fuzzy logic

Objectives…Objectives…Objectives…Objectives…Objectives…Objectives…Objectives…Objectives…

�� IntroductionIntroduction..

�� ApproachApproach..

�� ApplicationApplication..

9/12/2013 Mahesh J. vadhavaniya 1

�� ApplicationApplication..

�� SummarySummary..

�� DemoDemo..

IntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroduction

�� FuzzyFuzzy LogicLogic definesdefines thethe controlcontrol strategystrategy onon aa LinguisticLinguisticlevellevel..

�� ProblemProblem--solvingsolving controlcontrol systemsystem methodologymethodology..

What is Fuzzy Logic ?


�� ProblemProblem--solvingsolving controlcontrol systemsystem methodologymethodology..

�� LinguisticLinguistic oror “Fuzzy"“Fuzzy" variablesvariables

�� ExampleExample::

IFIF (process(process isis tootoo hot)hot)

ANDAND (process(process isis heatingheating rapidly)rapidly)

THENTHEN (cool(cool thethe processprocess quickly)quickly)

IntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroduction

DescribeDescribe thethe valuevalue ofof variablesvariables

Apparatus of Fuzzy logic is built on :

Fuzzy sets :

QualitativelyQualitatively andand quantitativelyquantitativelyLinguistic


QualitativelyQualitatively andand quantitativelyquantitativelydescribeddescribed byby fuzzyfuzzy setssets

LinguisticVariables :

AA knowledgeknowledgeFuzzy if -then rules :

LinguisticLinguistic valuesvalues toto numericalnumerical valuesvaluesDefuzzification :

IntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroductionIntroductionBasic Elements of a Fuzzy logic system :

3. D

efu

zzyfic

atio

n

Linguistic level

Command Variables(Linguistic Values)

Measured Variables(Linguistic Values)

1. F

uzzyfica

tio

n

2. Fuzzy Inference


De

fuzzyfic

atio

n

level

Numerical level

Measured Variables(Numerical Values)

Command Variables(Numerical Values)

1. F

uzzyfica

tio

n

ApproachApproachApproachApproachApproachApproachApproachApproach

Preliminary Evaluation :

Problem Analysis before Project start !

EvaluationEvaluation CriteriaCriteria :

AssessmentAssessment asas toto whetherwhether FuzzyFuzzy logiclogic isis applicableapplicable forforthethe givengiven applicationapplication..


�� HasHas fuzzyfuzzy logiclogic beenbeen previouslypreviously appliedapplied toto aa similarsimilar applicationapplicationWithWith success?success?

�� IsIs itit aa multimulti--variablevariable typetype controlcontrol problem?problem?

�� DoDo operatorsoperators andand engineersengineers possesspossess knowledgeknowledge aboutabout anyany relevantrelevantinterdependenciesinterdependencies ofof thethe processprocess variables?variables?

�� CanCan furtherfurther knowledgeknowledge aboutabout thethe processprocess behaviorbehavior bebe gainedgained bybyobservationobservation oror experiments?experiments?

�� IsIs itit difficultdifficult toto obtainobtain aa mathematicalmathematical modelmodel fromfrom thethe process?process?

UsageUsage�� UsageUsage1.1. Define the control objectives and criteriaDefine the control objectives and criteria

�� What am I trying to control? What am I trying to control? �� What do I have to do to control the system?What do I have to do to control the system?�� What kind of response do I need?What kind of response do I need?�� What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?


What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?2.2. Determine the input and output relationships Determine the input and output relationships

�� Choose a minimum number of variables for input to the Choose a minimum number of variables for input to the FL engineFL engine

3.3. Use the ruleUse the rule--based structure of FLbased structure of FL�� Break the control problem down into a series of rulesBreak the control problem down into a series of rules

4.4. Create FL membership functions Create FL membership functions �� Define the meaning (values) of Input / Output terms used Define the meaning (values) of Input / Output terms used

in the rulesin the rules5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest


�� The Rule MatrixThe Rule Matrix

�� Error (Columns)Error (Columns)

�� ErrorError--dot (Rows)dot (Rows)

�� Input conditions Input conditions


--veveErrorError

Zero Zero ErrorError

+ve +ve ErrorError

--veveErrorError--

dotdot�� Input conditions Input conditions

(Error and Error(Error and Error--dot)dot)

�� Output Response Output Response Conclusion Conclusion (Intersection of Row (Intersection of Row and Column)and Column)

dotdot

Zero Zero ErrorError--

dotdot

No No changechange

+ve +ve ErrorError--

dotdot

Rule MatrixRule Matrix9/12/2013 Mahesh J. vadhavaniya 7

�� ComponentsComponents

�� An electric heating elementAn electric heating element

VariableVariable--speed cooling fanspeed cooling fan

ApplicationApplicationApplicationApplicationApplicationApplicationApplicationApplication

SimpleSimple ProportionalProportional TemperatureTemperature ControllerController :

�� VariableVariable--speed cooling fanspeed cooling fan

�� FunctionalityFunctionality

�� Positive signal output: 0Positive signal output: 0--100% heat 100% heat

�� Negative signal output: 0Negative signal output: 0--100% cooling100% cooling



Block Diagram of the Control System



��WorkingWorking

��Establish a meaningful system for representing the Establish a meaningful system for representing the

linguistic variables in the Rule Matrixlinguistic variables in the Rule Matrix

"N" = "negative" error/ error"N" = "negative" error/ error--dot input level dot input level "N" = "negative" error/ error"N" = "negative" error/ error--dot input level dot input level

"Z" = "zero" error/ error"Z" = "zero" error/ error--dot input level dot input level

"P" = "positive" error/ error"P" = "positive" error/ error--dot input level dot input level

"H" = "Heat" output response "H" = "Heat" output response

""--" = "No Change" to current output " = "No Change" to current output

"C" = "Cool" output response "C" = "Cool" output response




�� What am I trying to control? What am I trying to control? �� What do I have to do to control the system?What do I have to do to control the system?�� What kind of response do I need?What kind of response do I need?�� What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?�� What are the possible (probable) system failure modes?What are the possible (probable) system failure modes?

2.2. Determine the input and output relationships Determine the input and output relationships �� Choose a minimum number of variables for input to the Choose a minimum number of variables for input to the

FL engineFL engine3.3. Use the ruleUse the rule--based structure of FLbased structure of FL

�� Break the control problem down into a series of rulesBreak the control problem down into a series of rules4.4. Create FL membership functions Create FL membership functions

�� Define the meaning (values) of Input / Output terms used Define the meaning (values) of Input / Output terms used in the rulesin the rules

5.5. Test, evaluate, tune and retestTest, evaluate, tune and retest


1.1. Define the control objectives and criteriaDefine the control objectives and criteria�� What am I trying to control?What am I trying to control?

System temperature System temperature

�� What do I have to do to control the system?What do I have to do to control the system?Proper balance and control of the functional devicesProper balance and control of the functional devices


Proper balance and control of the functional devicesProper balance and control of the functional devices

�� What kind of response do I need?What kind of response do I need?Stable Environment temperatureStable Environment temperature

�� What are the possible (probable) system failure What are the possible (probable) system failure modes?modes?The lack of the “No change” regionThe lack of the “No change” region


�� What is being controlled and how? What is being controlled and how?


Typical control system response Typical control system response 9/12/2013 Mahesh J. vadhavaniya 13


2.2. Determine the input and output relationships Determine the input and output relationships 2.2. Determine the input and output relationships Determine the input and output relationships �� Define the minimum number of possible input product Define the minimum number of possible input product

combinations and corresponding output response combinations and corresponding output response conclusions 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)) 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)/dtP=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


APPLICATION (Contd.)

3.3. Use the ruleUse the rule--based structure of FLbased structure of FL



4.4. CreateCreate FLFL membershipmembership functionsfunctions thatthat definedefine thethemeaningmeaning (values)(values) ofof Input/OutputInput/Output termsterms usedused inin thetherulesrules



A sample caseA sample case



Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…Backing up a Truck…

Loading dock ( Loading dock ( XXff , , YYff ))

RearRear

( X( X , Y, Y ))


FrontFront

ɸɸϴϴ

Diagram of Truck and Loading zoneDiagram of Truck and Loading zone


�� TheThe goalgoal isis toto makemake thethe trucktruck arrivearrive atat thethe loadingloading dockdockatat aa rightright angleangle ((ɸɸff==9090)) andand toto alignalign thethe positionposition (x,(x, y)y) ofofthethe trucktruck withwith thethe desireddesired loadingloading dockdock (( XXff ,, YYff ))..

�� TheThe trucktruck movesmoves backwardbackward byby somesome fixedfixed distancedistance atat

Goal ?


�� TheThe trucktruck movesmoves backwardbackward byby somesome fixedfixed distancedistance atateveryevery stagestage..

�� TheThe loadingloading zonezone correspondscorresponds toto planeplane [[00,,100100]] XX

[[100100,,00]] andand (( XfXf ,, YfYf )) equaledequaled ((5050,,100100))

�� AtAt everyevery stagestage thethe FuzzyFuzzy controllercontroller shouldshould produceproduce thethesteeringsteering angleangle ϴϴ thatthat backsbacks upup thethe trucktruck toto thethe loadingloadingdockdock fromfrom anyany initialinitial positionposition andand fromfrom anyany angleangle inin thetheloadingloading zonezone..


�� TheThe threethree statestate variablesvariables ɸɸ,, xx andand yy exactlyexactly determinedeterminethethe trucktruck positionposition..

�� TheThe coordinatecoordinate pairpair (x,(x, y)y) specifiesspecifies thethe positionposition ofof thetherearrear centercenter ofof thethe trucktruck inin thethe planeplane..

�� ɸɸ specifiesspecifies thethe angleangle ofof thethe trucktruck withwith thethe horizontalhorizontal..


rearrear centercenter ofof thethe trucktruck inin thethe planeplane..

� First specify controller’s input and output variables.

�� TheThe inputinput variablesvariables areare thethe trucktruck angleangle ɸɸ andand xx ––positionposition coordinatecoordinate xx..

�� TheThe outputoutput isis steeringsteering angleangle signalsignal ϴϴ..

�� WeWe assumeassume enoughenough clearanceclearance betweenbetween thethe trucktruck andand thethe loadingloading dockdock sosowewe cancan ignoreignore thethe yy –– positionposition coordinatecoordinate..


�� PositivePositive valuesvalues ofof ϴϴ representsrepresents clockwiseclockwise rotationsrotations..

� Next specify Fuzzy set values of input and outputvariables.

�� ɸɸ specifiesspecifies thethe angleangle ofof thethe trucktruck withwith thethe horizontalhorizontal..

�� NegativeNegative valuesvalues ofof ϴϴ representsrepresents countercounter clockwiseclockwiserotationsrotations..


Angle Angle Angle Angle Angle Angle Angle Angle ɸɸ

RB Right Below

RU Right Upper

RV Right Vertical

VE Vertical

LV Left Vertical

LU Left Upper

LB Left Below

XXXXXXXX--------position xposition xposition xposition xposition xposition xposition xposition x

LE Left

LC Left Center

CE Center

RC Right Center

RI Right

Steering Angle Steering Angle Steering Angle Steering Angle Steering Angle Steering Angle Steering Angle Steering Angle ϴϴϴϴϴϴϴϴ

NB Negative Big

NM Negative Medium

NS Negative Small

ZE Zero

PS Positive Small

PM Positive Medium

PB Positive Big


� Next specify Fuzzy Membership Functions.


0 ≤ x ≤ 1000 ≤ x ≤ 100




--90 ≤ 90 ≤ ɸɸ ≤ 270≤ 270




--30 ≤ 30 ≤ ϴϴ ≤ 30≤ 30


� Next specify Fuzzy “rulebase” or bank of FAM rules.

xxxxLE LC CE RC RI

RB PS PM PM PB PB


ɸɸɸɸɸɸɸɸ

RB PS PM PM PB PB

RU NS PS PM PB PB

RV NM NS PS PM PB

VE NM NM ZE PM PM

LV NB NM NS PS PM

LU NB NB NM NS PS

LB NB NB NM NM NS


� Next Defuzzification.


Correlation Correlation –– minimum inference with minimum inference with centroidcentroiddefuzzificationdefuzzification methodmethod

Summary …Summary …Summary …Summary …Summary …Summary …Summary …Summary …

1.1. TheThe plantplant isis observableobservable andand controllablecontrollable :: state,state, inputinputandand outputoutput variablesvariables areare usuallyusually availableavailable forforobservationobservation andand measurementmeasurement oror computationcomputation..

Assumptions in a Fuzzy control system design :

2.2. ThereThere existsexists aa bodybody ofof knowledgeknowledge comprisedcomprised ofof aa setset ofof


2.2. ThereThere existsexists aa bodybody ofof knowledgeknowledge comprisedcomprised ofof aa setset ofoflinguisticlinguistic rules,rules, engineeringengineering commoncommon sense,sense, intuition,intuition, oror aasetset ofof inputinput –– outputoutput measurementsmeasurements datadata fromfrom whichwhich rulesrulescancan bebe extractedextracted..

3.3. AA solutionsolution existsexists..

4.4. AA controlcontrol engineerengineer isis lookinglooking forfor aa “good“good enough”enough”solution,solution, notnot necessarilynecessarily thethe optimumoptimum oneone..


5.5. TheThe controllercontroller willwill bebe designeddesigned withinwithin anan acceptableacceptablerangerange ofof precisionprecision..

Assumptions in a Fuzzy control system design :


6.6. TheThe problemsproblems ofof stabilitystability andand optimalityoptimality areare notnotaddressedaddressed explicitlyexplicitly ,, suchsuch issuesissues areare stillstill openopen problemsproblemsinin FuzzyFuzzy controllercontroller designdesign..


1.1. IdentifyIdentify thethe variablesvariables (inputs,(inputs, statesstates andand outputs)outputs) ..

The Steps in designing a simple Fuzzy control system :

2.2. PartitionPartition thethe universeuniverse ofof disclosuredisclosure oror thethe intervalintervalspannedspanned byby eacheach variablevariable intointo aa numbernumber ofof FuzzyFuzzy subsets,subsets,assigningassigning eacheach aa linguisticlinguistic labellabel (subset(subset includeinclude allall thethe


assigningassigning eacheach aa linguisticlinguistic labellabel (subset(subset includeinclude allall thetheelementselements inin thethe universe)universe)..

3.3. AssignAssign oror determinedetermine aa membershipmembership functionfunction forfor eacheachFuzzyFuzzy subsetsubset..

4.4. AssignAssign thethe FuzzyFuzzy relationshipsrelationships betweenbetween thethe inputs’inputs’ ororstates’states’ FuzzyFuzzy subsetssubsets onon thethe oneone handhand andand thethe outputs’outputs’FuzzyFuzzy subsetssubsets onon thethe otherother hand,hand, thusthus formingforming thethe rulerule––basebase..


5.5. ChooseChoose appropriateappropriate scalingscaling factorsfactors forfor thethe inputinput andandoutputoutput variablesvariables inin orderorder toto normalizenormalize thethe variablesvariables toto thethe[[00,, 11]] oror thethe [[--11,, 11]] intervalinterval..

The Steps in designing a simple Fuzzy control system :

6.6. FuzzifyFuzzify thethe inputsinputs toto thethe controllercontroller..6.6. FuzzifyFuzzify thethe inputsinputs toto thethe controllercontroller..

7.7. UseUse FuzzyFuzzy approximateapproximate reasoningreasoning toto inferinfer thethe outputoutputcontributedcontributed fromfrom eacheach rulerule..

8.8. AggregateAggregate thethe FuzzyFuzzy outputsoutputs recommendedrecommended byby eacheachrulerule..

9.9. ApplyApply defuzzificationdefuzzification toto formform aa crispcrisp outputoutput..


9/12/2013 Mahesh J. Vadhavaniya 35

9/12/2013 Mahesh J. Vadhavaniya 37

fuzzy logic

Education

fuzzy logic system

control objectives

minimum number of variables

isis itit aa multimulti

aa knowledgeknowledgefuzzy

output relationshipsdetermine

problem analysis

fuzzy inference