Outline

* Introduction - Overview of Dyeing Processes - Current Status of Dyeing Process Control 9. DARG Approach to Dyeing Process Control

* Classical Fuzzy Logic Control - Basics of Fuzzy Logic Control - Structure of a Fuzzy Logic Controller

* Adaptive Fuzzy Logic Control - Self-scaling Factor Tuning Scheme - Self-Learning Scheme

* Fuzzy Logic Control for Multi-Input, Multi-Output Systems

- The Optimization Method - - Simulation Results .-

-.. * Concluding Remarks and Future Activities

Introduction Overview of Dyeing Processes

Description of Dyeing Processes

Influence Factors

- Controllable: Temperature, Time, pH, Salt, Liquor

- Uncontrollable: Fiber Shape and Properties, Con-

Ratio.. .

centration of Dye Sites, Merge, Maturity ... Current Market Trend

- Small Lots, High Quality, Quick Response ... Process Control

- Optimize Production EfFiciency, Improve Prod- uct Quality, Detect Mistaken Operations ...

Current Art of Dyeing Process Control

Open-Loop Control: Dyeing processes follow prede- termined standard procedures in order to produce consist en t resu Its.

Problems

- Different Process Requirements

- Uncontrollable Factors

- Mistaken Parameter Settings

- e e e e e e

DARG Approach to Dyeing Process Contro!

Closed-Loop Control: Dyeing processes are moni- tored and process parameters are adjusted on-line in such a way to arrive a t the desired end results.

Control Methods

- Parametric Methods: P ID, LQR ... - Nonparametric Methods: FL, ANN, ES ...

Reasons for Fuzzy Logic Control

- Lack of General Reliable Models

- Lack of Accurate On-Line Measurements

I

GOAL

DEVELOP A NON-MODEL (OR PARTIAL MODEL) BASED ADAPTIVE CONTROLLER FOR DYEING PRQCESSES.

APPROACH

EMPLOY FUZZY LOGIC CONTROL WITH

* SELF-LEARNING RULE BASE

* ON-LINE SCALING FACTOR TUNING

* APPLY METHOD TO DYEING PROCESS

* Issues For Discussion

Purpose of Control: Improve performance of system.

Control Strategies: * model-based vs. non-model based * what information is known before

start process with control?

Why Fuzzy Logic Control?

What are some of the important parameters in FLC?

How is FLC implemented in dyeing process?

What is the current state of FLC research that is applicable to the dyeing industry?

Classical Fuzzy Logic Control Basics of Fuzzy Logic Control

e Literature Review

- Theory of Fuzzy Sets and Fuzzy Logic(Zadeh,L.A.,

- Fuzzy Logic Control(Zadeh,L.A., 1973; Mam-

1965, 1968)

dani,E.H., 1974 ...)

e A Fuzzy Logic Controller: A knowledge-based con- troller that attempts to simulate the human control decision making using the theory of fuzzy logic and fuzzy sets.

Advantage of Fuzzy Logic Control

- Reject Disturbance - Cope with Nonlinearities - Adapt to New Situations

I

Fuzzy Logic Control

* Rule-Based

An Individual Rule is constructed using

IF <...qualitative terms ........... > THEN <....q ua/itative terms .... .... >

Examples of qualitative terms are:

big, small, hot, cold, fast, slow ...

A linguistic rule ( for balancing a stick):

IF the stick is inclined moderately to the left THEN move the hand quickly to the left.

These linguistic terms come from and are converted to numeric values

Rules are somewhat vague (resembling how humans think)

Fuzzy Set Theory allows a linguistic term to take on a range of values through a membership function.

I

Classical Fuzzy Logic Controller Algorithm:

1) Compute the current error (E) and rate of change of error (CE)

2) Convert numerical E and CE into fuzzy E and CE

3) Evaluate the control rules using the fuzzy logic operations

4) Compute the deterministic input required to control the process

* Fuzzifier: scaling, membership function

* Rule base: control surface

* Defuzzifier: scalar function

~ --

Structure of a Fuzzy Logic Controller

E

CE Fuzzifier

Control Rule Base 3-

Structure of a Fuzzifier

hmerical E Fuzzy E I

I

Numerical C Fuzzy C< -

Scaling Factors Membership Functions

Figure 2: Structure of a Fuzzifier

SCA

LIN

G F

AC

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FOR

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F IN

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OF

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ALE

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UM

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ICA

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4.0 {

2.0 {

-2.0

-4.0

+ -6.0 {

4.0- 1

11

11

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-4.0

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ror (

degr

ees)

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MEMBERSHIP FUNCTION:

TAKES SCALED VALUES AND ASSIGNS MEMBER- SHIP VALUES FOR EACH FUZZY CLASS

5'9" 62" 6'6" 5'0" 5'4" Universe of Discourse (U)

PURPOSE: FUZZIFY THE NUMERICAL VALUES INTO LINGUISTIC VALUES

INPUT: SCALED NUMERICAL VALUES

OUTPUT: FUZZY VALUES ACCORDING TO MEMBER- ~

SHIP CLASS AND MEMBERSHIP VALUE --

MANY DIFFERENT TYPES OF MEMBERSHIP FUNCTIONS CAN BE USED:

Bell Shaped Trapezoidal Triangular Sinusoidal

a b C d

* CAN CHOOSE DIFFERENT FUNCTIONS FOR DIFFERENT RANGE OF VALUES

* MUST SELECT HOW MEMBERSHIP CLASSES OVERLAP (COVER) RANGES OF VALUES

* FOR CONTROL PURPOSE, LINGUISTIC RULES USE MEMBERSHIP CLASSES LIKE LARGE POSITlVE OR SMALL NEGATIVE

I

Medium Positive 1 y = sin [K/4*(X-2)]

I I I

-6 -4 -2

Large Positive y = sin [K/4*(X4) J

- '

I 1

2 4 6

1

Medium Negative 1 - '

y = sin [rr/4*(x+6))

I I I

-6 3 -2 I I I

2 4 6

Small Positve y = sin [K/4*(X)]

-6 -4 -2 2 4 6

Large Negative 1 -- * y = sin [1~/4*(x+8)]

I I I

-6 -4 -2

Zero y = S i n [ K / 4 * ( X + 2 ) ]

I I I I I I

-6 -4 -2 2 4 6

-,

I I I

2 4 6

Small Negative y = sin [7t/4*(x+4)]

I I I I I I

-6 3 -2 2 4 6

I

LN MN S PI SP M p LP 1

< 1 1 \

-6 -4 -2 0 2 4 6 U

ANTECEDENT BLOCKS

Logic product example

Structure of a Rulebase

1) If E is LP, and CE is LP, then Ctrl is LN.

2) If E is LP, and CE is SP, then Ctrl is MN.

Fuzzy CE 0 0

Structure of a Rulebase

Rule Surface

-3

Fuzzy Process Control Input

Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (05%) (1:SP) (2:MP) (3:LP)

CONTROL RULE BASE:

* THIS IS THE ESSENTIAL COMPONENT OF THE FLC

PURPOSE: DEFINE CONTROL ACTION FROM FUZZY SET OF RULES AND FUZZY INPUT VALUES

INPUT: FUZZY SET OF VALUES OF INPUT

OUTPUT: FUZZY SET OF CONTROL ACTIONS

* MADE UP OF: IF <mmmQUALITATIVE TERMS=">

THEN <mmmmmQUALITATIVE TERMS".>

* EACH RULE MAY HAVE MANY CONDITIONS =

NEED WAY OF RESOLVING ONE RESULT: USE LOGICAL AND

*MAY HAVE MANY RULES, EACH OF WHICH DEFINES A CONTROL ACTION = NEED WAY OF RESOLVING -- ONE ACTION: USE LOGICAL OR

2 iD”

F iD”

F ii;

w E. (P

P w L

il Z

3 Z

i! Z

x z 0 0 0 0 0 b m

U

L

L

U

m

&

U 0 b c

i

U b U L a L

Structure of a Defuzzifier

Fuzzy Process Numerical Process

Control Input

Structure of a Defuzzifier

I

DEFUZZIFIER:

* TAKES FUZZY CONTROL ACTION AND PRODUCES A NUMERICAL CONTROL COMMAND

* MUST TAKE CONTROL ACTIONS FROM MULTIPLE MEMBERSHIP CLASSES AND PRODUCE ONE VALUE: USE METHOD OF CENTER OF GRAVITY

LN h4N SN SP MP LP

-6 -4 -2 0 2 4 6 U

PURPOSE: PRODUCE A NUMERICAL CONTROL COMMAND

INPUT: FUZZY CONTROL VALUE ~ --

OUTPUT: NUMERICAL CONTROL VALUE

Results

0 60 80 loo 40 20

1hI"min)

I a0 40 60 w loo

l i ~ . ( l l l l " )

- -- Process Response with and without Control(solid line : desired exhaustion) (dashed

line : actual exhaustion) (dashed-point line : controlled temperature)

Results

D"C-PROCESS(~OUr-CONTROL)

s

-.; Process Response with and without Control(solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

Adaptive f i z z y Logic Control Self-scaling Factor Tuning Scheme

Phase Portrait

Self-Scaling Factor Tuning Scheme

Else K,E+l = K,”

Else K,c+E1= KZE

Self-scaling Factor Tuning Scheme

IC:: scaling factor for E a t t i m e ti

K ? ~ : scaling factor for CE a t t i m e ti

L U P : length of universe of discourse for E LUDCE: length of universe of discourse for CE

6 and A: convergence coefficients (1 > 6, X > 0)

T h e sign(x) function is defined as

1 if x > o sign(x) = O if x = O

-1 if x < o

Results

I . . . . I . * . . ( . . . . I . . .

0 50 100 150 200

T"(min)

Process(With_Self_Tuning)

0 0 50 100 150 200

Xme(min)

Process Response with and without Self-tuning (solid line : desired exhaustion) (dashkd line : actual exhaustion) (dashed-point line : controlled temperature)

I

Vy Fuzzy/

Self-Learning Scheme

output

Control Rule Identification

* Copfroller > Process >

Structure of a self-Learning Fuzzy Logic Controller

If X i , And Y i , Then Zi = X i n Y i ' Z i

u(xi nYi) + z i

@ = f ( P , E , C E )

Results Rule Surface -- The Initial

-3

Process

0 z I 1 I I 1

The Initial Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

Results Rule Surface -- The First Run

-3

fime(min)

. The First Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

Results Rule Surface -- The Second Run

-3

Process

x/?

Time(min)

The Second Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:WI (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

Results Rule Surface -- The Third Run

-3

Process

Tirne(min)

. The Third Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

Results Rule Surface -- The Tenth Run

3

-3

Timc(min)

' The Tenth Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) ( 2 : ~ ) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

Results Rule Surface -- Tho Fifteenth R u n

-3

Process 0 E I I I 1 I

Process 0 E - l I I 1 I

_ - - - - c - -

* - - . L . _ . _ . _ . _ . _ . _ . _ . _ . J e d

I I

0 20 40 60 80 100 I I I I I I

0 20 40 60 80 100

Timc(min)

The Fifteen Run Control Rule Surface with (-3:LN) (-2:MN) (-1:SN) (0:ZE) (1:SP) (2:MP) (3:LP) and Process Response (solid line : desired exhaustion) (dashed line : actual exhaustion) (dashed-point line : controlled temperature)

f i z z y Logic Control for MIMO Systems

Rij: Rulebase between ith Input and jth Output

ej,Aej: Error and Error Change of j t h Output

Fuzzy Logic Control for MIMO Systems

Min

where

F =

I =

- fl f 2

Subject to : L < I(tn) < H

L , H are Constraints of Control Inputs

P, Q: Weighting Matrices

Results

Process

CO

0 0

I Q)

n N

0

I I I I

0 50 100 150 200

Tim e( min)

Process Response (solid line : dye component one) (dashed line : dye component two) (dashed-point line : dye component three)

~ --

I

Results

Process Response

0 0 7

0 03

- 0 o m W

f! e P

3 Y

P)

t-

0 Fl

0

Results

Control-Of-Temperature \

I I I I

0 50 00 150

Tim e( min)

Temperature Control

200

I

Results

Con trol-OCDye-Dosing

7 I I I I

I I 1 I

0 50 100 150 200

Time( min)

Dye Dosing Control

Results

Process

I I I I

I 4

f I I I I 1

0 50 100 150 200

Time(min)

Process Response (solid line : dye component one) (dashed line : dye component two) (dashed-point line : dye component three)

- --

I

Results

Process Response

Results

0 0 -

0 a3

Con trol-Of-Tempera ture

I I I I

0 cu

0 0 50 100 150

Time(min)

200

Temperature Control

I

Results

0

Control-Of-Dye-Dosing

I I I I 1

J 1

I , I I I I

50 100 150

Tim e( min)

200

Dye Dosing Control

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Concluding Remarks:

* Fuzzy Logic Control uses humanistic approach to define control rule base

* Fuzzy logic control does not require complete knowledge of the process being controlled

* Several parameters can be used to improve performance of FLC: scaling factor, adaptive control rule base, extension to MlMO case, selection of membership function, selection of membership ranges, defuzzifier function

* Have sho-wn through simulation results that adaptive FLC can be applied to the qe ing process

Future Activities:

* Experimental Implementation

* FLC Analysis - relationship to other control strategies - stability -- and convergence analysis