1. Industrial Application of
Fuzzy Logic Control
Tutorial and Workshop Fuzzy Logic Primer
© Constantin von Altrock
History, Current Level and Further
Inform Software Corporation Development of Fuzzy Logic
2001 Midwest Rd. Technologies in the U.S., Japan, and
Oak Brook, IL 60521, U.S.A. Europe
German Version Available! Types of Uncertainty and the
Modeling of Uncertainty
Phone 630-268-7550
Fax 630-268-7554 The Basic Elements of a Fuzzy
Email: fuzzy@informusa.com Logic System
Internet: www.fuzzytech.com Types of Fuzzy Logic Controllers
© INFORM 1990-1998 Slide 1

2. 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
Today, Fuzzy Logic Has 1995 Broad Application of Fuzzy Logic in the U.S.
Already Become the
2000 Fuzzy Logic Becomes a Standard Technology and Is
Standard Technique for
Also Applied in Data and Sensor Signal Analysis.
Multi-Variable Control !
Application of Fuzzy Logic in Business and Finance.
© INFORM 1990-1998 Slide 2

3. 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,..), 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
Role in Control Engineering !
© INFORM 1990-1998 Slide 3

4. Types of Uncertainty and the
Modeling of Uncertainty
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.
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!
© INFORM 1990-1998 Slide 4

5. Probability and Uncertainty
“... 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 ...”
Stochastics and Fuzzy Logic
Complement Each Other !
© INFORM 1990-1998 Slide 5

6. Fuzzy Set Theory
Conventional (Boolean) Set Theory:
38.7°C
38°C
40.1°C 41.4°C
Fuzzy Set Theory:
42°C
39.3°C
“Strong Fever” 38.7°C
37.2°C 38°C
40.1°C 41.4°C
42°C
39.3°C
“Strong Fever”
“More-or-Less” Rather Than “Either-Or” ! 37.2°C
© INFORM 1990-1998 Slide 6

7. Fuzzy Set Definitions
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
Continuous Definition: No More Artificial Thresholds!
µ(x)
1
0
36°C 37°C 38°C 39°C 40°C 41°C 42°C
© INFORM 1990-1998 Slide 7

8. Linguistic Variable
...Terms, Degree of Membership, Membership Function, Base Variable...
µ(x)
low temp normal raised temperature strong fever
1 … pretty much raised …
A Linguistic Variable
Defines a Concept of Our
... but just slightly strong … Everyday Language!
0
36°C 37°C 38°C 39°C 40°C 41°C 42°C
© INFORM 1990-1998 Slide 8

9. Basic Elements of a
Fuzzy Logic System
Fuzzy Logic Defines
Fuzzification, Fuzzy Inference, Defuzzification: the Control Strategy on
a Linguistic Level!
Measured Variables 2. Fuzzy-Inference Command Variables
(Linguistic Values) (Linguistic Values)
Linguistic
Level
1. Fuzzification 3. Defuzzification
Numerical
Level
Measured Variables Plant Command Variables
(Numerical Values) (Numerical Values)
© INFORM 1990-1998 Slide 9

10. Basic Elements of a
Fuzzy Logic System
Container Crane Case Study:
Two Measured
Variables and One
Command Variable !
© INFORM 1990-1998 Slide 10

11. Basic Elements of a
Fuzzy Logic System
Closing the Loop
Control Loop of the Fuzzy Logic Controlled Container Crane: With Words !
Angle, Distance 2. Fuzzy-Inference Power
(Numerical Values) (Linguistic Variable)
Linguistic
Level
1. Fuzzification 3. Defuzzification
Numerical
Level
Angle, Distance Container Crane Power
(Numerical Values) (Numerical Values)
© INFORM 1990-1998 Slide 11

12. 1. Fuzzification:
- Linguistic Variables -
Term Definitions: The Linguistic
Distance := {far, medium, close, zero, neg_close} Variables Are the
“Vocabulary” of a
Angle := {pos_big, pos_small, zero, neg_small, neg_big}
Fuzzy Logic System !
Power := {pos_high, pos_medium, zero, neg_medium,
neg_high}
Membership Function Definition:
µ zero
µ neg_close zero close medium far
neg_big neg_small pos_small pos_big
1 1
0.9
0.8
0.2
0.1
0 0
-90° -45° 0° 4° 45° 90° -10 0 10 20 30
Angle
12m
Distance [yards]
© INFORM 1990-1998 Slide 12

13. 2. Fuzzy-Inference:
- “IF-THEN”-Rules -
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
Aggregation: Computing the “IF”-Part
Composition: Computing the “THEN”-Part
The Rules of the Fuzzy
Logic Systems Are the
“Laws” It Executes !
© INFORM 1990-1998 Slide 13

14. 2. Fuzzy-Inference:
- Aggregation -
Boolean Logic Only Fuzzy Logic Delivers
Defines Operators for 0/1: a Continuous Extension:
A B AvB AND: µAvB = min{ µA; µB }
0 0 0
0 1 0 OR: µA+B = max{ µA; µB }
1 0 0 NOT: µ-A = 1 - µA
1 1 1
Aggregation of the “IF”-Part:
#1: min{ 0.9, 0.8 } = 0.8
#2: min{ 0.9, 0.2 } = 0.2 Aggregation Computes How
#3: min{ 0.1, 0.2 } = 0.1 “Appropriate” Each Rule Is for
the Current Situation !
© INFORM 1990-1998 Slide 14

15. 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 !
© INFORM 1990-1998 Slide 15

16. 3. Defuzzification
Finding a Compromise Using “Center-of-Maximum”:
µ neg_high neg_medium zero pos_medium pos_high
1
“Balancing” Out
the Result !
0
-30 -15 0 15 30
Power [Kilowatts] 6.4 KW
© INFORM 1990-1998 Slide 16

17. Types of Fuzzy Controllers:
- Direct Controller -
The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant:
Command
IF temp=low
AND P=high
Variables
THEN A=med
IF ...
Plant
Fuzzification Inference Defuzzification
Measured Variables
Fuzzy Rules Output
Absolute Values !
© INFORM 1990-1998 Slide 17

18. Types of Fuzzy Controllers:
- Supervisory Control -
Fuzzy Logic Controller Outputs Set Values for Underlying PID Controllers:
IF temp=low
Set Values PID
AND P=high
THEN A=med
PID Plant
IF ...
Fuzzification Inference Defuzzification PID
Measured Variables
Human Operator
Type Control !
© INFORM 1990-1998 Slide 18

19. Types of Fuzzy Controllers:
- PID Adaptation -
Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller:
Set Point Variable
IF temp=low
AND P=high P
THEN A=med
I Command Variable
D
IF ...
PID Plant
Fuzzification Inference Defuzzification
Measured Variable
The Fuzzy Logic System
Analyzes the Performance of the
PID Controller and Optimizes It !
© INFORM 1990-1998 Slide 19

20. Types of Fuzzy Controllers:
- Fuzzy Intervention -
Fuzzy Logic Controller and PID Controller in Parallel:
Set Point Variable
IF temp=low
AND P=high
THEN A=med Command Variable
IF ...
Plant
PID
Fuzzification Inference Defuzzification
Measured Variable
Intervention of the Fuzzy Logic
Controller into Large Disturbances !
© INFORM 1990-1998 Slide 20