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Industrial Application of Fuzzy Logic Control
© INFORM 1990-1998 Slide 1
Tutorial and Workshop© Constantin von Altrock
Inform Software Corporation2001 Midwest Rd.Oak Brook, IL 60521, U.S.A.
German Version Available!
Phone 630-268-7550Fax 630-268-7554Email: [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
History, State of the Art, and Future Development
© INFORM 1990-1998 Slide 2
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 1996
© INFORM 1990-1998 Slide 3
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.
Types of Uncertainty and the Modeling of Uncertainty
© INFORM 1990-1998 Slide 4
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 ...”
Probability and Uncertainty
© INFORM 1990-1998 Slide 5
Stochastics and Fuzzy Logic Stochastics and Fuzzy Logic Complement Each Other !Complement Each Other !
Conventional (Boolean) Set Theory:
Fuzzy Set Theory
© INFORM 1990-1998 Slide 6
“Strong Fever”
40.1°C
42°C
41.4°C
39.3°C
38.7°C38.7°C
37.2°C37.2°C
38°C38°C
Fuzzy Set Theory:
40.1°C
42°C
41.4°C
39.3°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:µ
SF(35°C) = 0 µ
SF(38°C) = 0.1 µ
SF(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 Definitions
© INFORM 1990-1998 Slide 7
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...
Linguistic Variable
© INFORM 1990-1998 Slide 8
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 …
... 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:
Basic Elements of a Fuzzy Logic System
© INFORM 1990-1998 Slide 9
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:
Basic Elements of a Fuzzy Logic System
© INFORM 1990-1998 Slide 10
Two Measured Two Measured Variables and One Variables and One Command Variable !Command Variable !
Control Loop of the Fuzzy Logic Controlled Container Crane:
Basic Elements of a Fuzzy Logic System
© INFORM 1990-1998 Slide 11
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}
1. Fuzzification:- Linguistic Variables -
© INFORM 1990-1998 Slide 12
Membership Function Definition:
-90° -45° 0° 45° 90°0
1
µ
Angle
zeropos_smallneg_smallneg_big pos_big
4°
0.8
0.2
-10 0 10 20 300
1
µ
Distance [yards]
zero close medium farneg_close
12m
0.9
0.1
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
2. Fuzzy-Inference:- “IF-THEN”-Rules -
© INFORM 1990-1998 Slide 13
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 -
© INFORM 1990-1998 Slide 14
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
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:Composition
© INFORM 1990-1998 Slide 15
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. Defuzzification
© INFORM 1990-1998 Slide 16
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 -
© INFORM 1990-1998 Slide 17
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 -
© INFORM 1990-1998 Slide 18
Fuzzy Logic Controller Outputs Set Values for Underlying PID Controllers:
Fuzzification Inference Defuzzification
IF temp=lowAND P=highTHEN A=med
IF ...
Set Values
Measured Variables
Plant
PID
PID
PID
Human Operator Human Operator Type Control ! Type Control !
Types of Fuzzy Controllers:- PID Adaptation -
© INFORM 1990-1998 Slide 19
Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller:
Fuzzification Inference Defuzzification
IF temp=lowAND P=highTHEN A=med
IF ...
P
Measured Variable
PlantPIDID
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 -
© INFORM 1990-1998 Slide 20
Fuzzy Logic Controller and PID Controller in Parallel:
Fuzzification Inference Defuzzification
IF temp=lowAND P=highTHEN A=med
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 !