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

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 DevelopmentHistory, State of the Art, and Future Development

© INFORM 1990-1998 Slide 4

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 !

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!

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 http://ai.iit.nrc.ca/IR_public/fuzzy/fuzzyShower.html

Fuzzy Controller for an Inverted Pendulum http://www.aptronix.com/fuzzynet/java/pend/pendjava.htm

Prevention of Load Sway by a Fuzzy Controller http://people.clarkson.edu/~esazonov/neural_fuzzy/loadsway/LoadSway.htm

http://ai.iit.nrc.ca/IR_public/fuzzy/fuzzyShower.html

http://www.aptronix.com/fuzzynet/java/pend/pendjava.htm

http://www.aptronix.com/fuzzynet/java/pend/pendjava.htm

http://people.clarkson.edu/~esazonov/neural_fuzzy/loadsway/LoadSway.htm

Preliminary Evaluation

Assessment As to Whether Fuzzy Logic Is Applicable for the Given Application 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 !Problem Analysis Before Project Start !

APPROACH

APPROACH (Contd.)

Usage1. 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


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








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


Typical control system response

What is being controlled and how?

APPROACH








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








3. Use the rule-based structure of FL

The rule structure

APPROACH








4. Create FL membership functions that define the meaning (values) of Input/Output terms used in the rules

The features of a membership function


A sample case

APPROACH







Thank you

Q / A

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

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