1. Industrial Application of Fuzzy Logic Control © INFORM 1990-1998Slide 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: fuzzy@informusa.com 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: fuzzy@informusa.com Internet: www.fuzzytech.com Fuzzy Logic Primer X XHistory, Current Level and Further Development of Fuzzy Logic Technologies in the U.S., Japan, and Europe X XTypes of Uncertainty and the Modeling of Uncertainty X XThe Basic Elements of a Fuzzy Logic System X XTypes of Fuzzy Logic Controllers Fuzzy Logic Primer X XHistory, Current Level and Further Development of Fuzzy Logic Technologies in the U.S., Japan, and Europe X XTypes of Uncertainty and the Modeling of Uncertainty X XThe Basic Elements of a Fuzzy Logic System X XTypes of Fuzzy Logic Controllers

2. History, State of the Art, and Future Development © INFORM 1990-1998Slide 2 1965Seminal Paper “Fuzzy Logic” by Prof. Lotfi Zadeh, Faculty in Electrical Engineering, U.C. Berkeley, Sets the Foundation of the “Fuzzy Set Theory” 1970First Application of Fuzzy Logic in Control Engineering (Europe) 1975Introduction of Fuzzy Logic in Japan 1980Empirical Verification of Fuzzy Logic in Europe 1985Broad Application of Fuzzy Logic in Japan 1990Broad Application of Fuzzy Logic in Europe 1995Broad Application of Fuzzy Logic in the U.S. 2000Fuzzy Logic Becomes a Standard Technology and Is Also Applied in Data and Sensor Signal Analysis. Application of Fuzzy Logic in Business and Finance. 1965Seminal Paper “Fuzzy Logic” by Prof. Lotfi Zadeh, Faculty in Electrical Engineering, U.C. Berkeley, Sets the Foundation of the “Fuzzy Set Theory” 1970First Application of Fuzzy Logic in Control Engineering (Europe) 1975Introduction of Fuzzy Logic in Japan 1980Empirical Verification of Fuzzy Logic in Europe 1985Broad Application of Fuzzy Logic in Japan 1990Broad Application of Fuzzy Logic in Europe 1995Broad Application of Fuzzy Logic in the U.S. 2000Fuzzy 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 !

3. Applications Study of the IEEE in 1996 © INFORM 1990-1998Slide 3 X XAbout 1100 Successful Fuzzy Logic Applications Have Been Published (an estimated 5% of those in existence) X XAlmost All Applications Have Not Involved the Replacement of a Standard Type Controller (PID,..), But Rather Multi-Variable Supervisory Control X XApplications Range from Embedded Control (28%), Industrial Automation (62%) to Process Control (10%) X XOf 311 Authors That Answered a Questionnaire, About 90% State That Fuzzy Logic Has Slashed Design Time By More Than Half X XIn This Questionnaire, 97.5% of the Designers Stated That They Will Use Fuzzy Logic Again in Future Applications, If Fuzzy Logic Is Applicable X XAbout 1100 Successful Fuzzy Logic Applications Have Been Published (an estimated 5% of those in existence) X XAlmost All Applications Have Not Involved the Replacement of a Standard Type Controller (PID,..), But Rather Multi-Variable Supervisory Control X XApplications Range from Embedded Control (28%), Industrial Automation (62%) to Process Control (10%) X XOf 311 Authors That Answered a Questionnaire, About 90% State That Fuzzy Logic Has Slashed Design Time By More Than Half X XIn 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 !

4. Stochastic Uncertainty: X XThe Probability of Hitting the Target Is 0.8 Lexical Uncertainty: X X"Tall Men", "Hot Days", or "Stable Currencies" X XWe Will Probably Have a Successful Business Year. X XThe Experience of Expert A Shows That B Is Likely to Occur. However, Expert C Is Convinced This Is Not True. Stochastic Uncertainty: X XThe Probability of Hitting the Target Is 0.8 Lexical Uncertainty: X X"Tall Men", "Hot Days", or "Stable Currencies" X XWe Will Probably Have a Successful Business Year. X XThe 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 1990-1998Slide 4 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!

5. “... 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 1990-1998Slide 5 Stochastics and Fuzzy Logic Complement Each Other !

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

7. Discrete Definition: µ SF (35°C) = 0µ SF (38°C) = 0.1µ SF (41°C) = 0.9 µ SF (36°C) = 0µ SF (39°C) = 0.35µ SF (42°C) = 1 µ SF (37°C) = 0µ SF (40°C) = 0.65µ SF (43°C) = 1 Discrete Definition: µ SF (35°C) = 0µ SF (38°C) = 0.1µ SF (41°C) = 0.9 µ SF (36°C) = 0µ SF (39°C) = 0.35µ SF (42°C) = 1 µ SF (37°C) = 0µ SF (40°C) = 0.65µ SF (43°C) = 1 Fuzzy Set Definitions © INFORM 1990-1998Slide 7 Continuous Definition: No More Artificial Thresholds!

8. ...Terms, Degree of Membership, Membership Function, Base Variable... Linguistic Variable © INFORM 1990-1998Slide 8 … pretty much raised …... but just slightly strong … A Linguistic Variable Defines a Concept of Our Everyday Language!

9. Fuzzification, Fuzzy Inference, Defuzzification: Basic Elements of a Fuzzy Logic System © INFORM 1990-1998Slide 9 Fuzzy Logic Defines the Control Strategy on a Linguistic Level!

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

11. Control Loop of the Fuzzy Logic Controlled Container Crane: Basic Elements of a Fuzzy Logic System © INFORM 1990-1998Slide 11 Closing the Loop With Words !

12. 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 - © INFORM 1990-1998Slide 12 Membership Function Definition: 4° 0.8 0.2 12m 0.9 0.1 The Linguistic Variables Are the “Vocabulary” of a Fuzzy Logic System !

13. 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 - © INFORM 1990-1998Slide 13 X XAggregation:Computing the “IF”-Part X XComposition: Computing the “THEN”-Part X XAggregation:Computing the “IF”-Part X XComposition: Computing the “THEN”-Part The Rules of the Fuzzy Logic Systems Are the “Laws” It Executes !

14. 2. Fuzzy-Inference: - Aggregation - © INFORM 1990-1998Slide 14 Boolean Logic Only Defines Operators for 0/1: ABAvB 000 010 100 111 Boolean Logic Only Defines Operators for 0/1: ABAvB 000000 010010 100100 111111 Fuzzy Logic Delivers a Continuous Extension: X X AND: µ AvB = min{ µ A ; µ B } X X OR: µ A+B = max{ µ A ; µ B } X X NOT: µ -A = 1 - µ A Fuzzy Logic Delivers a Continuous Extension: X X AND: µ AvB = min{ µ A ; µ B } X X OR: µ A+B = max{ µ A ; µ B } X X NOT: µ -A = 1 - µ 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 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 !

15. 2. Fuzzy-Inference: Composition © INFORM 1990-1998Slide 15 Result for the Linguistic Variable "Power": pos_highwith 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_highwith 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 !

16. 3. Defuzzification © INFORM 1990-1998Slide 16 Finding a Compromise Using “Center-of-Maximum”: 6.4 KW “Balancing” Out the Result !

17. Types of Fuzzy Controllers: - Direct Controller - Types of Fuzzy Controllers: - Direct Controller - © INFORM 1990-1998Slide 17 The Outputs of the Fuzzy Logic System Are the Command Variables of the Plant: Fuzzy Rules Output Absolute Values !

18. Types of Fuzzy Controllers: - Supervisory Control - Types of Fuzzy Controllers: - Supervisory Control - © INFORM 1990-1998Slide 18 Fuzzy Logic Controller Outputs Set Values for Underlying PID Controllers: Human Operator Type Control !

19. Types of Fuzzy Controllers: - PID Adaptation - Types of Fuzzy Controllers: - PID Adaptation - © INFORM 1990-1998Slide 19 Fuzzy Logic Controller Adapts the P, I, and D Parameter of a Conventional PID Controller: The Fuzzy Logic System Analyzes the Performance of the PID Controller and Optimizes It !

20. Types of Fuzzy Controllers: - Fuzzy Intervention - Types of Fuzzy Controllers: - Fuzzy Intervention - © INFORM 1990-1998Slide 20 Fuzzy Logic Controller and PID Controller in Parallel: Intervention of the Fuzzy Logic Controller into Large Disturbances !