-A

FAM

(solid) m

ean = 1.4449.

s.d. = 2.2594

-B

P-AFA

M

(dashed): m

ean = 6.6863.

s.d. = 1.0665

(b) Trajector}' E

rror, 5

~

:::~W\i~ (' A, ~!j. j~ hi!b\tl\(: ,::;l t : :'L'~"'1\J![V~W\lilVr 'tJ v

vw~

..

II..

Be

1••

Back-up T

rial

-D

CL

-AFA

M (solid)

mean =

1.1075. s.d. =

0.0839 -

BP-A

FAM

(dashed): m

ean = 1.1453.

s.d. = 0.1016

FIG

UR

E 9.16

(a) Docking errors and (b) trajectory errors of the D

CL-A

FA

M and

BP

-AF

AM

control systems.

(x, y) (x

, y) : Cartesian

coo

rdin

ate of the rear end, [0,100).

(u, v) : C

artesian coordinate o

f the joint.

<Pt : A

ngle of the trailer w

ith horizontal, [-90,270).

<Pc: Relative angle o

f the cab with trailer, [-90,90j.

e:S

teering angle, [-30,30).

~ : A

ngle of the trailer u

pd

ated at each step, [-30,30].

FIG

UR

E 9.17

Diagram

of the simulated truck-and-trailer system

.

11

CO

MP

AR

ISO

N O

F F

UZ

ZY

A

ND

KA

LM

AN

-FIL

TE

R

TA

RG

ET

-TR

AC

KIN

G

··CO

NTR

OL S

YS

TE

MS

P

eter J. Pacjni and B

art Kosko

In Chapter 9, w

e compared fuzzy and neural system

s for the comparatively sim

ple control problem

of backing up a truck to a fixed loading dock in an em

pty parking lot.

In this chapter, we com

pare a fuzzy system w

ith a Kalm

an filter system for real­

time target tracking. T

he Kalm

an filter is an optimal stochastic linear adaptive filter,

or controller, and requires an explicit m

athematical m

odel of how

control outputs depend on control inputs. In this sense the K

alman filter is a paragon o

f math-m

odel co

ntro

llers-and

a challenging benchmark for alternative control system

s.

FU

ZZ

Y A

ND

MA

TH

-MO

DE

L CO

NT

RO

LLER

S

Fuzzy controllers differ from

classical m

ath-model controllers.

Fuzzy con­

trollers do not require a mathem

atical model o

f how control outputs functionally

depend on control inputs. F

uzzy controllers also differ in the type of uncertainty they

represent and how they represent it.

The fuzzy approach represents am

biguous or

fuzzy-system behavior as partial im

plications or approximate "rules o

f thu

mb

"-as

fuzzy associations (.-1.,. Bi ).

379

-I I

I-