Industrial Application of Fuzzy Logic Control © INFORM 1990-1998Slide 1 Tutorial and Workshop © Constantin von Altrock Inform Software Corporation 2001

Industrial Application of Fuzzy Logic ControlIndustrial Application of Fuzzy Logic Control

© INFORM 1990-1998 Slide 1

Tutorial and Workshop

© Constantin von Altrock

Inform Software Corporation

2001 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

Tutorial and Workshop

© Constantin von Altrock

Inform Software Corporation

2001 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 Logic Technologies 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

Fuzzy Logic Primer

History, Current Level and Further Development of Fuzzy Logic Technologies 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

History, State of the Art, and Future DevelopmentHistory, 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.

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 Today, Fuzzy Logic Has Already Become the Already Become the Standard Technique for Standard Technique for Multi-Variable Control !Multi-Variable Control !

Applications Study of the IEEE in 1996Applications 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,..), But Rather 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

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,..), But Rather 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 Fuzzy Logic Will Play a Major Role in Control Engineering !Role in Control Engineering !

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.

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 Types of Uncertainty and the Modeling of Uncertainty


Most Words and Evaluations We Use in Our Daily Reasoning Are Most Words and Evaluations We Use in Our Daily Reasoning Are Not Clearly Defined in a Mathematical Manner. This Allows Not Clearly Defined in a Mathematical Manner. This Allows Humans to Reason on an Abstract Level!Humans to Reason on an Abstract Level!

“... a person suffering from hepatitis shows in 60% of all cases a strong fever, in 45% of all cases yellowish colored skin, and in 30% of all cases suffers from nausea ...”

“... a person suffering from hepatitis shows in 60% of all cases a strong fever, in 45% of all cases yellowish colored skin, and in 30% of all cases suffers from nausea ...”

Probability and UncertaintyProbability and Uncertainty


Stochastics and Fuzzy Logic Stochastics and Fuzzy Logic Complement Each Other !Complement Each Other !

Conventional (Boolean) Set Theory:Conventional (Boolean) Set Theory:

Fuzzy Set TheoryFuzzy Set Theory


“Strong Fever”

40.1°C40.1°C

42°C42°C

41.4°C41.4°C

39.3°C39.3°C

38.7°C38.7°C

37.2°C37.2°C

38°C38°C

Fuzzy Set Theory:Fuzzy Set Theory:

40.1°C40.1°C

42°C42°C

41.4°C41.4°C

39.3°C39.3°C

38.7°C

37.2°C

38°C

““More-or-Less” Rather Than “Either-Or” !More-or-Less” Rather Than “Either-Or” !

“Strong Fever”

Discrete Definition:

µSF

(35°C) = 0 µSF

(38°C) = 0.1 µSF

(41°C) = 0.9

µSF

(36°C) = 0 µSF

(39°C) = 0.35 µSF

(42°C) = 1

µSF

(37°C) = 0 µSF

(40°C) = 0.65 µSF

(43°C) = 1

Discrete Definition:

µSF

(35°C) = 0 µSF

(38°C) = 0.1 µSF

(41°C) = 0.9

µSF

(36°C) = 0 µSF

(39°C) = 0.35 µSF

(42°C) = 1

µSF

(37°C) = 0 µSF

(40°C) = 0.65 µSF

(43°C) = 1

Fuzzy Set DefinitionsFuzzy Set Definitions


Continuous Definition:Continuous Definition:

39°C 40°C 41°C 42°C38°C37°C36°C

1

0

µ(x)No More Artificial Thresholds!No More Artificial Thresholds!

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

Linguistic VariableLinguistic Variable


39°C 40°C 41°C 42°C38°C37°C36°C

1

0

µ(x)low temp normal raised temperature strong fever

… pretty much raised … … pretty much raised …

... but just slightly strong … ... but just slightly strong …

A Linguistic Variable A Linguistic Variable Defines a Concept of Our Defines a Concept of Our Everyday Language!Everyday Language!

Fuzzification, Fuzzy Inference, Defuzzification:Fuzzification, Fuzzy Inference, Defuzzification:

Basic Elements of a Fuzzy Logic SystemBasic Elements of a Fuzzy Logic System


LinguisticLevel

NumericalLevel

Measured Variables

Measured Variables

(Numerical Values)

(Linguistic Values)2. Fuzzy-Inference Command Variables

3. Defuzzification

Plant

1. Fuzzification

(Linguistic Values)

Command Variables(Numerical Values)

Fuzzy Logic Defines Fuzzy Logic Defines the Control Strategy on the Control Strategy on a Linguistic Level!a Linguistic Level!

Container Crane Case Study:Container Crane Case Study:



Two Measured Two Measured Variables and One Variables and One Command Variable !Command Variable !

Control Loop of the Fuzzy Logic Controlled Container Crane:Control Loop of the Fuzzy Logic Controlled Container Crane:



LinguisticLevel

NumericalLevel

Angle, Distance

Angle, Distance

(Numerical Values)

(Numerical Values)2. Fuzzy-Inference

Power

Power

(Numerical Values)

(Linguistic Variable)

3. Defuzzification

Container Crane

1. Fuzzification

Closing the Loop Closing the Loop With Words !With Words !

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}

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 -1. Fuzzification:- Linguistic Variables -


Membership Function Definition:Membership Function Definition:

-90° -45° 0° 45° 90°0

1

µ

Angle

zeropos_smallneg_smallneg_big pos_big

4°4°

0.80.8

0.20.2

-10 0 10 20 300

1

µ

Distance [yards]

zero close medium farneg_close

12m12m

0.90.9

0.10.1

The Linguistic The Linguistic Variables Are the Variables Are the “Vocabulary” of a “Vocabulary” of a Fuzzy Logic System !Fuzzy Logic System !

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

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 -2. Fuzzy-Inference:- “IF-THEN”-Rules -


Aggregation: Computing the “IF”-Part Composition: Computing the “THEN”-Part

Aggregation: Computing the “IF”-Part Composition: Computing the “THEN”-Part

The Rules of the Fuzzy The Rules of the Fuzzy Logic Systems Are the Logic Systems Are the “Laws” It Executes !“Laws” It Executes !

2. Fuzzy-Inference:- Aggregation -2. Fuzzy-Inference:- Aggregation -


Boolean Logic Only Defines Operators for 0/1:

A B AvB0 0 00 1 01 0 01 1 1

Boolean Logic Only Defines Operators for 0/1:

A B AvB0 0 00 1 01 0 01 1 1

Fuzzy Logic Delivers a Continuous Extension:

AND: µAvB = min{ µA; µB }

OR: µA+B = max{ µA; µB }

NOT: µ-A = 1 - µA

Fuzzy Logic Delivers a Continuous Extension:

AND: µAvB = min{ µA; µB }

OR: µA+B = max{ µA; µB }

NOT: µ-A = 1 - µA

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 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 } = 0.1Aggregation Computes How Aggregation Computes How “Appropriate” Each Rule Is for “Appropriate” Each Rule Is for the Current Situation !the Current Situation !

2. Fuzzy-Inference:Composition2. 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

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 Composition Computes How Each Rule Influences How Each Rule Influences the Output Variables !the Output Variables !

3. Defuzzification3. Defuzzification


Finding a Compromise Using “Center-of-Maximum”:Finding a Compromise Using “Center-of-Maximum”:

-30 -15 0 15 300

1

µ

Power [Kilowatts]

zeroneg_mediumneg_high pos_medium pos_high

6.4 KW6.4 KW

““Balancing” Out Balancing” Out the Result !the Result !

Types of Fuzzy Controllers:- Direct Controller - Types of Fuzzy Controllers:- Direct Controller -


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

Fuzzification Inference Defuzzification

IF temp=lowAND P=highTHEN A=med

IF ...

Variables

Measured Variables

Plant

Command

Fuzzy Rules Output Fuzzy Rules Output Absolute Values ! Absolute Values !

Types of Fuzzy Controllers:- Supervisory Control - Types of Fuzzy Controllers:- Supervisory Control -


Fuzzy Logic Controller Outputs Set Values for Underlying PID Controllers: Fuzzy Logic Controller Outputs Set Values for Underlying PID Controllers:



IF ...

Set Values

Measured Variables

Plant

PID

PID

PID

Human Operator Human Operator Type Control ! Type Control !

Types of Fuzzy Controllers:- PID Adaptation - Types of Fuzzy Controllers:- PID Adaptation -


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



IF ...

P

Measured Variable

PlantPID

ID

Set Point Variable

Command Variable

The Fuzzy Logic System The Fuzzy Logic System Analyzes the Performance of the Analyzes the Performance of the PID Controller and Optimizes It !PID Controller and Optimizes It !

Types of Fuzzy Controllers:- Fuzzy Intervention - Types of Fuzzy Controllers:- Fuzzy Intervention -


Fuzzy Logic Controller and PID Controller in Parallel:Fuzzy Logic Controller and PID Controller in Parallel:



IF ...

Measured Variable

PlantPID

Set Point Variable

Command Variable

Intervention of the Fuzzy Logic Intervention of the Fuzzy Logic Controller into Large Disturbances !Controller into Large Disturbances !

Documents

Industrial Application of Fuzzy Logic Control © INFORM 1990-1998Slide 1 Tutorial and Workshop © Constantin von Altrock Inform Software Corporation 2001