Fuzzy Logic CSE-435: A Presentation on Presented by Osama Ahmed Khan Dr. Hector Munoz-Avila

OVERVIEW  BACKGROUND  INTRODUCTION  DEMOS  APPROACH  APPLICATION

BACKGROUND  Professor Lotfi Zadeh, UC Berkeley, 1965 “People do not require precise, numerical information input, and yet they are capable of highly adaptive control.”  Accepts noisy, imprecise input!

History, State of the Art, and Future Development © INFORM Slide Seminal 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 !

Stochastic Uncertainty: XThe Probability of Hitting the Target Is 0.8 Lexical Uncertainty: X"Tall Men", "Hot Days", or "Stable Currencies" XWe Will Probably Have a Successful Business Year. XThe Experience of Expert A Shows That B Is Likely to Occur. However, Expert C Is Convinced This Is Not True. Stochastic Uncertainty: XThe Probability of Hitting the Target Is 0.8 Lexical Uncertainty: X"Tall Men", "Hot Days", or "Stable Currencies" XWe Will Probably Have a Successful Business Year. 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 Slide 5 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!

“... 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 Slide 6 Stochastics and Fuzzy Logic Complement Each Other !

Conventional (Boolean) Set Theory: Fuzzy Set Theory © INFORM Slide 7 “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”

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 Slide 8 Continuous Definition: No More Artificial Thresholds!

INTRODUCTION  What is Fuzzy Logic?  Problem-solving control system methodology  Linguistic or "fuzzy" variables  Example: IF (process is too hot) AND (process is heating rapidly) THEN (cool the process quickly)

INTRODUCTION (Contd.)  Advantages  Mimicks human control logic  Uses imprecise language  Inherently robust  Fails safely  Modified and tweaked easily

INTRODUCTION (Contd.)  Disadvantages  Operator's experience required  System complexity

DEMOS Fuzzy Logic Anti-sway Crane Controller

DEMOS (Contd.) Control of a Flexible Robot

DEMOS (Contd.) Anti-Swing Control of an Overhead Crane

DEMOS (Contd.) Robot Skating

DEMOS (Contd.)  Fuzzy Shower   Fuzzy Controller for an Inverted Pendulum   Prevention of Load Sway by a Fuzzy Controller 

Preliminary Evaluation Assessment As to Whether Fuzzy Logic Is Applicable for the Given Application Evaluation Criteria:  Has Fuzzy Logic Been Previously Applied to a Similar Application With Success?  Is It a Multi-Variable Type Control Problem?  Do Operators and Engineers Possess Knowledge About Any Relevant Interdependencies of the Process Variables?  Can Further Knowledge About the Process Behavior Be Gained By Observation Or Experiments?  Is It Difficult to Obtain a Mathematical Model from the Process? Evaluation Criteria:  Has Fuzzy Logic Been Previously Applied to a Similar Application With Success?  Is It a Multi-Variable Type Control Problem?  Do Operators and Engineers Possess Knowledge About Any Relevant Interdependencies of the Process Variables?  Can Further Knowledge About the Process Behavior Be Gained By Observation Or Experiments?  Is It Difficult to Obtain a Mathematical Model from the Process? Problem Analysis Before Project Start ! APPROACH

APPROACH (Contd.)  Usage 1.Define the control objectives and criteria  What am I trying to control?  What do I have to do to control the system?  What kind of response do I need?  What are the possible (probable) system failure modes? 2.Determine the input and output relationships  Choose a minimum number of variables for input to the FL engine 3.Use the rule-based structure of FL  Break the control problem down into a series of rules 4.Create FL membership functions  Define the meaning (values) of Input/Output terms used in the rules 5.Test, evaluate, tune and retest

APPROACH (Contd.)  The Rule Matrix  Error (Columns)  Error-dot (Rows)  Input conditions (Error and Error-dot)  Output Response Conclusion (Intersection of Row and Column) -ve Error Zero Error +ve Error -ve Error- dot Zero Error- dot No change +ve Error- dot Rule Matrix

APPLICATION  Simple Proportional Temperature Controller  Components  An electric heating element  Variable-speed cooling fan  Functionality  Positive signal output: 0-100% heat  Negative signal output: 0-100% cooling

APPLICATION (Contd.) Block Diagram of the Control System

APPLICATION (Contd.)  Working  Establish a meaningful system for representing the linguistic variables in the Rule Matrix "N" = "negative" error/ error-dot input level "Z" = "zero" error/ error-dot input level "P" = "positive" error/ error-dot input level "H" = "Heat" output response "-" = "No Change" to current output "C" = "Cool" output response

APPROACH  Usage 1.Define the control objectives and criteria  What am I trying to control?  What do I have to do to control the system?  What kind of response do I need?  What are the possible (probable) system failure modes? 2.Determine the input and output relationships  Choose a minimum number of variables for input to the FL engine 3.Use the rule-based structure of FL  Break the control problem down into a series of rules 4.Create FL membership functions  Define the meaning (values) of Input/Output terms used in the rules 5.Test, evaluate, tune and retest

APPLICATION (Contd.) 1.Define the control objectives and criteria  What am I trying to control? System temperature  What do I have to do to control the system? Proper balance and control of the functional devices  What kind of response do I need? Stable Environment temperature  What are the possible (probable) system failure modes? The lack of the “No change” region

APPLICATION (Contd.) Typical control system response  What is being controlled and how?

APPROACH  Usage 1.Define the control objectives and criteria  What am I trying to control?  What do I have to do to control the system?  What kind of response do I need?  What are the possible (probable) system failure modes? 2.Determine the input and output relationships  Choose a minimum number of variables for input to the FL engine 3.Use the rule-based structure of FL  Break the control problem down into a series of rules 4.Create FL membership functions  Define the meaning (values) of Input/Output terms used in the rules 5.Test, evaluate, tune and retest

APPLICATION (Contd.) 2.Determine the input and output relationships  Define the minimum number of possible input product combinations and corresponding output response conclusions INPUT#1: ("Error", positive (P), zero (Z), negative (N)) INPUT#2: ("Error-dot", positive (P), zero (Z), negative (N)) CONCLUSION: ("Output", Heat (H), No Change (-), Cool (C)) INPUT#1 System Status Error = Command-Feedback P=Too cold, Z=Just right, N=Too hot INPUT#2 System Status Error-dot = d(Error)/dt P=Getting hotter Z=Not changing N=Getting colder OUTPUT Conclusion & System Response Output H = Call for heating - = Don't change anything C = Call for cooling

APPROACH  Usage 1.Define the control objectives and criteria  What am I trying to control?  What do I have to do to control the system?  What kind of response do I need?  What are the possible (probable) system failure modes? 2.Determine the input and output relationships  Choose a minimum number of variables for input to the FL engine 3.Use the rule-based structure of FL  Break the control problem down into a series of rules 4.Create FL membership functions  Define the meaning (values) of Input/Output terms used in the rules 5.Test, evaluate, tune and retest

APPLICATION (Contd.) 3.Use the rule-based structure of FL The rule structure

APPROACH  Usage 1.Define the control objectives and criteria  What am I trying to control?  What do I have to do to control the system?  What kind of response do I need?  What are the possible (probable) system failure modes? 2.Determine the input and output relationships  Choose a minimum number of variables for input to the FL engine 3.Use the rule-based structure of FL  Break the control problem down into a series of rules 4.Create FL membership functions  Define the meaning (values) of Input/Output terms used in the rules 5.Test, evaluate, tune and retest

APPLICATION (Contd.) 4.Create FL membership functions that define the meaning (values) of Input/Output terms used in the rules The features of a membership function

APPLICATION (Contd.) A sample case

APPROACH  Usage 1.Define the control objectives and criteria  What am I trying to control?  What do I have to do to control the system?  What kind of response do I need?  What are the possible (probable) system failure modes? 2.Determine the input and output relationships  Choose a minimum number of variables for input to the FL engine 3.Use the rule-based structure of FL  Break the control problem down into a series of rules 4.Create FL membership functions  Define the meaning (values) of Input/Output terms used in the rules 5.Test, evaluate, tune and retest

Thank you Q / A