SLP DUNG OAI S6 GIA TLPOOl VOI L6 NHIET

TAP CHi KHOA HOC VA CONG NGHE Tap 48, s6 2, 2010 '^ Tr. 109-121

SO S A N H CAC BO OIEU KHIEN M Q V O I BO OIEU KHIEN SLP DUNG OAI S6 GIA TLPOOl VOI L 6 NHIET

NGUYEN TI^N DUY, v u NHU'LAN

l . M d D A U • '"'' '

•\

Li thuyet dai so gia ttr (DSGT) [9, 10] da dugc nghien ciiu phat ttien tu cuoi nhung nam 80, dau nhung nam 90 the ki truoc va da dugc iing dung vao mgt so linh vuc tin bgc va dieu khien hoc nhu li thuyet co sa dir lieu voi thong tin khong chac chan, phuong phap ho trg quyet dinh va ling dung cho mgt so bai toan dieu khien trong moi truang thong tin ma. Nhieu ket qua nghien ciiu da dugc cong bo tren nhiing tap chi quoc te va trong ki yeu hgi nghi quoe te. Muc tieu eiia bai bao nay la phat trien hon niia li thuyet DSGT va dae biet nghien ciiu ma rgng iing dung ciia no trong lmh vuc dieu khien de khang dinh them y nghia ciia DSGT, mgt cau tnic dai so ngu nghia dinh tinh eua mien gia tri ngon ngu ciia bien ngon ngii. Neu xem li thuyet tap ma nhu la mgt tiep can giai tich cho viec giai quyet nhiem vu neu tren, thi DSGT co the dugc xem nhu la mgt each tiep can dai so. No rat khae biet vai each tiep can giai tich va do do huong va ngi dung nghien ciiu co dae tnmg khac biet vai eac huang nghien ciiu dua tten li thuyet tap ma. DSGT la mgt li thuyet mai. Nhieu ket qua da dugc cong bo tren cac tap chi va hgi nghi quoe te rat c6 uy tin [11 - 17] va dieu do chiing to rang li thuyet da duge thua nhan tren binh dien quoe te. Tiep can DSGT co dac trung khae biet so vai each tiep can dua tren tap ma a eho vai tro ciia gia tu ngon ngu luon luon hien dien (explicit) va duge xem nhu la cac toan tu l-ngoi ciia dai so. Vi vay CO the xem li thuyet DSGT la mgt tiep can tinh toan tren tu (word computing) mgt each true tiep Ichong thong qua bat ki ham thugc eiia nhan ngon ngQ'.

Mgt so ket qua ciia li thuyet DSGT da dugc nhieu tac gia nuoc ngoai sir dung de phat trien phuong phap luan hay tham chieu y tuong de phat trien cong trinh ciia hg. Co the ke den mgt so huong nghien ciiu ciia eae tae gia nuac ngoai sir dung hoac tham chieu den li thuyet DSGT nhu sau:

- Xay dung hg cac tap ma sao cho thoa cac tien de ciia DSGT va xay dung phuang phap lap luan xap xi [1 - 3];

- Bai toan tro choi trong linh vuc xa hgi vai ma ttan dinh gia boi gia tri ngon ngii eua DSGT [4, 5];

- Xay dung dan cac gia tri chan li ngon ngii dua tren gia bi va phuong phap lap luan dua tren logic gia tti chan li ngon ngii vai iing dung ttong trg giiip quyet dinh [6, 7].

Sau phan ma dSu, bai bao c6 ngi dung ca ban nhu sau: Phan Dat van de neu len bai toan nghien ciiu so sanh mgt so phuong phap dieu khien 16 nhiet truyen thong vai phuang phap dua tren li thuyit DSGT. Nhung phSn tiep theo xay dung mo hinh mo phong tren ea so SIMULINK MATLAB dk so sanh phuong phap diSu khien ma truyen thong doi tugng 16 nhiet va phuang phap di8u khiln sii dung li thuyet DSGT. Fhkn Phu lue la ket qua thu dugc tu qua trinh mo phong tren co sa SIMULINK, qua do thay ro hieu qua dieu khien sii dung li thuyet DSGT. Phan Ket luan t6m tat ket qua thu duge qua cae nghien eiiu so sanh.

2. VAI KHAI NIEM CO S d VE DAI SO GIA TU*

Xet mgt tap gia tri ngon ngii la mien eiia biSn ngon ngii (linguistic domain) ciia bien chan li TEMPERATURE g6m cac tit sau:

T = dom(TEMPERATURE) = {Large, Small, very Large, very Small, more Large, more Small, approximately Large, approximately Small, little Large, little Small, less Large, less Small, very more Large, very more Small, very possible Large, very possible Small, ...}

Khi do mien ngon ngii T = dom(TEMPERATURE) e6 thi biiu thi nhu la mgt cau tnic dai s6 AT = (T, G, H, <), trong do: T la tap nen eua AT; G la tap eac tii nguyen thuy (tap cac phan tli sinh: Large, Small; H la tap cac toan tu mgt ngoi, ggi la cac gia tu (eac trang tit nhan); < la bieu thi quan be thii tu tren eae ttr (eac khai niem ma), no dugc "cam sinh" tii ngii nghia tu nhien <etia eac tii>. Vi du: dua tten ngir ngbia, cae quan he thii tu sau la diing: Small < Large, more Large < very Large, very Small < more Small, possible Small < Large, Small < possible Small, ... •

Binh nghia 2.1. Cbo DSGT ma rgng doi xiing AT = (T, G, H, <), f: T ^ [ 0 , 1] la mgt bam dinh lugng ngli nghia (DLNN) cua AT neu Vh, k G H+ hoac Vh, k e H- va Vx, y G T, ta co:

/(/^x)-/(x) / ( ^ ) - / ( x )

f{hy)-f(y)

nky)-f(y)

^(2.1)

Xet cac gia tri: Large, Very Small, ... Tren quan diem DSGT, ta co mgt each dinh nghTa tinh ma kha true quan dua tten kich co cua tap H(x) nhu hinh 2.1.

Cho truac mgt bam DLNN / eua X. Xet bat ki XG X, tinh mo ciia x khi do dugc do bang duong kinh tapXH(x)) c [0, 1].

0.5 LittleLarge PossLarge Large MoreLarge VeryLarge 1 1 1

•<

Diameter of f(H(LittleLarge))

1 1 1

Diameter of f(H(PossLarge))

— 1 — 1

;<

Diameter of f(H(MoreLarge))

1

Diameter of f(H(VeryLarge))

1

^1

1

Hinh 2.1. Tinh ma cua gia tri ngon ngir Dinh nghia 2.2. Do do tinh ma.

Ham/m: T^>[0, 1] dugc ggi la do do tinh mo n e u : ^ ( c - ) = 6 > 0 v a ^ ( e + ) = 1 - 6 > 0, trong do e- va c+ la cac phan tii sinh am va duong.

Gia sii tap cae gia tu H = H+uH-, H- = {hi, bz, ..., bp} voi hi>h2> ... >hp, H+ = {hp-n, h p+2, ..., h p-i-q} vai hp-n<bp-^2< ... <bp-^q. Khi do:

Vai bat ki x, y G T hG H - ^ ^ • = ^ , ding thiic nay khong phu thugc vao cae

fm(x) fm(y)

phan tii X, y va do do ta co thi ki hieu la //(h) va ggi la do do tinh ma (fiizziness measure) ciia gia tli h.

Tinh chat c i l a X x ) va //(h).

X h x ) = //(b)/m(x), VxG T (2.2)

p+q

'^ fm(hiC) = fm(c), voice {c-, c+} (2.3)

p+q

J^fm(h.x) = fm(x)

;=i

p 9

'^jU(hi) = or va ^ ju(h.) = Pvoia, P> Ova a+P = 1

(2.4)

(2.5)

i=l i=p+\

2.1. Xay durng ham dinh lirong ngu nghia tren co so do do tinh mo cua gia tw Xet mo hinh ma sau day:

IF X = Al THEN y = Bl i;:>-^' - IFx = A2THENy = B2

(2.6) IF X = An THEN y = Bn'

Gia su cho truoc do do tinh ma cua eae gia tii |i(h) va cac gia tri do do tinh mo ciia cac phan tli sinh fm(c~) , fm(c^)va 9 la phan tii tiling hoa (neutial).

Ham dinh lugng ngii nghia v cua T dugc xay dung nhu sau vai x = bin,.. .bi2biie:

v(c') = 0-afm(c~), v(c^)-d + afm(c*)

fm(x) = fm(h,^...h.^h.,c) = ju(hj...p(h,^)ju(h,^)fm(c) v(hjx) = v(x) -\- sga(hjx)

neu j<p va

v(hjX) = v(x) -I- sgn(hjx)

p 2

^ fm(h,x) - - (1 - sgn(/z,.x) sgn(\h.x)(p - a)fm(h.x)

J I

2 ] fm(h,x) - - (1 - sgn(h,x) sgn(\h,x)(P - a)fm(h.x)

i=p+l ^

neuj>p. (2.7) Mgt each true cam ta c6 thi xem moi menh de if - then xae dinh mgt diem vao va do do n

menh di cua mo binh (2.6) se xae dinh cho ta mgt duong cong trong khong gian ngon ngii XxY va ggi la duang eong ma C. Khi do bai toan lap luan xap xi tren tap ma co the chuyen ve bai

toan ngi suy doi vai duong eong mo C. Gia su f^ va fy la eac ham ngii nghia dinh lugng tuong ling cua X va Y. Cac ham nay se chuyin duong cong ma C thanh duong cong thue C trong khong gian [0, 1] x [0, 1]. Nhu vay bai toan lap luan mo dugc chuyen vi bai toan ngi suy thong thuong nha ham dinh lugng ngir nghia.

2.2. Dieu khien sir dung dai so gia tii'

Tren co so li thuyet DSGT [9, 10 ], trong [17] da dua ra so d6 diiu khiin su dung DSGT (HAC: Hedge Algebras - based controller) voi anh xa DLNN (Semantieally Quantifying Mappings) nhu sau: , "';'

HA-based controller

r

^

1

Semantization (NgQ nghTa hoa)

- ^ -^

y.

QSMs

(Anh xa NNDL) -^ Desemantization (Giai nghTa)

—1

-t—> 1 u Plant (Doi tugng)

/fin/z 2.2. Sa do dieu khien sir dung DSGT

Su dung tiep can DSGT trong bai toan dieu khien 16 nhiet se dugc xem xet cu the duai day.

3. DAT VAN DE

Ham truyen ciia 16 la mgt khau quan tinh bac nhat eo tte: .;

exp(-rP)

WJP) = K-

^(3.1)

Vai K la be s6 khuieh dai cua d6i tugng, K = 10°C/s6; T hang so thai gian, T = 1300 s;

T thai gian tre, x = 30 s.

-rP -30/'

W„(S) = K = 10-^^

ra + 1 13005' + !

(3.2) Van de dat ra la nghien ciiu so sanh dua tren mo phong tten SIMULINK MATLAB mgt so phuang phap dieu khien 16 nhiet nhu dieu khien mo va phuang phap dieu khien su dung DSGT.

4. MO HINH MO PHONG CAC BO DIEU KHIEN LO NHIET TREN SIMULINK MATLAB

4.1. Mo hinh mo phong cac bo dieu khien mo" va bo dieu khien dua tren DSGT khi khong CO tac dong cua nhieu phu tai doi voi 16 nhiet

//;«/! ^.7. He thong khong CO tac dgng cua nhiiu phu tai

4.2. Mo hinh mo phong cac bo dieu khien mo- va bo dieu khiin dya tren DSGT khi co tac dong cua nhieu phu tai doi vol 15 nhiet

step

m

^{1300s-^1 909}

T

^

ransp-s rt h /

^\

Fuzzy Log i c

^ontec-l lef

€^ in

L6vel-2 M-fil6 S-Functicn Derivatives

Gain1

9-09

Transfef Fcn2 Gain2

Delay 1

TranspcTt Delay2

^

S t e p l Transp<jrt Delav3

Sc&pe

Hinh 4.2. He thong co tac dgng ciia nhieu phu tai

Cac bg dieu khien mo va bg dieu khien HAC dugc mo ph6ng sir dung phan mem SIMULINK MATLAB cho hai truang hgp khong c6 nhieu phu tai (hinh 4.1) va eo nhieu phu tai (hinh 4.2), ttong do phep mo hoa dugc xay dung dua tten phan hoach cae tap ma dang tam giac d6i voi cac diu vao ET (hinh 4.3), DET (hinh 4.4) va dha ra diiu khien OUT (hinh 4.5). He luat dieu khien dugc cho ttong bang 4.1. Ket qua mo ph6ng mo ta trong Phan 6. Phu Luc.

mfl mf2 mfi mf4 mf5 mf6 mf7 mf8 mf9

ET -5 -4

mfl

0

DET -2

- 3 - 2 - 1 0 1 2 3 4

Hinh 4.3. Phan hoach cac ham thugc dau vao ET mf2 mf3 mf4 mf5 mf6 mf7 mf8

(Volt)

mf9

-1 0 1 Hinh 4.4. Phan hoach cac ham thuoc dau vao DET

(Volt)

mfl mf2 mf3 mf4 mf5 mf6 mH mf8 mf9

0

OUT 0 0.5 1

Hinh 4.5. Phan hoach cac ham thuoc dau ra dieu khiin OUT

(Volt)

Tu [8] eae luat dugc mo ta trong bang 4.1.

DET ET mfl

mf2 mfi mf4 mf5 mf6 mf7 mf8 mf9

mfl mfl

mf2

mf2

Bdng 4.1. FAM

mf3

mfi mf4

mf4 mf5

mf5 mf6

mf6 mf7

mf7 mf8

mf8 mf9

mf9

Trong do mfi (i = 1 ... 9) la eae ham thugc dang tam giac dugc phan bo tren cac khoang xae dinh ciia hai bien vao ET, DET va 1 bien ra dieu khien OUT eo thii nguyen don vi la Volt vai cac khoang xae dinh [-5, 5], [-2, 2] va [0, 1] tuong iing.

4.3. Dieu khien dua tren dai so gia tir (hinh 4.1 va hinh 4.2)

4.3.1. Ngit nghia hod (Semantization) cdc bien vdo vd Men ra dieu khien

Bg tham s6 tinh toan cac gia tri tren du6ng cong ngii nghia dinh lugng gom:

C={0, Small, 0, Large,!}; H- = {Little} = {h-1}; q = 1; H+ = {Very} = { b l } ; p = 1; e = 0,5 ;a = [3 = 0,5; |.i(Very) = 0,5 = |i(hl); ^t(Little) = 0,5 = |i(h-l);

Nhu vay: fm(Small) = 0 = 0,5 va fm(Large) = l-fm(Small) = 1 - 0,5 = 0,5.

Cac gia tri ngii nghia dinh lugng cu the cua 2 bien vao ET, DETva 1 bien ra dieu khien OUT duge tinh tren ea so cac cong thiic (2.7) nhu sau:

; ; v(Small) = 0- cfm(Small) = 0,25

2) v(Very Small) = v(Small) + Sign(Very Small) * {^fm(h ^Small) - 0,5 fm(h^Small)} = 0,125

i = l

3) v(Little Small) = v(Small) + Sign (Little Small) * -1

{ TMhiSmall)-0.5fm(h_jSmall)} = 0.375 i=-l

4) v(Large) = 6+ afm(Large) = 0,75

5) v(VeryLarge) = v(Large) + Sign(VeiyLarge)*

{^fm(biLarge)-0,5/w(/j,Large)} = 0,875

6) v(Little Large) = v(Large) + Sign(Little Large) *

-1 ...

{ Y^fm(hjLarge)-0.5fm(h_]Large)} = 0.625 '[.

i=-l

Bang 4.2 mo ta eac bien ngon ngii va dinh lugng boa ngii nghia eae bien nay tren co so muc 4.2 cho ea 2 dku vao ET, DET va 1 dau ra dieu khien OUT.

Bdng 4.2. Ngii nghTa dinh lugng eae tap ma fmi (i = 1, 2 , . . 9)

fml fm2 fm3 fm4 fm5 fm6 fm7 fm8 fm9

Absolute Small = 0,0 Very Small = 0,125 Small = 0,25 Little Small = 0,375 Medium = 0,5 Little Large = 0,625 Large = 0,75 Very Large = 0,875 Absolute Large =1,0 4.3.2. Anh xg ngie nghia dinh luong (SQMs)

Chuyen bang FAM sang bang SAM - bang 4.3 tren ea sa eae ket qua tinh toan tai phan tren va eac chuyen doi a bang 4.2.

Bdng4.3.^NM.

ET DET ^ \ ^ ^ mfl

mf2 mfi mf4 mf5 mf6 mf7 mf8 mf9

0 0,125 0,25 0,375 0,5 0,625 0,75 0,875 1

mfl 0 0

mf2 0,125

0,125 mfi 0,25

0,25 mf4 0,375

0,375 mf5 0,5

0,5 mf6 0,625

0,625 mf7 0,75

0,75 mf8 0,875

0,875 mf9

1

1

4.4 Xay dung duong cong ngir nghia djnh luong voi phep AND=PRODUCT

5fl«g^.^. AND=PRODUCT ET

0 0,125

0,25 0,375

0,5 0,625

0,75 0,875

1

DET 0 0,125

0,25 0,375

0,5 0,625

0,75 0,875

1

ET & DET 0 0,015625

0,0625 0,140625

0,25 0,390625

0,5625 0,765625

1

OUT 0 0,125

0,25 0,375

0,5 0,625

0,75 0,875

1

0,2

C

DLfong cong ngu- nghia dieu khien

•

) 0.2 0,4 0.6 0,8 ET'DET

1 2

>

Hinh 4.6. Tap diem tten ducmg cong ngii nghia

4.5. Giai nghia (Desematization) bien dieu khien ra

Tren co so diiu kien dat nhiet do 16 ban d§u (150°, 175°, 200°, 225°, 250°) hoac ting hgp theo qua ttinh tang hoac giam nhiet do ttong khoang [150°, 250°] tinh dugc cac dai lugng ET va DET tuong ling. Day la dieu kien ban dau cho qua trinh tinh toan ngii nghTa cua hai bien vao ET va DET dua tten phep ngii ngbia hoa (Sematization). Tren ea so anh xa NNDL (SQMs Hinh 4.6) tinh dugc ngii nghTa dinh lugng cua bien ra dieu khien OUT. Tu do, phep giai nghTa (Desemantization) cho phep tinh gia tri thuc ciia bien ra dieu khien OUT.

De so sanh, ket qua dieu khien dua tten DSGT dugc the hien tten ciing do thi vai cac phuang phap dieu khien ma truyen thong ttong Phan 6 Phu lue.

Trong vi du cu the tten, doi tugng 16 gia nhiet cong nghiep [8] dugc eho duod dang ham tinyin la mot khau quan tinh bac nhat co tte (3.1) va (3.2). Cac bg diiu khiin 16 nhiet nhu bg

dieu khien ma va bg dieu khien sii dung DSGT duge thiet ke va mo ph6ng bang SIMULINK MATLAB. Qua mo phong qua trinh dieu khien 16 nhiet cua cac bg diiu khien tten, eo the thay ro v i tong the tinh vm viet rieng cua bg dieu khien theo tiep can DSGT so vai bg dieu ma:

- Thoi gian qua do ciia dieu khien dua tten DSGT vai cac gia tti dat nhiet do khae nhau luon tit ban diiu khiin ma. Tuy nhien, luong qua dieu chinh ctia tiip can dieu khien bang DSGT trong mot vdi truong hop chua phdi da tot hem dip can md.

- Khi khong c6 nhiiu phu tai, trong qua trinh dieu khien tong hgp theo chieu tang nhiet do (150°:200°:250°C) hoac giam nhiet do (250°:200°:150°C), diiu khiin dua tren DSGT luon cho chat lugng diiu khiin tot han hdn_so vm bg dieu khien ma.

- Dac biet khi co nhiiu phu tai tac dgng vao he thong, dieu khien dua tren DSGT luon co chat lugng diiu khien tot han so vai bg dieu khien ma.

5. KET LUAN

- Tinh quyit dinh trong bai toan dieu khien thong minh la lap luan xap xi dua tren eac thong tin uac lugng, khong ehinh xae (lap luan mo, suy luan ma). Han che cua phuong phap lap luan xap xi dua tten tap ma trong dieu khien ma la:

+ Co nhiiu yiu t i anh huong din ket qua dieu khien qua eae giai doan mo boa, suy luan ma va kbit mo.

+ Khong dam bao thii tu ngii nghTa trong qua trinh xii li dtr lieu eho dieu khien.

- Vai tiep can DSGT, viee tinh toan la don gian va eo kha nang dieu khien vai do chinh xae cao hon so vai phuang phap dieu khien ma vi co rat it cac yeu to anh huong den qua trinh lap luan.

- Vai 16 nhiet, la mgt doi tirgng duge sii dung rgng rai ttong cac ITnh vuc khae nhau, khi biet ro ham truyen ciia doi tugng thi viee thiet ke mgt bg dieu khien kinh dien la kha de dang.

Tuy nhien trong thuc te, thuong ta khong biet r5 tham so ciia he thong, ngoai viec thong qua nhan dang ta c6 the dua tren kinh nghiem van hanh de thiet ke bg dieu khien mo eho he thong.

Trong truang hgp nay, viec thiet ke mgt bg dieu khien dua tren co so DSGT cho tm diem ro ret.

- Nhiing nghien ciiu tiep tue trong tuong lai gan ve DSGT se huong den bai toan dieu khien doi tugng eo do phiie tap cao ban va bai toan toi tm boa chat lugng dieu khien tren co so bg tham so cua DSGT.

Ldi cam an. Bai bao diro'c sir ho trg cua Phong thf nghiem trong diem Cong nghe Mang va Da phu'ang tien.

6. PHU LUC 6.1. Dap irng cua bo diiu khiln khi khong co nhilu

a. Dat nhiet do 16 200°C b. Dat nhiet do 16 225°C

/ 4

/ / i

200 400

— fuJ.^y Logit

GOD 1DD0 \2K 1*00 2S0

50

/|' 1

7 ]

?0D 400

I

1-- - Fuiiy l.(^< 1

GOQ SOO 1D00 1»0 M X

c. Dat nhiet do 16 250°C d. Dat nhiet do 16 175°C

»D d M MQ 1 « 4 1200 1 J «

-Hiii^-LOflie - I"«)ge A^rtBss

200 400 BOO BOO 10«r )2(»

e. Dat nhiet do 16 150°C g. Dieu khien tong hgp theo qua ttinh tang nhiet (150:200:250)°C

U L.

./ ;

• Ftirry L C91C

TDO 400 1 1 l _ _

BDO fOOD 17l»

b. Diiu khiin ting hgp theo qua trinh giam nhiet (250:200:150)°C

1DDD im uoo

6.2. Dap UTig cua bo dieu khien khi co tac dong cua nhieu phu tai

- • : - / • •

AOO WO W W 13C0 14C0

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16. N. C. Ho, V. N. Lan - Hedge Algebras - An order - based structure of terms - domains:

An algebraic approach to human reasoning, Joumal of Science and Technology 45 (6) 77-108.

17. N. C. Ho, V. N. Lan, and L. X. Viet - Optimal hedge-algebras-based controller: Design and apphcation. Fuzzy Sets and Systems 159 (2008) 968-989.

SUMMARY

PERFOMACE COMPARISON BETWEEN FUZZY LOGIC CONTROLLERS AND HEDGE ALGEBRAS - BASED CONTROLLER FOR FURNACE

In this paper, two controllers such as FLC (Fuzzy Logic Conttoller) and HAC (Hedge Algebras - Based Controller) are simulated in MATLAB SIMULINK. All the successfully designed controllers were compared. The responses of each controller were plotted in one window to verify the performance of each conttol algorithm. Simulation study has been done in MATLAB SIMULINK shows that tbe new conttoller - HAC produced better response and better performance compared to FLC sttategies for controlling the temperature plant.

Bia chi:

Nguyen Tien Duy,

Dai hgc Ky thuat cong nghiep Thai Nguyen.

VQ Nhu Lan,

Vien Cong nghe thong tin, VAST.

Nhdn bdi ngdy 12 thdng 8 ndm 2008