APSC150 - Lecture 3.7 - Fuzzy Control

7/23/2019 APSC150 - Lecture 3.7 - Fuzzy Control

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APSC 150APSC 150

Engineering Case StudiesEngineering Case StudiesCase Study 3Case Study 3

Part 3: AutomationPart 3: AutomationLecture 3.8. Fuzzy ControlLecture 3.8. Fuzzy Control

John A. MeechJohn A. MeechProfessor and Director of CEM3Professor and Director of CEM3

Centre for En!ironmental esearch inCentre for En!ironmental esearch in

Minerals" Metals" and MaterialsMinerals" Metals" and Materials

htt#:$$%%%.minin&.u'c.ca$faculty$meech$a#sc()*.htmhtt#:$$%%%.minin&.u'c.ca$faculty$meech$a#sc()*.htm

http://www.mining.ubc.ca/faculty/meech/apsc150.htm





What is Fuzzy Logic?What is Fuzzy Logic?

+ A method to de!elo# a##ro,imate solutions that tolerate A method to de!elo# a##ro,imate solutions that tolerate

im#recisionim#recision+ Con!entional mathematical models often demand a de&ree ofCon!entional mathematical models often demand a de&ree of

#recision that is difficult to achie!e -#recision that is difficult to achie!e -ada#tation may also 'e a #ro'lemada#tation may also 'e a #ro'lem

+ Models may only %or/ o!er a small re&ion in time or s#ace"Models may only %or/ o!er a small re&ion in time or s#ace"

#articularly non0linear ones#articularly non0linear ones

When the only tool you have is a hammer, all your problems look likeWhen the only tool you have is a hammer, all your problems look like

- Lotf Zadeh, University o Caliornia,- Lotf Zadeh, University o Caliornia,

The ather o u!The ather o u!



The Whole World is FuzzyThe Whole World is Fuzzy

+ 1e all use FL e!eryday in a natural %ay %ithout e!en realizin& it1e all use FL e!eryday in a natural %ay %ithout e!en realizin& it

+ FL is a method that 2com#utes %ith %ords rather than %ith num'ersFL is a method that 2com#utes %ith %ords rather than %ith num'ers

+ FL deals %ith ho% %e thin/ a'out control rather than modelin& theFL deals %ith ho% %e thin/ a'out control rather than modelin& the

#rocess itself #rocess itself

+ A FL system is ho% %e !er'alize our understandin& of the #rocess A FL system is ho% %e !er'alize our understandin& of the #rocess



Fuzzy Set Ter!inologyFuzzy Set Ter!inology

100

0 " e g

r e e o # $ e l i e # % "

o $ &



Fuzzy "ay to 'ightFuzzy "ay to 'ight



Fuzzy Set E(a!)lesFuzzy Set E(a!)les

+ An automo'ile chan&in& lanes %hile #assin& An automo'ile chan&in& lanes %hile #assin&

+ 4he #osition of the shoreline durin& tidal inflo% or outflo%4he #osition of the shoreline durin& tidal inflo% or outflo%

+ A door 'ein& closed or o#ened -it5s a6ar7 A door 'ein& closed or o#ened -it5s a6ar7+ A %ater !al!e 'ein& o#ened or closed A %ater !al!e 'ein& o#ened or closed

+ A &lass of %ater -s it half0full or half em#ty9 A &lass of %ater -s it half0full or half em#ty9

+ 4he mi,in& to&ether of t%o #rimary colours4he mi,in& to&ether of t%o #rimary colours

+ 4he a&e of a youn& customer in a 'ar -is D reuired94he a&e of a youn& customer in a 'ar -is D reuired9

+ 4he time it ta/es to dri!e from home to %or/4he time it ta/es to dri!e from home to %or/

+ 4he %aitin& time in a ueue4he %aitin& time in a ueue



Fuzzy Logic *ersus $inary LogicFuzzy Logic *ersus $inary Logic

+ ;inary Lo&ic 0 thin&s are either 4rue or False;inary Lo&ic 0 thin&s are either 4rue or False

+ 1hile that may 'e ultimately the case" as %e1hile that may 'e ultimately the case" as %e

&ra##le %ith tryin& to #redict this state of affairs"&ra##le %ith tryin& to #redict this state of affairs"the de&ree to %hich %e 'elie!e somethin& is truethe de&ree to %hich %e 'elie!e somethin& is true

or false can chan&e on a scale from * to (**or false can chan&e on a scale from * to (**

+;inary Lo&ic deals %ith the set <*"(**=;inary Lo&ic deals %ith the set <*"(**=

+ Fuzzy Lo&ic deals %ith the set -*"(**Fuzzy Lo&ic deals %ith the set -*"(**



Fuzzy State!entsFuzzy State!ents

+ am >*? sure a'out this. am >*? sure a'out this.

+ t is %arm today.t is %arm today. -same meanin& in @ello%/nife as in Miami9-same meanin& in @ello%/nife as in Miami9

+ t may rain today.t may rain today. -%here" %hen" ho% intense" for ho% lon&9-%here" %hen" ho% intense" for ho% lon&9

+ A 2recession is a 2decline in DP o!er B consecuti!e uarters. A 2recession is a 2decline in DP o!er B consecuti!e uarters.

+ A 2de#ression is a se!ere -(*? DP dro# or #rolon&ed -30 year A 2de#ression is a se!ere -(*? DP dro# or #rolon&ed -30 year

recession.recession.

+ 22Read my lipsRead my lips: no ne% ta,es: no ne% ta,es ..1. ;ush" (>88..1. ;ush" (>88

+ t de#ends on %hat the meanin& of the %ord 5is5 is.t de#ends on %hat the meanin& of the %ord 5is5 is. 1.J. Clinton" (>>81.J. Clinton" (>>8



Parado(esParado(es

+ A man says: Don5t 4rust Me. A man says: Don5t 4rust Me.

Ghould you trust him9 f you do" then you don5t7Ghould you trust him9 f you do" then you don5t7

+ A #olitician says: All #oliticians are liars. A #olitician says: All #oliticians are liars.s this true9 f so" then he is not a liar.s this true9 f so" then he is not a liar.

+ A card states on one side: A card states on one side:4he sentence on the other side is false...4he sentence on the other side is false...

+ Hn the other side a##ears:Hn the other side a##ears:4he sentence on the other side is true...4he sentence on the other side is true...

o% do you inter#ret this card9o% do you inter#ret this card9



Parado(esParado(es

;ertrand ussell5s Famous Parado,:;ertrand ussell5s Famous Parado,:

2 2 All rules ha!e e,ce#tions. All rules ha!e e,ce#tions.

s this a rule9s this a rule9f so" then %hat is its e,ce#tion9f so" then %hat is its e,ce#tion9

+ 4he Liar5s Parado, re#resented 'y4he Liar5s Parado, re#resented 'y

4his sentence is false.4his sentence is false.

can only 'e understood as a half truth. t can ne!er 'e a truecan only 'e understood as a half truth. t can ne!er 'e a true

statement and it ne!er can 'e a false statement.statement and it ne!er can 'e a false statement.



Parado(esParado(es

+ Parado,es all ha!e the same form:Parado,es all ha!e the same form:

2 2 A statement G and its ne&ation not0G A statement G and its ne&ation not0G

'oth of %hich ha!e the same truth0!alue t-G'oth of %hich ha!e the same truth0!alue t-G

t-G I t-not0Gt-G I t-not0G

+ 4he t%o statements are 'oth 4E -( and FALGE -* at the4he t%o statements are 'oth 4E -( and FALGE -* at the

same time. ;ut 'i!alent lo&ic states that ne&ation #roduces thesame time. ;ut 'i!alent lo&ic states that ne&ation #roduces the

re!erse truth !alue. ence:re!erse truth !alue. ence:

t-not0G I ( 0 t-Gt-not0G I ( 0 t-G



Parado(esParado(es

+ Com'inin& these t%o e,#ressions" %e &et:Com'inin& these t%o e,#ressions" %e &et:

t-G I ( 0 t-Gt-G I ( 0 t-G

+ 4his is contradictory since if G is true" then ( I * and if G is false"4his is contradictory since if G is true" then ( I * and if G is false"

then * I (. ;ut a fuzzy inter#retation of truth !alues can sol!e for t-Gthen * I (. ;ut a fuzzy inter#retation of truth !alues can sol!e for t-Gallo%in& it to assume a !alue other than the set <*" (=. Go:allo%in& it to assume a !alue other than the set <*" (=. Go:

t-G I *.)t-G I *.)

+ 1ith fuzzy lo&ic" a Parado, reduces to a literal half0truth %hich can1ith fuzzy lo&ic" a Parado, reduces to a literal half0truth %hich can

'e considered the uncertainty inherent in e!ery em#irical statement'e considered the uncertainty inherent in e!ery em#irical statement

and many mathematical e,#ressions.and many mathematical e,#ressions.



Parado(esParado(es

eturnin& to the LiarKs Parado," it must ha!e a !alue of *.) on a trutheturnin& to the LiarKs Parado," it must ha!e a !alue of *.) on a truthscale from * to (.scale from * to (.

;ut it is #ossi'le to &enerate similar sentences that can ta/e on a;ut it is #ossi'le to &enerate similar sentences that can ta/e on a

!alue any%here alon& the full ran&e of the truth scale. For e,am#le:!alue any%here alon& the full ran&e of the truth scale. For e,am#le:

Do; -?Do; -?

4his sentence is sometimes false.4his sentence is sometimes false. )*(**)*(**

4his sentence is rarely false.4his sentence is rarely false. *)**)*

Hther sentences that use ualifiers" hed&es" or modifiers such asHther sentences that use ualifiers" hed&es" or modifiers such as

could 'e or mi&ht 'e2 #ro!ide a %ay to ma/e all #arado,icalcould 'e or mi&ht 'e2 #ro!ide a %ay to ma/e all #arado,ical

sentences truly fuzzy.sentences truly fuzzy.

-and" #erha#s" sensi'le7-and" #erha#s" sensi'le7



Fuzzy Linguistic +edgesFuzzy Linguistic +edges

+ Lin&uistic e,#ressions fla!our our certainty in a conce#t or factLin&uistic e,#ressions fla!our our certainty in a conce#t or fact

+ A hed&e is a ualifier used to a!oid total commitment or to ma/e a A hed&e is a ualifier used to a!oid total commitment or to ma/e a

statement more !a&ue or more definitestatement more !a&ue or more definite

+ 4he andom ouse 1ord Menu 'y Gte#hen lazier lists )4he andom ouse 1ord Menu 'y Gte#hen lazier lists )

cate&ories of ualifiers that include:cate&ories of ualifiers that include:

0 Limitations and Conditions0 Limitations and Conditions 3B) entries3B) entries

0 A##ro,imations and eneralizations0 A##ro,imations and eneralizations ()* entries()* entries0 Em#hasizers0 Em#hasizers 8) entries8) entries

0 Ma,imizers and Gu#erlati!es0 Ma,imizers and Gu#erlati!es (*) entries(*) entries

0 A'solutes and uarantees0 A'solutes and uarantees (8) entries(8) entries



Fuzzy Linguistic +edgesFuzzy Linguistic +edges

+ En&lish is full of rich lin&uistic terms to #ro!ide shades of &rey to aEn&lish is full of rich lin&uistic terms to #ro!ide shades of &rey to a

conce#t. Consider the follo%in& set of %ords:conce#t. Consider the follo%in& set of %ords:

'eautiful" #retty" &or&eous" !olu#tuous" se,y" attracti!e"'eautiful" #retty" &or&eous" !olu#tuous" se,y" attracti!e"

stunnin&" handsome" fa'ulous" mar!ellous" outstandin&"stunnin&" handsome" fa'ulous" mar!ellous" outstandin&"

cute" remar/a'le" lo!ely" ma&nificent" e,traordinary" etc.cute" remar/a'le" lo!ely" ma&nificent" e,traordinary" etc.

+ Each may descri'e a #ersonKs a##earance" 'ut the meanin& is differentEach may descri'e a #ersonKs a##earance" 'ut the meanin& is different

de#endin& on the %ord or conte,t in %hich it is used.de#endin& on the %ord or conte,t in %hich it is used.

+ otice ho% your mind instantly s%itches conte,t as you mo!e from oneotice ho% your mind instantly s%itches conte,t as you mo!e from one%ord to another.%ord to another.

+ 4he term handsome" for e,am#le" is often reser!ed for males %hile4he term handsome" for e,am#le" is often reser!ed for males %hile

#retty and &or&eous ty#ically descri'e a female.#retty and &or&eous ty#ically descri'e a female.



"egree o# Fuzziness"egree o# Fuzziness



FL is Part o# A,FL is Part o# A,

+ A I Artificial ntelli&ence A I Artificial ntelli&ence

+ Com#onents of ACom#onents of A

+E,#ert Gystems -rule 'ase structureE,#ert Gystems -rule 'ase structure

+ Fuzzy Lo&ic -uncertainty mana&ementFuzzy Lo&ic -uncertainty mana&ement

+ Artificial eural et%or/s -learnin& method Artificial eural et%or/s -learnin& method

+ enetic Al&orithms -o#timization searchenetic Al&orithms -o#timization search

+ G1AM ntelli&ence -a&ent0'ased a##roachG1AM ntelli&ence -a&ent0'ased a##roach



+o- a Fuzzy Controller Wor.s+o- a Fuzzy Controller Wor.s

+ Ada#tation and E,tension are done %ith ease in one or more of four %ays: Ada#tation and E,tension are done %ith ease in one or more of four %ays:+ edefinin& fuzzy sets dynamicallyedefinin& fuzzy sets dynamically

+ edefinin& the rule 'ase dynamicallyedefinin& the rule 'ase dynamically

+ Chan&in& the nferencin& method on the flyChan&in& the nferencin& method on the fly

+ Chan&in& the Defuzzification method on the flyChan&in& the Defuzzification method on the fly



E(a!)le /uleE(a!)le /ule

+ ules are constructed as s#o/en 'y anules are constructed as s#o/en 'y an

e,#erienced o#erator -an E,#ert:e,#erienced o#erator -an E,#ert:

f CE4 DA1 is LH1

4hen CEAGE FEEDA4E A LH4

Pro!ided GCEE ; LEEL is not 4HH0

+ A set of rules li/e this #ro!ides a %ay to A set of rules li/e this #ro!ides a %ay to

im#lement control ra#idly and effecti!elyim#lement control ra#idly and effecti!ely



/ule )erations/ule )erations

+ ADin& ta/es the Minimum Do; ADin& ta/es the Minimum Do;

+ Hin& ta/es the Ma,imum Do;Hin& ta/es the Ma,imum Do;

+ 4he et De&ree of 4ruth of the #remise is assi&ned4he et De&ree of 4ruth of the #remise is assi&nedto the conclusion statement usin& the follo%in&to the conclusion statement usin& the follo%in&

euation:euation:

Do;Do;-conc-conc I d4 N CF $ (**I d4 N CF $ (**

+ %here CF I Certainty Factor of the rule conclusion%here CF I Certainty Factor of the rule conclusion

statement -f no !alue is &i!en" it is ta/en as (**?statement -f no !alue is &i!en" it is ta/en as (**?

= d4



E(a!)leE(a!)le

FF 2A2A Do;-A I >)Do;-A I >)

AD AD 2;2; Do;-; I 8)Do;-; I 8)

HH 2C2C Do;-C I 88Do;-C I 88

AD AD 2D2D Do;-D I O)Do;-D I O)

4E4E 2F CF I >*2F CF I >*

==

8)

O)= 8)

Go the !alue of the d4 I 8)Go the !alue of the d4 I 8)

And 2F is assi&ned a Do; I 8)N>*$(** I O.)? And 2F is assi&ned a Do; I 8)N>*$(** I O.)?



E(a!)le %inclusi*e /&E(a!)le %inclusi*e /&

FF 2A2A Do;-A I >)Do;-A I >)

AD -2; AD -2; Do;-; I 8)Do;-; I 8)

HH 2C2C Do;-C I 88Do;-C I 88

AD AD 2D2D Do;-D I O)Do;-D I O)

4E4E 2F CF I >*2F CF I >*

= 88

}

O)

Go the !alue of the d4 I O)Go the !alue of the d4 I O)

And 2F is assi&ned a Do; I O)N>*$(** I O.)? And 2F is assi&ned a Do; I O)N>*$(** I O.)?



Secondary Crushing PlantSecondary Crushing Plant



Feed /ate Fuzzy Control /uleSetFeed /ate Fuzzy Control /uleSet

Current "ra-Current "ra-+,2++,2+

Current "ra-Current "ra-E",4+,2+E",4+,2+

Current "ra-Current "ra-

Current "ra-Current "ra-E",4LWE",4LW

Current "ra-Current "ra-LWLW

Screen $in Le*elScreen $in Le*el



/ A'" A'" A'"


+,2++,2+

/

Cha!6er Le*elCha!6er Le*el

+,2++,2+

' 7ES' 7ES ' 7ES

Feed /ate

Change

'C+A'2E

Feed /ate

Change

'E2AT,8E$,2

Feed /ate

Change

PS,T,8E$,2

Feed /ate

Change

PS,T,8ESALL

Feed /ate

Change

'E2AT,8ESALL

Feed ate Chan&e -discrete I1ei&hted A!era&e of Fuzzy Get Gu#remums 'ased on es#ecti!e De&rees of ;elief



/ule$ase atri(/ule$ase atri(

Current Dra%Current Dra%Gcreen ;in Le!elGcreen ;in Le!el

Lo%Lo% ot0HQot0HQ HQHQ i&hi&h

i&hi&h ;; ;; ;; ;;

Medium0i&hMedium0i&h GG GG GG ;;

HQHQ CC CC GG ;;

Medium0Lo%Medium0Lo% PGPG PGPG GG ;;

Lo%Lo% P;P; P;P; CC ;;

; I e&ati!e0;i&; I e&ati!e0;i& P; I Positi!e0;i&P; I Positi!e0;i&

G I e&ati!e0GmallG I e&ati!e0Gmall PG I Positi!e GmallPG I Positi!e Gmall

C I o0Chan&eC I o0Chan&e



Fuzzy Sets %!e!6ershi) #unctions&Fuzzy Sets %!e!6ershi) #unctions&

* B 8 )*

(**

*

D e & r e e o f ; e l i e f

Current Dra% -am#s

Lo%Lo% MediumMedium

Lo%Lo%MediumMedium MediumMedium

i&hi&hi&hi&h

* B* * * 8* (**

(**

*

D e & r e e o f ;

e l i e f

;in Le!el -?

Lo%Lo% HQHQ i&hi&hot0HQot0HQ



ut)ut Fuzzy Singletonsut)ut Fuzzy Singletons

0)* 0(* * R(* R)*

(**

*

D e & r e e o f

; e l i e f

Feed ate Chan&e -t#h

e&ati!ee&ati!e

;i&;i&e&ati!ee&ati!e

GmallGmalloo

Chan&eChan&ePositi!ePositi!e

GmallGmallPositi!ePositi!e

;i&;i&



Controller Per#or!ance 9 cris) setsController Per#or!ance 9 cris) sets

P;

PG

C

G

;

F

e e d a t e C h a n

& e

- t # h . Current Dra%

-am#sLH1 MEDM MEDM MEDM

LH1

GCEE ; LEEL I LH1

CGP GE4G



Controller Per#or!ance 9 #uzzy setsController Per#or!ance 9 #uzzy sets

P;

PG

C

G

;

F

e e d a t e C h a n

& e

- t # h . Current Dra%

-am#sLH1 MEDM MEDM MEDM

LH1

GCEE ; LEEL I LH1

FSS@ GE4G



4sing a Fuzzy Con#idence Le*el4sing a Fuzzy Con#idence Le*el

ormally C I *" 'ut it may 'e reasona'le for C to 'e chosenormally C I *" 'ut it may 'e reasona'le for C to 'e chosen

to e,clude lo% 'elief informationto e,clude lo% 'elief information



/esults 9 $est Production/esults 9 $est Production



/esults Sta6ility/esults Sta6ility



+o- to $uild a Fuzzy Controller +o- to $uild a Fuzzy Controller

+ ;e&in 'y selectin& a s#ecific out#ut;e&in 'y selectin& a s#ecific out#ut+ Fan G#eed -for e,am#leFan G#eed -for e,am#le

+ Gelect at least three terms to characterize theGelect at least three terms to characterize the

out#ut !aria'le -fi!e is 'etterout#ut !aria'le -fi!e is 'etter+ Hff Hff

+ Lo%Lo%

+ MediumMedium

+ i&hi&h

+ ery i&hery i&h

+ Determine the minimum and ma,imum le!el of theDetermine the minimum and ma,imum le!el of the

out#ut !aria'le -discrete !alueout#ut !aria'le -discrete !alue

in : 0in : 0 a( : 100 a( : 100




+ Gelect t%o !aria'les that %ould affect the le!el ofGelect t%o !aria'les that %ould affect the le!el ofthe out#ut !aria'lethe out#ut !aria'le

+ oom 4em#eratureoom 4em#erature

+ elati!e umidityelati!e umidity

+ Gelect at least three terms to characterize these t%oGelect at least three terms to characterize these t%oin#ut !aria'les -here %e ha!e )in#ut !aria'les -here %e ha!e )

+ 4em#erature4em#erature+ ColdCold

+CoolCool

+ HQHQ

+ otot

+ ery otery ot

+ Lo%Lo%

+ MediumMedium

+ Medium0i&hMedium0i&h

+ i&hi&h

+ ery i&hery i&h

+umidityumidity

in : 0 a( : 30

in : 0 a( : 100




+ Formulate a set of rules to lin/ each in#utFormulate a set of rules to lin/ each in#utstate com'ination to an out#ut statestate com'ination to an out#ut state

elati!eelati!eumidityumidity

-?-?

4em#erature -TC4em#erature -TC

ColdCold CoolCool HQHQ otot ery otery ot

Lo%Lo%

MediumMedium

Medium0i&hMedium0i&h

i&hi&h

ery0i&hery0i&h

Hff Hff

Hff Hff

Hff Hff

Hff Hff

Hff Hff

Lo%Lo%

Lo%Lo%

Hff Hff Lo%Lo%

Lo%Lo%

Lo%Lo% MediumMedium

MediumMedium

MediumMedium

MediumMedium

MediumMedium

i&hi&h

i&hi&h

i&hi&h

i&hi&h

i&hi&h

i&hi&h

ery0i&hery0i&h

ery0i&hery0i&h ery0i&hery0i&h




+ Create Fuzzy Gets for n#ut aria'les ( U BCreate Fuzzy Gets for n#ut aria'les ( U B(**

*

D e & r e e

o f ; e l i e f

4em#erature TC

* B 8 (* (B ( ( (8 B* BB B B B8 3*

Cold Cool HQ otery

ot

(**

*

D e & r e e

o f ; e l i e f

elati!e umidity -?

* (* B* 3* * )* * O* 8* >* (**

Lo% Medium Medium

i&h

i&hery

i&h




+ Create Fuzzy Gin&letons for Hut#ut aria'leCreate Fuzzy Gin&letons for Hut#ut aria'le

(**

*

D e & r e

e

o f ; e l i e f

Fan G#eed -?

* (* B* 3* * )* * O* 8* >* (**

Lo% MediumHff i&h ery i&h



Te!)erature Su6setsTe!)erature Su6sets

Su6set A $ C "

Cold * * * (

Cool * ( ( B*

HQ ( B* B* B)

ot B* B B 3*ery ot B) 3* 3* 3*

+ Consider each fuzzy set as a tra#ezoidConsider each fuzzy set as a tra#ezoid

(**(**

**

Do;Do;

ni!erse of Discourseni!erse of Discourse A Aii ; ;

ii C Cii D D

ii

FuzzyFuzzy

Gu'set iGu'set i



+u!idity Su6sets+u!idity Su6sets

+ Consider each fuzzy set as a tra#ezoidConsider each fuzzy set as a tra#ezoid

Su6set A $ C "

Lo% * * * )*

Medium * ) )* )

Medium0i&h )* ) O* 8*

i&h O* 8B 8B >)ery0i&h 8* >) (** (**

(**(**

**

Do;Do;

ni!erse of Discourseni!erse of Discourse A A 6 6 ; ;

6 6 C C 6 6 D D

6 6

FuzzyFuzzy

Gu'set 6Gu'set 6



e!6ershi) %"o$& E;uationse!6ershi) %"o$& E;uations

+ eneric euation for each set is as follo%s:eneric euation for each set is as follo%s:

+ Let 2, I measured tem#erature -TCLet 2, I measured tem#erature -TC

Do;-VDo;-V

ii

leftleft I Min-(**" Ma,-*"(**N-, 0 AI Min-(**" Ma,-*"(**N-, 0 A

ii$-;$-;

ii 0 Ai0 Ai

Do;-VDo;-Viiri&htri&ht I Min-(**" Ma,-*"(**N-DI Min-(**" Ma,-*"(**N-D

ii 0 ,$-D0 ,$-Dii 0 C0 C

ii

Do;-VDo;-Viifinalfinal I Min-Do;I Min-Do;

leftleft" Do;" Do;ri&htri&ht

+ Let 2y I measured humidity -?Let 2y I measured humidity -?

Do;-@Do;-@ 6 6leftleft I Min-(**" Ma,-*"(**N-y 0 AI Min-(**" Ma,-*"(**N-y 0 A

6 6$-;$-; 6 6 0 A0 A

6 6

Do;-@Do;-@ 6 6ri&htri&ht I Min-(**" Ma,-*"(**N-DI Min-(**" Ma,-*"(**N-D

6 6 0 y$-D0 y$-D 6 6 0 C0 C

6 6

Do;-@Do;-@ finalfinal I Min-Do;I Min-Do;leftleft" Do;" Do;

ri htri ht



E(a!)leE(a!)le

, I BB and y I 8(, I BB and y I 8(

4em#erature4em#erature

Do;-ColdDo;-Cold I *I *

Do;-CoolDo;-Cool I *I *

Do;-HQDo;-HQ I Min-Min-(**" Ma,-*"(**N-BB 0 ($-B*I Min-Min-(**" Ma,-*"(**N-BB 0 ($-B* 0 ("0 (" -Min-(**" Ma,-*"(**N-B) 0 BB$-B) 0 B*-Min-(**" Ma,-*"(**N-B) 0 BB$-B) 0 B*

I Min-Min-(**" (33" Min-(**" *I Min-Min-(**" (33" Min-(**" *

I *I *

Do;-otDo;-ot I Min-Min-(**" Ma,-*"(**N-BB 0 B*$-BI Min-Min-(**" Ma,-*"(**N-BB 0 B*$-B 0 B*"0 B*"

-Min-(**" Ma,-*"(**N-B 0 BB$-B 0 B*-Min-(**" Ma,-*"(**N-B 0 BB$-B 0 B*I Min-Min-(**" 33" Min-(**" I Min-Min-(**" 33" Min-(**"

I 33I 33

Do;-ery0otDo;-ery0ot I *I *



E(a!)leE(a!)le

, I BB and y I 8(, I BB and y I 8(

umidityumidity

Do;-Lo%Do;-Lo% I *I *

Do;-MediumDo;-Medium I *I *

Do;-Medium0i&hDo;-Medium0i&h I *I * Do;-i&hDo;-i&h I Min-Min-(**" Ma,-*"(**N-8( 0 O*$-8BI Min-Min-(**" Ma,-*"(**N-8( 0 O*$-8B 0 O*"0 O*"

-Min-(**" Ma,-*"(**N->) 0 8($->) 0 8B-Min-(**" Ma,-*"(**N->) 0 8($->) 0 8B

I Min-Min-(**" >B" Min-(**" (*8I Min-Min-(**" >B" Min-(**" (*8

I >BI >B

Do;-ery0i&hDo;-ery0i&h I Min-Min-(**" Ma,-*"(**N-8( 0 8*$->)I Min-Min-(**" Ma,-*"(**N-8( 0 8*$->) 0 8*"0 8*" -Min-(**" Ma,-*"(**N-(** 0 8($-(** 0 (**-Min-(**" Ma,-*"(**N-(** 0 8($-(** 0 (**

I Min-Min-(**" O. Min-(**"I Min-Min-(**" O. Min-(**" ∞∞

I OI O

Pass the ,n)ut "o$s through thePass the ,n)ut "o$s through the



Pass the ,n)ut "o$s through thePass the ,n)ut "o$s through the

/ules/ules

+ 4a/e the Minimum Do; and a##ly it to the4a/e the Minimum Do; and a##ly it to theres#ecti!e Hut#ut su'setres#ecti!e Hut#ut su'set

elati!eelati!eumidityumidity

-?-?

4em#erature -TC4em#erature -TC

ColdCold CoolCool HQHQ otot ery otery ot

Do;Do; ** ** ** 3333 **

Lo%Lo% **

MediumMedium **

Medium0i&hMedium0i&h **

i&hi&h >B>B

ery0i&hery0i&h OO

**

OO OO

3333



"e#uzzi#ication"e#uzzi#ication Gu#remumGu#remum

Do;-mediumDo;-medium I *I * * *

Do;-hi&hDo;-hi&h I O or 33I O or 33 O* O*

Do;-!ery0hi&hDo;-!ery0hi&h I OI O (** (**

Accu!ulation ethodAccu!ulation ethod

Fan G#eedFan G#eed I -*N* R ONO* R 33NO* R ON(**$-*ROR33ROI -*N* R ONO* R 33NO* R ON(**$-*ROR33RO

I -B** R >* R B3(* R O**$(*OI -B** R >* R B3(* R O**$(*O

I )B**$(*O I 8.I )B**$(*O I 8.

a(i!u! ethoda(i!u! ethod

Fan G#eedFan G#eed I -*N* R 33NO* R ON(**$-*R33ROI -*N* R 33NO* R ON(**$-*R33RO I -B** R B3(* R O**$(**I -B** R B3(* R O**$(**

I )(*$(** I ).(I )(*$(** I ).(



Ada)tationAda)tation

+ 4he system can 'e easily ada#ted to another !aria'le 'y4he system can 'e easily ada#ted to another !aria'le 'y

one or more of the follo%in&:one or more of the follo%in&:

+ Allo% fuzzy sets to mo!e alon& the ni!erse of Discourse Allo% fuzzy sets to mo!e alon& the ni!erse of Discourse

+ Chan&e rule 'aseChan&e rule 'ase

+ Chan&e method of inferencin&Chan&e method of inferencin&

+ Chan&e method of defuzzificationChan&e method of defuzzification

+n the #re!ious e,am#le" if %e feel cautious then then the #re!ious e,am#le" if %e feel cautious then theaccumulation method mi&ht 'e #referred %hereas" if %eaccumulation method mi&ht 'e #referred %hereas" if %e

are #re#ared to ta/e ris/s then the ma,imum methodare #re#ared to ta/e ris/s then the ma,imum method

could 'e used.could 'e used.



Wuestions 9Wuestions 9

APSC150 - Lecture 3.7 - Fuzzy Control

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