e_p_dv1industrial fuzzy

8/12/2019 e_p_dv1industrial fuzzy

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Industrial Application of

Fuzzy Logic Control

INFORM 1990-1998 Slide 1

Tutorial and Workshop

Constant in vo n Altrock

Inform Software Corporation2001 Midwest Rd.

Oak Brook, IL 60521, U.S.A.

German Version Available!

Phone 630-268-7550

Fax 630-268-7554

Email: [email protected]

Internet: www.fuzzytech.com

Fuzzy Logic Primer

History, Current Level and Further

Development of Fuzzy LogicTechnologies in the U.S., Japan, and

Europe

Types of Uncertainty and the

Modeling of Uncertainty

The Basic Elements of a Fuzzy Logic

System

Types of Fuzzy Logic Controllers


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History, State of the Art, and

Future Development


1965 Seminal Paper Fuzzy Logic by Prof. Lotfi Zadeh,

Faculty in Electrical Engineering, U.C. Berkeley, Sets

the Foundation of the Fuzzy Set Theory

1970 First Application of Fuzzy Logic in Control

Engineering (Europe)

1975 Introduction of Fuzzy Logic in Japan

1980 Empirical Verification of Fuzzy Logic in Europe

1985 Broad Application of Fuzzy Logic in Japan

1990 Broad Application of Fuzzy Logic in Europe

1995 Broad Application of Fuzzy Logic in the U.S.

2000 Fuzzy Logic Becomes a Standard Technology and Is

Also Applied in Data and Sensor Signal Analysis.

Application of Fuzzy Logic in Business and Finance.

Today, Fuzzy Logic Has

Already Become the

Standard Technique for

Multi-Variable Control !


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Applications Study of the

IEEE in 1996


About 1100 Successful Fuzzy Logic Applications Have

Been Published (an estimated 5% of those in existence)

Almost All Applications Have Not Involved the

Replacement of a Standard Type Controller (PID,..), ButRather Multi-Variable Supervisory Control

Applications Range from Embedded Control (28%),

Industrial Automation (62%) to Process Control (10%)

Of 311 Authors That Answered a Questionnaire, About

90% State That Fuzzy Logic Has Slashed Design Time

By More Than Half

In This Questionnaire, 97.5% of the Designers Stated

That They Will Use Fuzzy Logic Again in Future

Applications, If Fuzzy Logic Is Applicable

Fuzzy Logic Will Play a Major

Role in Control Engineering !


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Stochastic Uncertainty:

The Probability of Hitting the Target Is 0.8

Lexical Uncertainty:

"Tall Men", "Hot Days", or "Stable Currencies"

We Will Probably Have a Successful Business Year.

The Experience of Expert A Shows That B Is Likely to

Occur. However, Expert C Is Convinced This Is Not True.

Types of Uncertainty and the

Modeling of Uncertainty


Most Words and Evaluations We Use in Our Daily Reasoning Are

Not Clearly Defined in a Mathematical Manner. This Allows

Humans to Reason on an Abstract Level!


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... a person suffering from hepatitis shows in

60% of all cases a strong fever, in 45% of allcases yellowish colored skin, and in 30% of all

cases suffers from nausea ...

Probability and Uncertainty


Stochastics and Fuzzy LogicComplement Each Other !


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Conventional (Boolean) Set Theory:

Fuzzy Set Theory


Strong Fever

40.1C

42C

41.4C

39.3C

38.7C

37.2C

38C

Fuzzy Set Theory:

40.1C

42C

41.4C

39.3C

38.7C

37.2C

38C

More-or-Less Rather Than Either-Or !

Strong Fever


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Discrete Definition:

SF

(35C) = 0 SF

(38C) = 0.1 SF

(41C) = 0.9

SF

(36C) = 0 SF

(39C) = 0.35 SF

(42C) = 1

SF

(37C) = 0 SF

(40C) = 0.65 SF

(43C) = 1

Fuzzy Set Definitions


Continuous Definition:

39C 40C 41C 42C38C37C36C

1

0

(x)No More Artificial Thresholds!


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...Terms, Degree of Membership, Membership Function, Base Variable...

Linguistic Variable


39C 40C 41C 42C38C37C36C

1

0

(x)

lo w tem p no rm alra is ed tem per ature

s t ron g fever

pretty much raised

... but just slightly strong

A Linguistic VariableDefines a Concept of Our

Everyday Language!


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Fuzzification, Fuzzy Inference, Defuzzification:

Basic Elements of a

Fuzzy Logic System


LinguisticLevel

NumericalLevel

Measur ed Variables

Measur ed Variables

(Numerical Values)

(Linguist ic Values)2. Fuzzy-Inference Command Variables

3. Defuzzification

Plant

1. Fuzzification

(Linguist ic Values)

Command Variables(Numer ical V alues)

Fuzzy Logic Defines

the Control Strategy

on a Linguistic Level!


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Container Crane Case Study:

Basic Elements of a

Fuzzy Logic System


Two Measured

Variables and One

Command Variable !


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Control Loop of the Fuzzy Logic Controlled Container Crane:

Basic Elements of a

Fuzzy Logic System


LinguisticLevel

NumericalLevel

Angle, Distance

Angle, Distance

(Numerical Values)

(Numerical Values)2. Fuzzy-Inference

Power

Power

(Numer ical V alues)

(Linguist ic Variable)

3. Defuzzification

Container Crane

1. Fuzzification

Closing the Loop

With Words !


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Term Definitions:

Distance := {far, medium, close, zero, neg_close}

Angle := {pos_big, pos_small, zero, neg_small, neg_big}

Power := {pos_high, pos_medium, zero, neg_medium,

neg_high}

1. Fuzzification:

- Linguistic Variables -


Membership Function Definition:

-90 -45 0 45 900

1

Angle

zero

pos_sma l l neg_smal lneg_big pos_big

4

0.8

0.2

-10 0 10 20 300

1

Distance [yards]

zero c lose medium far neg_c lose

12m

0.9

0.1

The Linguistic

Variables Are the

Vocabulary of a

Fuzzy Logic System !


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Computation of the IF-THEN-Rules:

#1: IF Distance = medium AND Angle = pos_small THEN Power = pos_medium

#2: IF Distance = medium AND Angle = zero THEN Power = zero

#3: IF Distance = far AND Angle = zero THEN Power = pos_medium

2. Fuzzy-Inference:

- IF-THEN-Rules -


Aggregation: Computing the IF-Part

Composition: Computing the THEN-Part

The Rules of the Fuzzy

Logic Systems Are the

Laws It Executes !


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2. Fuzzy-Inference:

- Aggregation -


Boolean Logic Only

Defines Operators for 0/1:

A B AvB

0 0 0

0 1 0

1 0 0

1 1 1

Fuzzy Logic Delivers

a Continuous Extension:

AND: AvB = min{ A; B}

OR: A+B = max{ A; B}

NOT: -A = 1 - A

Aggregation of the IF-Part:

#1: min{ 0.9, 0.8 } = 0.8

#2: min{ 0.9, 0.2 } = 0.2

#3: min{ 0.1, 0.2 } = 0.1

Aggregation Computes How

Appropriate Each Rule Is for

the Current Situation !


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2. Fuzzy-Inference:

Composition


Result for the Linguistic Variable "Power":

pos_high with the degree 0.0

pos_medium with the degree 0.8 ( = max{ 0.8, 0.1 } )

zero with the degree 0.2

neg_medium with the degree 0.0

neg_high with the degree 0.0

Composition Computes

How Each Rule Influences

the Output Variables !


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3. Defuzzification


Finding a Compromise Using Center-of-Maximum:

-30 -15 0 15 300

1

Power [Kilowatts]

zeroneg_mediumneg_h igh pos_medium pos_h igh

6.4 KW

Balancing Out

the Result !


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Types of Fuzzy Controllers:

- Direct Controller -


The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant:

Fuzzification Inference Defuzzification

IF temp=low

AND P=high

THEN A=med

IF ...

Variables

Measured Variables

Plant

Command

Fuzzy Rules Output

Absolute Values !


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- Supervisory Control -


Fuzzy Logic Controller Outputs Set Values for Underlying PID Controllers:


IF temp=lowAND P=high

THEN A=med

IF ...

Set Values

Measured Variables

Plant

PID

PID

PID

Human Operator

Type Control !


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- PID Adaptation -


Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller:


IF temp=low

AND P=high

THEN A=med

IF ...

P

Measured Variable

PlantPID

I

D

Set Point Variable

Command Variable

The Fuzzy Logic System

Analyzes the Performance of the

PID Controller and Optimizes It !


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- Fuzzy Intervention -

INFORM 1990 1998 Slid 20

Fuzzy Logic Controller and PID Controller in Parallel:


IF temp=low

AND P=high

THEN A=med

IF ...

Measured Variable

PlantPID

Set Point Variable

Command Variable

Intervention of the Fuzzy Logic

Controller into Large Disturbances !

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