NDH-2009 Luanan Public

8/4/2019 NDH-2009 Luanan Public

1/173

B GIO DC V O TO B CNG THNG

VIN NGHIN CU IN T, TIN HC, T NG HA

NGUYN DUY HNG

V MT PHNG PHP TNG HP HIU KHIN M DNG MNG NRON

NG DNG TRONG CNG NGHIP

Chuyn ngnh: K thut in t

M ngnh: 62.52.70.01

LUN N TIN S K THUT

HNG DN KHOA HC:GS. TSKH. NGUYN XUN QUNH

H NI 2009


2/173

LI CM N

Tc gi xin by t li cm n v lng knh trng i vi thy hng dn:GS. TSKH. Nguyn Xun Qunh bi nhng ch dn qu bu v phng php

lun v nh hng nghin cu lun n c hon thnh.Tc gi cng by t li cm n i vi Vin NC in t, Tin hc, T

ng ha B Cng Thng to iu kin thun li v c s vt cht v

thi gian tc gi hon thnh lun n.

Tc gi xin trn trng cm n cc nh khoa hc v cc ng nghip phn bin, l lun, ng gp cc kin xy dng v trao i v cc vn l

thuyt cng nh thc tin lun n c hon thin.

Cui cng tc gi xin by t li cm n su sc nht n gia nh v ngi

thn lun chia s, gnh nhng kh khn cng nh dnh nhng tnh cm

v l ngun c v, ng vin tinh thn khng th thiu i vi tc gi trong

sut qu trnh thc hin lun n ny.


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LI CAM OAN

Ti xin cam oan lun n ny l cng trnh nghin cu khoa hc ca ti vkhng trng lp vi bt k cng trnh khoa hc no khc. Cc s liu trnh

by trong lun n c kim tra k v phn nh hon ton trung thc. Cc

kt qu nghin cu do tc gi xut cha tng c cng b trn bt k tpch no n thi im ny ngoi nhng cng trnh ca tc gi.

H Ni, ngy 15 thng 9 nm 2009

Tc gi lun n

Nguyn Duy Hng


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-i-

M U

Vn iu khin n nh cc h ng hc phi tuyn c phng trnh nghc chuyn c v dng tuyn tnh ha phn hi trng thi (state feedbacklinearizable) hoc tuyn tnh ha phn hi vo-ra (input-output feedbacklinearizable) c cha cc thnh phn khng r nhm bm theo tn hiu mu chotrc vi sai s b chn l mc tiu gii quyt ca lun n. y l vn phctp do c tnh phi tuyn ca ng hc cng nh ca cc thnh phn cha bittrong phng trnh ng hc ca i tng. Cc cng trnh nghin cu hin naych yu tm cch gii quyt cc vn v iu khin n nh v bn vng h

phi tuyn c cc thnh phn bt nh da trn iu khin thch nghi, tuy nhincc phng php cn kh phc tp v cha ch r kh nng v m hnh p dngtrn cc h thng iu khin cng nghip.

Nhm ng gp, a ra mt phng php tng hp c kh nng p dng trncc h thng iu khin t ng tin tin hot ng trong cc phn cp mngcng nghip, tc gi trnh by mt phng php tng hp mi da trn tngthay th c lng (khng cn gn ng nh cc phng php hin nay) cc

hm trng thi cha bit bng cc hm s bit, t tm cch xp x sai lchchung do php thay th c lng gy nn v thit k thnh phn b lin tcnhm trit tiu tc ng ny. c im ca phng php l s dng b xp xvn nng m nron (xp x sai lch nu trn) lm thnh phn b trong lut iukhin phn hi. xy dng c mt c s ton hc chng minh cho phng

php xut, lun n ln lt pht trin phng php cho cc trng hp btnh (lut iu khin phn hi tnh) v trng hp b ng (lut iu khin thch

nghi). Ngoi ra lun n cn phn tch v gii quyt mt s vn khc lin quann cc iu kin gii hn ca qu o trng thi v u vo ca h phi tuyncng nh m rng phng php trong trng hp h kh tuyn tnh ha phnhi cht (strict-feedback linearizable system).

Ngoi c s l thuyt c chng minh, lun n cng phn tch v ch ra khnng p dng phng php trn cc h thng iu khin cng nghip (PLC,IPC) thng qua th nghim trn mt m hnh phn mm ng dng c xydng cho h thng SIMATIC S7 ca hng Siemens.


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- ii -

B cc ca lun n

Lun n chia thnh 4 chng. Chng 1 trnh by tng quan cc vn trong iu khin cc h phi tuyn v ng dng, t a ra mc tiu v ni

dung nghin cu ca lun n gii hn vo cc h kh tuyn tnh ha phn hi ccha cc thnh phn khng r trong bi ton bm theo tn hiu mu b chn chotrc.

Chng 2 trnh by chi tit vn cn gii quyt cng nh tng quan ccnghin cu v cc kt qu t c n nay. Da trn phng php thit knh ngha h sai s tha mn gi thit ban u, lun n xy dng mt s c ston hc (cc nh l v b ) hnh thnh phng php mi theo hng n

gin v c kh nng ng dng c gi l phng php thay th c lnghm trng thi lm tin pht trin cc b iu khin n nh tnh v ngtrong cc chng tip theo.

Trong Chng 3, tc gi gii thiu mt s c s ton hc nhm a ra lutiu khin tnh dng b xp x vn nng m nron lm thnh phn b lin tc nghim ca h sai s vng kn b chn ti hn u (uniformly ultimately

bounded) cng nh trnh by phng php tnh ton, xc nh tham s iu

khin v cc iu kin cn trong phng php qu o trng thi v tn hiuiu khin b chn theo thit k. Ngoi ra Chng 3 cn tip tc m rng

phng php cho thit k b iu khin n nh tnh cc h chuyn ng hnlon (chaotic systems) c phng trnh ng hc dng tuyn tnh ha phn hicht.

Chng 4 tp trung vo gii quyt vn b ng da trn lut iu khintnh v s dng b xp x m nron xy dng c b iu khin thch nghi

n nh cng nh trnh by m hnh phn mm ng dng. Nhm chng minhtnh kh thi ca phng php trong pht trin b iu khin vi thnh phn bng, lun n s dng iu khin thch nghi trc tip p dng phng phpchnh nh chnh nh tham s ca b xp x m nron trong cc trnghp b xp x tuyn tnh v phi tuyn i vi tham s. Tc gi cng a ra mhnh phn mm ng dng cho php p dng cc kiu iu khin tnh v ngtrn cc h thng iu khin cng nghip v phn tch kh nng ng dng trnh thng t ng ha SIMATIC S7 ca hng Siemens.

Phn cui l kt lun v kin ngh ca lun n, tip theo sau l Ph lc baogm mt s chng minh v thit k.


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- iii -

MC LC

CHNG 1: TNG QUAN ....................................................................................... 11.1. t vn ....................................................................................................... 1

1.2. Mc tiu v nhim v nghin cu ................................................................ 9

CHNG 2: IU KHIN N NH CC H THNG KH TUYNTNH HA PHN HI BNG PHNG PHP THAYTHC LNG HM TRNG THI ...................................... 11

2.1. Gii thiu chung ........................................................................................... 11

2.1.1. t vn ........................................................................................... 11

2.1.2. Biu din cc h thng kh tuyn tnh ha phn hi .......................... 122.1.3. Vn trong iu khin n nh cc h kh tuyn tnh ha

phn hi trng thi ............................................................................. 15

2.2. iu khin n nh cc h thng kh tuyn tnh ha phn hitrng thi bng phng php thay thc lng hm trng thi ......... 212.2.1. C s ton hc ca phng php ....................................................... 212.2.2. Tnh bn vng ca h vng kn trong phng php ........................... 31

2.3. iu khin n nh cc h thng kh tuyn tnh ha phn hi vo-ra bng phng php thay thc lng hm trng thi ...................... 44

2.3.1. Bi ton iu khin v c s ton hc ................................................ 442.3.2. iu khin n nh bng phng php thay th c lng hm

trng thi............................................................................................. 472.3.3. Tnh bn vng ca h vng kn i vi thnh phn khng r

trong phng trnh ng hc .............................................................. 51

2.4. Tng hp thit k b iu khin tnh n nh ........................................... 55

2.5. Kt lun ......................................................................................................... 56

CHNG 3: PHNG PHP THAY THC LNG HMTRNG THI DNG B XP X M NRON .......................... 58

3.1. t vn v c s l thuyt xy dng phng php ............................. 58

3.1.1. Gii thiu chung.................................................................................. 583.1.2. B xp x vn nng.............................................................................. 593.1.3. C s ton hc xy dng cc b xp x dng h m v mng

nron ................................................................................................... 60

3.2. Thay thc lng hm trng thi ........................................................... 69

3.2.1. C s ton hc ca phng php ....................................................... 693.2.2. Xc nh tham s b iu khin .......................................................... 743.2.3. M phng iu khin tay rbt ........................................................... 79

3.3. Thay thc lng hm trng thi m rng trong iu khin nnh cc h kh tuyn tnh ha phn hi cht........................................... 84


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- iv -

3.3.1. Phng php cun chiu .................................................................... 843.3.2. Phng php thay th c lng hm trng thi khi h cha

cc thnh phn khng r .................................................................... 85

3.4. Tng hp v kt lun ................................................................................... 93CHNG 4: IU KHIN THCH NGHI TRC TIP DNG H M

NRON TRONG PHNG PHP THAY THCLNG HM TRNG THI ......................................................... 96

4.1. Gii thiu chung ........................................................................................... 96

4.1.1. S cn thit pht trin b iu khin thch nghi ................................. 964.1.2. Vn v c s ton hc xy dng b iu khin thch nghi

trc tip ............................................................................................... 98

4.2. iu khin m nron thch nghi trc tip cc h thng kh tuyn

tnh ha phn hi ....................................................................................... 1014.2.1. H kh tuyn tnh ha phn hi trng thi ....................................... 1014.2.2. H kh tuyn tnh ha phn hi vo-ra ............................................ 108

4.3. Tng hp thit k b iu khin thch nghi trc tip n nh ............... 110

4.4. M hnh iu khin thch nghi trn h thng iu khin cngnghip .......................................................................................................... 111

4.4.1. Gii thiu chung................................................................................ 1114.4.2. M hnh phn mm ng dng v kh nng p dng trn h

thng iu khin cng nghip ........................................................... 113

4.5. Kt lun ....................................................................................................... 121

KT LUN V KIN NGH ................................................................................. 122

CC CNG TRNH CNG B LIN QUAN CA TC GI......................... 124

TI LIU THAM KHO ....................................................................................... 125

PH LC ............................................................................................................ 1345.1. Mt s thut ng ting Anh ...................................................................... 134

5.2. B 1 trang 23.......................................................................................... 1365.3. B 3 trang 40 v kt qu (2-64) ........................................................... 1395.4. Tuyn tnh ha phng trnh ng lc hc (3-23) ................................. 1435.5. Chng trnh m phng v d iu khin tay rbt trang 79 ............... 145

5.6. B 6 trang 100........................................................................................ 152

5.7. Mt s mun phn mm trong m hnh phn mm ng dng ............ 155


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-v-

MC LC HNH V

Hnh 1 : Hm ( , E) 1 sign( E)bsig( , E) ..........................................................33Hnh 2 : Hm ( , E) E( , E) .............................................................................34Hnh 3 : Hm Lambert w(x)ew( x) x .......................................................................35

Hnh 4 : Hm E( , , E) E sign(E)bsig( , E) ........................................41Hnh 5 : Hm E

m

(

,

) v E _ max

(

,

) E

(

,

,

Em

) ...................................41Hnh 6 : H m MISO ..................................................................................................63

Hnh 7 : Mng nron 2 lp ...........................................................................................65

Hnh 8 : M phng trong trng hp khng s dng thnh phn b ..........................81

Hnh 9 : M phng s dng thnh phn b tnh vi 1 v 1.0 ......................82Hnh 10 : M phng s dng thnh phn b tnh vi 1 v 0.8 ....................83Hnh 11 : iu khin thch nghi trong h thng iu khin cng nghip ..................114Hnh 12 : S ng i d liu trong m hnh iu khin thch nghi ....................115

Hnh 13 : Cc mun phn mm chnh trong m hnh h thng NF .........................117

Hnh 14 : Cu trc b m v d liu qu trnh cung cp cho PC-Server .................155

Hnh 15 : Cc khi mun phn mm trn giao din STEP7 V5 ..............................157


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- vi -

BNG CH VIT TT

ABSANFIS

CNC

CSDL

DC

DCS

DVD

GUAS

HD DVD

IE

IEC

IPC

ISPS

ISS

KH&CN

LTI

MIMO

MLP

NF/NFN

PC

PID

PLC

R&DRBF

RBN

SCADA

SCL

SISO

UAS

Antilock Braking SystemAdaptive-Network-based Fuzzy Inference System

Computerized Numerical Control

C s d liu

Direct Current

Distributed Control System

Digital Video Disc

Globally Uniformly Asymtotically Stable

High Density DVD

Industrial Ethernet

International Electrotechnical Commission

Industrial Personal Computer

Input-to-State Practically Stable

Input-to-State Stable

Khoa hc v Cng ngh

Linear Time InvariantMulti-Input Multi-Output

Multilayer Perceptron (Network)

Neuro-Fuzzy/Neuro-Fuzzy Network

Personal Computer

Proportional Integral Differential

Programmable Logic Controller

Research and DevelopmentRadial Basis Function Network

Radial Basis Neural Network

Supervisory Control and Data Acquisition

Structured Control Language

Single-Input Single-Output

Uniformly Asymtotically Stable


10/173

-1-

CHNG 1

TNG QUAN

1.1. t vn

Trong nhng thp k gn y, s pht trin mnh m ca khoa hc v cngngh (KH&CN) trong cc lnh vc cng ngh ch to, cng ngh vt liu mi

v cng ngh thng tin cho ra i cc b vi x l mnh, kch c nh gn, tiu

th in nng thp v gi thnh h. Nh con ngi c th to ra hng lot sn

phm cng ngh cao tinh vi v thng minh cng nh cc sn phm cng nghcao ny ngy cng tr nn ph bin hn v l mt phn khng th thiu trong s

pht trin ca x hi vn minh hin i. Nhng thit b dn dng cng ngh cao

nh my in thoi di ng, iPod, u a HD DVD v Blu-ray hay my git,

my ra bt, ... khng cn xa l i vi nhiu ngi dn trong khi cc thit b

khc nh my rt tin t ng, my bn hng, bn v tu xe t ng, thit b tr

gip y t, thit b dn ng, rbt gip vic, ... ang tr nn gn gi vi conngi hn bao gi ht. C th ni s pht trin ca KH&CN v ang to ra

nhng thay i ln trong x hi loi ngi nhm p ng nhu cu ngy mt cao

ca con ngi v mi trng v iu kin sng.

Cng vi s pht trin ny l s ln mnh ca cc ngnh cng nghip nhm

khai thc v cung cp cc sn phm, dch v c cht lng tt nht vi gi

thnh h ti ngi tiu dng. Kinh nghim ca cc nc pht trin cho thy vic

p dng KH&CN trong ci tin, to ra cc sn phm mi cng nh vic nngcao cht lng, gim chi ph sn xut v h gi thnh sn phm, dch v c

ngha sng cn i vi mi nh sn xut nhng ngc li cng i hi KH&CN

phi lun i trc mt bc, p ng c yu cu pht trin ca nh sn xut

ni ring v ca x hi ni chung. Mc d hin nay th gii ang phi i mt

vi cc vn nghim trng v khng hong ti chnh v tnh trng suy thoi

kinh t ton cu nh hng ln n cc hot ng sn xut, tuy nhin ng trnquan im trit hc th bn cht ca pht trin v pht trin l bn cht ca x


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-2-

hi v do chng ta hon ton c th tin tng rng trong tng lai khng xa,vic cc nn kinh t c khi phc v tip tc pht trin l tt yu, trong

KH&CN vn l ng lc thc y pht trin kinh t x hi.

Tnh phi tuyn v vai tr ca l thuyt iu khin hin i

Trong s pht trin ca KH&CN, l thuyt iu khin hin i c vai tr ht

sc quan trng gii quyt nhiu vn nh nng cao cht lng iu khin,

n nh ca h thng, tit kim nng lng hay nh s dng my mc thay

th con ngi trong cc ng dng iu khin phc tp hoc nguy hi. Hng lot

cc cng trnh nghin cu v iu khin bn vng, iu khin thch nghi, iu

khin ti u hay iu khin m v mng nron c cng b trong nhng nm

gn y cho thy s quan tm ln ca cc nh khoa hc trn khp th gii v

nhng vn , cc hng nghin cu pht trin trong lnh vc ny ([35], [40],

[41], [42], [44], [46], [48], [52], [53], [54], [56], [57], [59], [60], [61], [62], [63],

[64], [65], [66], [67], [71], [73], [75], [77], [79], [80], [81], [82], [83], [92], [93],

[94], [95], [96], [98], [99], [100], [101], [102], [103], [104], [105], [106], [107],[108]).

Nh chng ta bit, cc h thng thc l cc m hnh phi tuyn ht scphc tp nn cc phng php thit k kinh in da trn iu khin tuyn tnh

trong nhiu trng hp khng m bo c yu cu do c tnh phi tuyn ca

ng hc i tng iu khin, c tuyn u o hoc c cu chp hnh cng

nh tnh cht khng y , chnh xc ca cc m hnh thay th (ng hc cha

bit, nhiu, iu kin ban u).

Trong cng nghip, u o v c cu chp hnh l nhng v d r nht vtnh phi tuyn. Tuy nhin c tnh phi tuyn cn th hin r trong cc h c in

(ng c DC khng chi than, ng c in cm ng), tay my, cc h thng

trang b trn t (Power train, ABS, Precision Control), cc qu trnh ha hc,

sinh hc v cc h chuyn ng hn lon (chaos). Cn lu rng cc h chuyn

ng hn lon l cc h ng hc phi tuyn tin nh (deterministic) ngha l -khc vi ngu nhin - ng hc tng lai ca h thng c nh ngha bi cc


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-3-

iu kin ban u nn h cn c xem l rt nhy vi cc iu kin ban u.V d in hnh ca h chuyn ng hn lon trong t nhin l thi tit kh hu

cn trong cng nghip l cc qu trnh ha hc, sinh hc, dng chy.Ngoi ra mt vn khc cng c t ra l rt nhiu h cn iu khin c

cc tham s khng r (nh h truyn ng servo, rbt), c cc tham s bin i

chm (v d nh cc tham s ph thuc vo nhit ) hoc c cc tham s thay

i khng d on c (nh cc h thng nng lng).

gii quyt cc vn phc tp trn, l thuyt iu khin bn vng v

thch nghi c xem l cc cng c hu hiu. Thc t hin nay iu khin thchnghi c p dng thnh cng trong nhiu lnh vc nh iu khin rbt,

my cng c, CNC, iu khin qu trnh (ha hc, sinh hc, ...), iu khin

truyn ng hay nh iu khin li tu, my bay t ng. Tuy nhin vic thit

k cc b iu khin phi tuyn ni chung v iu khin thch nghi ni ring l

khng n gin v t ra hng lot vn cn gii quyt nh vn v n nh

h vng kn, vn iu khin bm theo tn hiu mu, vn chng nhiu hoc

lm suy gim nhiu cng nh khi kt hp cc vn trn vi nhau. Ging nhtrong iu khin tuyn tnh, phn hi vn l cha kha thit k cc b iu

khin phi tuyn ni chung. V mt l thuyt, nu ton b cc trng thi ca h

o c khi ta ni n iu khin phn hi trng thi, cn trong trng hp

ch c vct u ra o c, iu khin phn hi u ra c p dng. Cc

phng php thit k b iu khin phi tuyn nh tuyn tnh ha phn hi

(feedback linearization), iu khin tch phn (integral control), iu chnh nh

trnh khuch i (gain scheduling) l cc phng php ch o hin nay ([32],

[45], [50], [51], [68]).

iu khin m nron

Mc d cc nghin cu v iu khin phi tuyn c nhiu bc tin quan

trng, tuy nhin vn tr nn phc tp hn khi h phi tuyn c cha cc thnh

phn khng r lm mt n nh h. Cc c tnh khng r ny c th xut phtt cc ngun nh nhiu u vo, ng hc cha bit ca i tng, sai s ca


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-4-

cc m hnh thay th hoc tc ng bn ngoi. iu khin n nh h, ccphng php thit k s dng iu khin m nron (hay cn gi l iu khin

m dng mng nron) nhm xp x cc thnh phn cha bit t tm cchgim tr tc ng ca cc thnh phn ny t c cht lng iu khin tt

nht. Vic p dng iu khin m nron cn cho php pht trin cc b iu

khin thch nghi do tham s c th chnh nh c trc tuyn trong qu trnh

hot ng.

Cn lu thm rng v mt thut ng, iu khin m nron trong lun n

cn c hiu l iu khin (phi tuyn) da trn c s h m (fuzzy system),mng nron nhn to (artificial neural network), mng nron m lai (hybrid

fuzzy neural network) hoc h m nron (neuro-fuzzy system).

Chng ta bit rng l thuyt tp m c gii thiu t nhng nm 60 cath k trc, tuy nhin phi ti u thp k 90 cc h thng iu khin m mi

thc s c a vo ng dng trong i sng v sn xut. H m chng t

c tnh u vit so vi cc h iu khin c dng trc trong gii quyt

cc bi ton nh iu khin qu trnh sn xut da trn kinh nghim vn hnh,iu khin phi tuyn, iu khin cc thng s mi trng, cc h thng d bo

kh tng, thy vn. Trong cng nghip, iu khin m cn c nghin cu

kt hp vi iu khin PID kinh in nhm tn dng c cc u im ca c

hai h thng, cho php nng cao cht lng iu khin ([21], [28], [34], [47],

[69], [86]). Hin nay cc h thng iu khin m trong cng nghip c pht

trin da trn c s cc mun phn mm cho cc h thng thit b kh trnh

(PLC), my tnh cng nghip (IPC) cho php gii quyt c nhiu bi ton

trc y kh thc hin c.

Mng nron nhn to thng c dng iu chnh cc hm lin thucca cc h m trong cc thit b iu khin. Mc d logic m c th m ha trc

tip tri thc chuyn gia s dng cc lut vi cc nhn ngn ng nhng logic m

li i hi nhiu thi gian thit k v chnh nh cc hm lin thuc nh

lng cc nhn ngn ng. K thut luyn mng nron cho php t ng ha


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-5-

qu trnh ny v gim ng k thi gian, chi ph pht trin trong khi ci thinc tc x l ([76], [86], [91]).

Mc d v l thuyt cc mng nron v cc h thng m l tng ngnhau theo ngha chng c kh nng chuyn i c tuy nhin trong thc t mi

h thng li c u v nhc im ring. i vi cc mng nron, tri thc c th

thu c t ng bi thut ton hi quy nhng qu trnh luyn li tng i

chm v vic phn tch mng luyn l kh khn. Ngoi ra ta cng khng c

kh nng rt ra c tri thc c dng cu trc (cc lut) t mng nron luyn

cng nh khng th a thm cc thng tin bit vo trong mng nron n gin ha qu trnh luyn mng.

Cc h thng m tt hn theo ngha hot ng ca chng c th gii thchc da trn cc lut m v nh vy tc thc thi ca h c th thay i

c bng cch chnh nh cc lut. Tuy nhin thng thng vic thu c tri

thc l kh kh khn v vic phi chia bin u vo thnh nhiu min nn ng

dng ca cc h thng m b gii hn trong cc vng m tri thc chuyn

gia phi c cng nh a phn trong thc t ch p dng c vi s lng ccbin u vo nh.

Vic kt hp cc u im ca h m v mng nron dn n cc h thng laivi cc cu trc c s dng rng ri l mng nron m lai (hybrid FNN) v

h m nron (NFS). Trong l thuyt iu khin hin i, h m, mng nron v

s kt hp ca h m vi mng nron c coi l nhng cng c a nng

gii quyt cc vn v phi tuyn v tnh khng chc chn trong iu khin cch phi tuyn ni chung.

H thng iu khin cng nghip v xu hng pht trin

Khi nim h thng iu khin cng nghip thng thng c hiu l cc

h thng SCADA, cc h iu khin phn tn (DCS) v cc thit b (logic) kh

trnh (PLC). V mt thut ng, SCADA l h thng my tnh phc v gim st

v iu khin mt qu trnh no . Qu trnh y c th l qu trnh cngnghip (nh ch to, sn xut, tinh ch c ch hot ng lin tc, gin on


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-6-

hay c tnh cht theo m hoc lp li), c s h tng (nh x l, cp nc; x l,thu hi nc thi; cc ng ng dn du, kh ga; phn phi v truyn dn in;

cc h thng thng tin) hoc c s tin nghi (nh ta nh, cng hng khng, hicng, trm v tr). Trong khi , DCS ch cc h iu khin c cc thnh

phn iu khin nm phn tn (khng tp trung) trong ton h thng, trong

mi h con c iu khin bi mt hoc nhiu thnh phn iu khin. Trong

cng nghip cc h DCS gim st v iu khin cc thit b phn tn c dng

trong cc nh my in, lc du, ha cht, x l nc, nc thi, ... Mt dng

h iu khin cng nghip khc l PLC dng trong t ng ha cc qu trnh c

in v cc thit b iu khin my mc. PLC l mt dng my tnh s, so vi

my tnh thng thng PLC c thit k hot ng di nhit rng hn,

kh nng chng nhiu cao, chu c rung ng v va p tt cng nh c tnh

nng x l thi gian thc.

Tuy nhin vic phn chia cc h iu khin cng nghip nu trn ch c ngha tng i m khng c ranh gii r rng. Ngy nay nhiu h PLC c th

thc thi nhim v ca mt h DCS nh trong khi cc h DCS li c th c cch con hot ng nh cc PLC thc th. S pht trin ca KH&CN trong nhng

nm gn y cho thy xu hng tch hp cc h thng iu khin trn li vi

nhau to ra cc h thng mnh, c tnh m v s dng cc ngn ng lp trnh

bc cao. PAC (Process Automation Control) l mt v d ca xu hng pht

trin ny.

Trong h thng iu khin cng nghip, h thng mng cng nghip c mtvai tr quan trng hin ti cng nh trong tng lai. Nh s pht trin nhanh

chng ca cng ngh thng tin v yu cu ngy cng cao ca t ng ha cng

nghip m vic s dng cc mng cng nghip ngy mt rng ri hn. Tuy

nhin khc vi mng thng tin, mng cng nghip phi p ng c cc yu

cu v tc truyn thch hp vi gi thnh tt cng nh phi m bo hot

ng n nh, tin cy trong mi trng cng nghip.

H thng mng cng nghip thng c s dng theo m hnh phn cpty thuc vo yu cu trao i d liu gia cc thit b trong mng (nh p ng


16/173

-7-

thi gian thc, ln d liu, dch v truyn thng). Theo cp trn cng (gil cp nh my) c s dng kt ni gia cc my tnh trong h thng qun

l v iu hnh hot ng sn xut ca nh my (thng thng i hi thi gianp ng d liu di 1s). Trong khi , cp trung gian (cell/control level) dng

kt ni cc b iu khin (phn tn) vi nhau cho thc thi cc nhim v iu

khin chung nn yu cu thi gian p ng d liu phi nhanh hn (di

100ms). Di cng l cp trng (field level) thc hin vic kt ni thit b iu

khin vi cc I/O phn tn (u o, c cu chp hnh), do p ng phi

nhanh hn c m bo b iu khin x l c cc I/O thi gian thc

(thng thng thi gian p ng di 10ms).

Trao i d liu trong h thng mng cng nghip c thc hin thng quabus trng (fieldbus). Bus trng l tn gi chung ca h cc giao thc mng

cng nghip dng trong cc ng dng iu khin phn tn thi gian thc v

c tiu chun ha (tiu chun IEC 61158). Mt s chun bus trng c th k

ra nh Foundation Fieldbus (H1, HSE), Profibus, ProfiNet IO, ControlNet, P-

Net, Interbus v WorldFIP. Tuy nhin cc chun bus trng khng tng thchvi nhau do c pht trin bi cc hng ring bit nn kh khn cho ngi s

dng la chn cng ngh v thit b. Ngy nay cng vi vic Ethernet h tr

phn ln cc giao thc mng v c dng rng ri trong mng thng tin d

liu, Ethernet cng nghip ang l s la chn pht trin s mt ca nhiu hng

t ng ha. Ethernet cng nghip khng ch s dng trong cc phn cp trn

m ang c xu th hng ti c phn cp di (cp trng). C th ni cng

ngh Ethernet ha hn s mang n s thay i ln trong lnh vc iu khin

cng nghip ([39], [84]).

Tnh hnh nghin cu hin nay trn th gii v ti Vit Nam

Trong nhng nm gn y vn v thit k b iu khin thch nghi cho

cc h thng ng hc phi tuyn lun l mt trong cc ch chnh trn cc tp

ch chuyn ngnh v iu khin, t ng ha trn th gii v ngy cng thu htc nhiu nh khoa hc tham gia nghin cu. c nhiu bc tin, kt qu


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-8-

t c c v mt l thuyt v thc tin ng dng ([41], [44], [45], [46], [50],[51], [57], [59], [66], [97], [100]), c bit theo hng s dng h m v/hoc

mng nron xp x phng trnh ng hc ca i tng phi tuyn v dngcc phng php tuyn tnh ha phn hi trng thi hoc phn hi u ra ca h

thng ([35], [40], [45], [52], [54], [56], [57], [75], [94], [95], [98], [101], [102],

[106]) thit k b iu khin n nh tnh. b iu khin c c tnh thch

nghi vi nhng sai lch khng r khi hot ng trc tuyn, cc b iu khin

c thit k s dng cu trc mng nron hoc logic m vi cc lut chnh

nh cc trng s trong qu trnh lm vic. y cng l phng php thng

dng thit k cc b iu khin thch nghi trong cc ng dng cng nghip.

i vi trong nc, cc nghin cu v iu khin m, mng nron nhn tov h thng m nron cng c nhiu c s KHCN tp trung nghin cu

trong nhiu nm tr li y ([2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12],

[13], [14], [15], [16], [17], [18], [20], [23], [24], [26], [27], [29], [30], [31], [36],

[78]) v c khng t cng trnh hng ti vic ng dng c cng b nhng

nhn chung cc kt qu t c cn kh khim tn. Mt s c s nh Vin NCin t, Tin hc, T ng ha (VIELINA), i hc Bch khoa H Ni, i hc

Bch khoa thnh ph H Ch Minh, Phn vin T ng ha - Vin cng ngh

thng tin, Vin T ng ha K thut qun s, Hc vin Cng ngh Bu chnh

Vin thng, ... l nhng n v c nhiu nm nghin cu v iu khin m

nron v c mt s kt qu nht nh, tuy nhin cc nghin cu su rng hn

nhm ng dng cng ngh ny trong cc h thng t ng ha cng nghip tin

tin cn l nhng bc i ban u.

Vn nghin cu v ng gp chnh ca lun n

Nhng vn cn tn ti hin nay c v l thuyt v thc tin ng dng

trong iu khin cc h phi tuyn c cha cc thnh phn khng r i hi

nhng nghin cu, pht trin tip nhm gii quyt cc vn nu. Trong

khun kh ca lun n, tc gi chn hng nghin cu p dng h m v mngnron trong iu khin cc h ng hc phi tuyn tuy nhin ch gii hn vo cc


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-9-

h phi tuyn c phng trnh ng hc chuyn c v dng tuyn tnh haphn hi c cha cc thnh phn khng r do y l mt trong nhng dng in

hnh trong cng nghip. Ngoi ra y cng l vn cha c gii quyt y trn th gii ([40], [50], [52], [53], [54], [56], [57], [60], [61], [62], [63],

[72], [73], [75], [81], [92], [94], [95], [98], [104], [105]) cng nh c rt t cng

trnh nghin cu trong nc c cng b ([14], [81]). Chng 2 s trnh by

v phn tch r hn nhng hn ch trong cc phng php gii hin nay v

tng hnh thnh phng php mi nhm trnh phi gii quyt cc vn trn.

Nh vy ng gp chnh ca lun n l mt phng php mi (gi lphng php thay th c lng hm trng thi) cho php tng hp b iu

khin n nh tnh v ng cc h thng kh tuyn tnh ha phn hi trng thi

v kh tuyn tnh ha phn hi vo-ra c cc thnh phn khng r trong phng

trnh ng hc cho lp bi ton iu khin bm tn hiu mu cho trc. Phng

php mi a ra cch thc phn tch c nh hng ca php thay th ln h

sai s nhm trnh phi gii quyt mt s vn thng gp trong cc phng

php gii hin nay. Ngoi ra phng php c kh nng p dng c trn cc hthng iu khin cng nghip tin tin vi PLC mnh hoc s dng Soft-

PLC (nh WinAC RTX ca hng Siemens).

1.2. Mc tiu v nhim v nghin cu

Mc tiu

Xy dng phng php thay th c lng hm trng thi trn c s p dngh m v mng nron cho php tng hp b iu khin n nh tnh v ng

(thch nghi) cc h kh tuyn tnh ha phn hi (feedback linearizable system)

c cha cc thnh phn khng r trong phng trnh ng hc gii quyt bi

ton iu khin bm theo tn hiu mu cho trc v c kh nng p dng trn

cc h thng iu khin cng nghip.

Nhim v nghin cuVi mc tiu trn, nhim v nghin cu t ra ca lun n nh sau:


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- 10 -

- Nghin cu cc vn trong iu khin n nh cc h kh tuyn tnh haphn hi c cha cc thnh phn khng r trong bi ton bm theo tn hiu

mu cho trc, tp trung vo cc h kh tuyn tnh ha phn hi trng thiv kh tuyn tnh ha phn hi vo-ra.

- Xy dng c s ton hc ca phng php tng hp mi nhm gii quyt vtrnh c mt s vn trong cc phng php hin nay.

- Xy dng lut iu khin tnh v ng trong phng php mi.

- Xy dng m hnh phn mm ng dng trn mt h thng iu khin cng

nghip in hnh nhm phn tch kh nng p dng ca phng php.

Phng php nghin cu

Xut pht t nhng vn ca cc phng php gii v cc hng nghin

cu tip theo hin nay, lun n chn phng php nghin cu p dng h m v

mng nron trong iu khin gii quyt vn phi tuyn v khng r trong

phng trnh ng hc ca h. Lin quan n vn n nh v tnh bn vng

ca h vng kn, lun n la chn mt s c s ton hc phn tch, xy dngv pht trin c s ton hc ca phng php. Cc c s ton hc chnh gm

phng php lp h sai s, phn tch n nh h theo tiu chun Lyapunov, l

thuyt xp x vn nng m nron v iu khin thch nghi trc tip. thc

hin tng ca phng php (thay th c lng cc hm trng thi khng

phi xp x gn ng nh nhiu phng php hin nay), tc gi vn dng mt s

kt qu nghin cu c cng b gn y v s dng cc c s ton hc nutrn tng bc chng minh cch gii quyt cc vn trong phng php

tng hp nhm t c mc tiu v ni dung nghin cu ra. Ngoi ra mt

s c s ton hc quan trng xy dng trong lun n cng c tc gi lp trnh

m phng trn Matlab kim tra li tnh chnh xc ca cc kt qu t c.


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- 11 -

CHNG 2

IU KHIN N NH CC H THNG KH TUYN TNHHA PHN HI BNG PHNG PHP THAY TH C

LNG HM TRNG THI

2.1. Gii thiu chung

2.1.1. t vn

Mt trong nhng vn c bn trong l thuyt iu khin l nghin cu sdng phn hi lm thay i ng hc ca i tng nhm t c c tnh

theo mun. i vi h tuyn tnh bt bin theo thi gian (LTI) vn ny

c gi l t im cc, cn trong trng hp tng qut ca h phi tuyn vn

c gi l tuyn tnh ha phn hi (feedback linearization).

Tuyn tnh ha phn hi trong h phi tuyn l tm cch (nu c) thay i ta khng gian trng thi qua php bin i vi ng phi (diffeomorphism) ton

cc v s dng lut phn hi tnh biu din h thng trong khng gian trng

thi mi, tuyn tnh v iu khin c ([32], [50], [51]). Tuy nhin trong nhiu

trng hp php bin i vi ng phi ch xc nh trong ln cn ca im cn

xt, khi php bin i c gi l cc b.

Cc phng php tuyn tnh ha phn hi ch yu a v dng tuyn tnhha phn hi trng thi hay cn gi l tuyn tnh ha u vo-trng thi hoc

tuyn tnh ha y trng thi, trong ton b phng trnh trng thi ctuyn tnh ha v dng tuyn tnh ha phn hi vo-ra hay cn gi l tuyn tnh

ha khng y trng thi, trong ch c nh x u vo - u ra v mt

phn phng trnh trng thi c tuyn tnh ha.

Trong chng ny ca lun n, cc nghin cu tp trung vo phng phpiu khin n nh cc h phi tuyn a c v dng tuyn tnh ha phn hi

trng thi c dng (2-6) v m rng i vi cc h kh tuyn tnh ha phn hi


21/173


22/173

x1 1 T x T L h() q1 Tn1() 1(x,

vi x = = = , q , (x, q) =

qd Tn d () d

L h()xn Tn

v f(x, q) Lfn h() , g(x, q) Lg Lfn1h() trong = T1 .

0 0 1 0 0

0 0 0 1

y = cT .

y = cT .

q (x, q)

x1 x2

xn1 xn

(2-3)

xn f(x, q) g(x, q)u

y x1

h()2 2f

n1 f x q

0

Nu k hiu A

00

1 0 0 0

, b

0 0 0 0

0 1 , c vi A : nn ,

0 1 0

b : n 1 , c : n 1th phng trnh (2-3) c th vit di dng:

q (x, q)

x Ax b f(x, q) g(x, q)u (2-4)xq

Chn lut phn hi u g1(x, q) f(x, q) , h v n g k n s c d n g :q (x, q)

x Ax b (2-5)xq


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- 14 -

Phng trnh (2-5) cho thy h c phn tch thnh hai h con gm mt hcon tuyn tnh c chiu n , biu din quan h vo-ra (cn gi l h con ngoi

ng hc [50]) v mt h con (phi tuyn) c chiu dnhng khng c tc ngti u ra ca h (h con ni ng hc). Ngoi ra h con tuyn tnh nu trn (h

con ngoi ng hc) l iu khin c v quan st c, c hm truyn l

H (s) 1 sn hay c im cc bi bc n ti s 0 .

Phng trnh ng hc ca h con (phi tuyn) trn (h con ni ng hc) khi

x 0 l q (0, q) c gi l ng hc khng (zero dynamics, [32], [33]) ca

h thng. ng hc khng cho bit u ra ca h (2-4) lun bng 0 khi cctrng thi ban u ca h l (x,q) (0,q0) hay x 0 nhng q0 q(0) c th

chn ty v u vo ca h phi t bng u(t ) g1 0, q(t ) f 0, q(t ) v i

q(t ) l nghim ca phng trnh ng hc khng vi iu kin ban u

q(0) q0 . Ngoi ra c th nhn thy vi mi tp hp iu kin ban u

(x,q) (0,q0) lun tn ti mt u vo duy nht gi cho u ra lun bng 0.Nh vy ng hc khng cn c th xc nh c bng cch gi cho u ra

lun bng 0 bi u vo thch hp m khng nht thit phi bin i h sang

dng chun tc.

c tnh n nh ca ng hc khng ng vai tr quan trng trong phngphp tuyn tnh ha phn hi vo-ra. Trng hp d 0 hay bc tng i bng

vi bc ca h phi tuyn, khi php tuyn tnh ha l y ngha l ton b

quan h vo-ra c tuyn tnh ha v do vy vn bn vng ca h c

gii quyt. Tuy nhin trong trng hp d 0 th ch h con ngoi ng hc

c tuyn tnh ha, h con ni ng hc l phi tuyn v khng quan st c

t u ra. Khi c tnh n nh ca h con ni ng hc c xc nh t

ng hc khng.

Ging nh trng hp h tuyn tnh c ton b cc im cc v cc im

khng nm bn na mt phng phc tri gi l h pha ti thiu (minimum-phasesystem, [70]), h phi tuyn (2-1) c ng hc khng c im cn bng q 0 l


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vi x = [ x1 2 ,, xn ] = x1 1,, x1(n1) n l vect trng thi gi thit oT

x1 1 1(n1) )u= f( x1 1 1 1,, x) + g( x , x, x ,, x

- 15 -

n nh tim cn cng c gi l h pha ti thiu v c th dng phn hi trngthi n nh tim cn h ([32]). Nu ng hc khng c im cn bng

khng n nh tim cn th phng php tuyn tnh ha vo-ra khng c nghathc tin do khng a ra c lut iu khin thc. Mc 2.3 s phn tch vn

ny thng qua mt phng php thit k n nh h trong trng hp h

c cha thnh phn khng r.

Lu l trng hp d 0 th h cn c th biu din c c di dng

tuyn tnh ha phn hi trng thi c phn tch trong mc 2.1.3 di y.

2.1.3. Vn trong iu khin n nh cc h kh tuyn tnh ha phn hi

trng thi

Xt h phi tuyn SISO biu din c di dng phng trnh trng thi vu ra sau:

x1 x2

xn1 xn (2-6)xn f(x) g(x)u

y x1

T, x , x

c ca h phi tuyn; u(t) , y(t) tng ng l cc u vo iu khin

v u ra ca i tng; f(x)

, g(x)

l cc hm s thc lin tc b chntha mn cc iu kin s c gi thit sau trong mi trng hp. H (2-6) cn

c th biu din cc dng:

(n) (n1)

hoc

y x1

y(n) f( y, y , ,y(n1) ) g( y, y , , y(n1) )u

(2-7)


25/173

vi A = , b = [0,,0,1] .

r = [r1, r2 ,, rn ] = r, r,, r(n1) vi ri = d r/ dti 1, i = 1..n . Ngoi ra

l sai s bm vi r= r, r,, r(n1) th ng hc ca sai s bm l:

- 16 -

x Ax b f(x) g(x)uy x1

0 I T0 0 (2-8)

R rng h (2-6) iu khin c ta cn g(x) 0vi mi x trong min

hp lx n . Ngoi ra do g(x) lin tc nn sau y ta lun gi thit rngg(x) 0 vi mi x x m khng lm mt tnh tng qut do trng hpg(x) 0 ta ch cn o du tn hiu u vo u .

Bi ton t ra y l cn tm lut iu khin phn hi b chn u v(z) vi

z l vect cha cc tn hiu o c thch hp i vi phng php thit k saocho u ra ca h lun bm theo c tn hiu mu r(t) cho trc b chn hay

vct trng thi x ca h phi bm theo c vct tn hiu mu

T

T

i1

cng gi thit rng tn hiu mu c o hm n bc n bit v vct tn hiu

mu b chn bi r r M .

Sau y l tng hp mt s phng php gii hin nay v vn ca ccphng php gii ny trong 2 trng hp. Trng hp 1 xem xt vi gi thit

ton b phng trnh ng hc ca h cn phn tch bit trong khi Trng

hp 2 s phn tch h phi tuyn vi gi thit c cc thnh phn khng r trong

phng trnh ng hc ca h v y cng chnh l vn cn gii quyt ca

lun n. Mc d cc vn trong Trng hp 1 c gii quyt v khng

nm trong ni dung pht trin mi ca lun n, tuy nhin thun tin cho victrnh by v theo di, lun n xem xt vn trong c hai trng hp.

Trng hp 1Trng hp f(x) , g (x) bit hon ton, khi bng phng php tuyn

tnh ha phn hi kinh in ([50], [51], [57]), t e x r e 1, e1,, e1n1)T

T


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u =g 1 ( x ) ( f (x) + r( n) ke

e = Ae bk e = (A bkT)e = Ake .

Chn hm Lyapunov V = e Pe vi P l ma trn i xng xc nh dng

th V = eTPe + e Pe = eT(PAk+ ATP)e . R rng l cn chn P sao cho

k

- 17 -

S d n g l u t i u k h i n p h n h i :

e x r Ae b f(x) g(x)u r(n) (2-9)

T (2-10)vi kTk1, k2 , ,kn c c h n s a o c h oxn knxn1 k1 l a thcHurwitz (c ton b cc nghim nm bn na tri ca mt phng phc) dn n

T

T

T

PAk AT P Q vi Q cng l ma trn i xng xc nh dng h vngkn n nh v do lim e 0 .

t

Trng hp 2Trng hp 2 c th xem xt di nhiu iu kin gi thit khc nhau. Trc

tin xt trng hp gi thit f(x) bit v g(x) l hm phi tuyn cha bit

hoc c cha thnh phn cha bit tha mn g(x)gL 0 vix x , khi phng php gii thng thng l thit k mt trt v lut iu khin phn hi

trng thi qu o trng thi ca h lun chuyn ng bm xung quanh mt

trt ny ([50], [51]). Ngoi ra mt khi trng thi ca h nm trn mt trt th

cn gi qu o trng thi khng thot ra khi mt trt . i vi bi tonbm y, ta cn thit phi n nh gc ca h phng trnh sai s sau:

e1 e2

en1 en

(2-11)

en f(x) g(x)u r(n)

Nu coi en l u vo iu khin ca h n 1 phng trnh u tin trong(2-11) th gc ca h c n nh bi lut iu khin tuyn tnh:


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chn v = (x)sign(s) vi sign(s) = 0 s = 0 , (x) + 0 , 0 > 0 v1 s < 0

hm Lyapunov V = s 2 th o hm ca V theo qu o ng hc (2-12) ca

g + 0

- 18 -

en k1e1 kn1en1

vi k1..kn1 c chn sao cho a thc xn kn1xn1k1 l Hurwitz. Khi

thit k mt trt l s k1e1 kn1en1 en 0 th:

s k1e2 kn1en f(x) g(x)u r(n) .

Bng lut iu khin phn hi:

u g1(x)k1e2 kn1en f(x) r(n) v

vi g(x) l m hnh thay th ca g(x) ta c th biu din s dng:

Gi thit:

s g(x)v (t, x, v) (2-12)

(t, x, v)g(x) ( x)0 v , 00 1 (2-13)

vi mi (t, x, v)0,D , D n trong (x) v0 bit, khi 1s 0 (x)

1 012

mt trt s l:

V

ss sg(x) (x)sign(s) s (t, x, v)

g s g0 s g s (1 0 ) 1 0

0 (10 ) gL s

R rng l vi m hnh thay th p ng iu kin gi thit (2-13) nu trn

th sai s bm s lun tin n 0 khi t .


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- 19 -

Vn tr nn phc tp hn trong trng hp c tnh phi tuyn ca c

f(x) v g(x) u cha bit hoc c cha thnh phn khng r. Khi cc

phng php gii ch yu theo hng iu khin thch nghi ([40], [50], [52],[53], [54], [56], [57], [60], [61], [62], [63], [72], [73], [75], [81], [92], [94], [95],

[98], [104], [105]) c th tng hp nh di y.

1. Tm cch thay th g(x) bng m hnh xp x gn ng g(x, ) vi l

vct tham s hay cc trng s c lng ca m hnh.

m bo m hnh gn ng lun p ng g(x, ) 0 vix x , mt

s phng php gii quyt nh sau:

a) Chn tham s khi to ban u (0) gn nht vi gi tr ti u bng

phng php luyn ngoi tuyn trc khi a vo hot ng ([92]).

b) S dng cc thut ton quy chiu (projection) vi mt s gi thit bit

khc v h cho php xc nh g(x, ) 0 ([72], [73]).

c) S dng mng nron hoc h m xp x o ca g(x) nu g g

H vig H bit ([56]).

d) Thit k b iu khin thch nghi c cha thnh phn iu khin theo ch

trt gi cho bin ca tn hiu iu khin b chn ([50]).

e) Xy dng hm Lyapunov sa i cho php cu trc b iu khin thchnghi da trn hm Lyapunov trnh trng hp 0 nu trn ([81], [104]).

2. a ra m hnh thay th hn hp cc hm f(x) , g(x) :a) S dng cc m hnh cc b v xp x tuyn tnh i vi tham s cng

nh dng phng php quy chiu tham s (parameter projection) gii

quyt vn g(x) 0 vi g(x) l c lng ca g(x) trong m hnh

hn hp ([53], [60], [61], [62]).

b) Dng m hnh iu khin m thch nghi bn vng gii quyt trng hp0 nu trn thay cho s dng phng php quy chiu tham s v chuyn

i lin tc tn hiu u vo iu khin ([54])


29/173

- 20 -

3. Thit k m hnh xp x tn hiu iu khin phn hi (2-10) dng mngnron hoc h m ([57]).

c im chung ca cc phng php gii hin nay l s dng cc m hnh

thay th xp x cc thnh phn khng bit (vi cc iu kin gi thit v gii

hn khc nhau) v phi gii quyt vn g(x, ) 0 trong m hnh thay th.

Ngoi ra do m hnh xp x c nhiu u vo (cc trng thi, sai s, tn hiu

mu v cc o hm) nn phi xc nh c tham s ban u lut chnh

nh tham s hot ng ng cng nh phn ln u gi thit rng m hnh xpx m bo sai s trong min lm vic ca qu o trng thi. Mc d mt s

kt qu nghin cu cng b gn y ([53], [54], [71], [93], [103], [105]) gii

quyt c vn xc nh tham s v n gin hn do lut iu khin phn

hi lun m bo khng xy ra g(x) 0 tuy nhin ch gii hn trong cc iu

kin ca tc gi. V mt ng dng, cc tc gi khng ch r m hnh thc t nn

cha nh gi c tnh kh thi ca cc phng php xut khi p dng trn

thit b iu khin cng nghip.

Vi nhng vn nu, lun n sau y i vo nghin cu, xut mtphng php tip cn mi da trn tng thay th c lng (khng cn gn

ng) cc hm trng thi cha bit v s dng h m v mng nron gii

quyt vn b sai lch do php thay th c lng gy nn. Phng php tip

cn mi nhm n gin ha vic thit k m hnh thay th nh trnh phi gii

quyt mt s vn thng gp trong cc phng php nu trn. Ngoi ra lunn cng xy dng m hnh phn mm ng dng nhm th nghim, nh gi kh

nng p dng phng php trn cc h thng iu khin cng nghip. Cc c s

l thuyt xy dng phng php mi c tc gi s dng bao gm phng

php phn tch da trn h sai s, iu khin phi tuyn n nh theo tiu chun

Lyapunov, l thuyt xp x vn nng m nron v iu khin thch nghi trc

tip c tc gi trch dn ch yu trong cc ti liu [32], [50], [51], [57], [66]

v [68].


30/173

vi x(t) = [ x1 2,, xn ] n l vect trng thi; u(t) , y(t) l cc u, x

x x (t, E ) vi mi t, x : l hm s b chn vi E b chn v

- 21 -

2.2. iu khin n nh cc h thng kh tuyn tnh ha phn hi trng

thi bng phng php thay thc lng hm trng thi

2.2.1. C s ton hc ca phng php

Phng php thay th c lng hm trng thi trong lun n c xutnhm gii quyt bi ton nu trn c s phn tch tnh bn vng ca h vng

kn cng nh theo hng pht trin cc b iu khin thch nghi cho cc ng

dng cng nghip. Trc khi i su vo c s ton hc ca phng php, ta

xem xt mt phng php tip cn khc ([57]) da trn nh ngha h sai s

tha mn Gi thit 1 di y c th p dng cho cc h phi tuyn SISO tngqut dng:

x f(x) g(x)u

y h(x)(2-14)

T

vo iu khin v u ra ca i tng; f(x)n , g(x)n , h(x) l cchm phi tuyn i vi i s x ca chng v kh vi vi bc bt k (hm trn).

Gi thit 1: H sai sE(t, x) c nh ngha sao cho E 0 th y(t)r(t) v

x (t, u ) khng gim dn (nondecrescent) i vi u khi tkhng i.Nu Gi thit 1 c tha mn th khi h sai s b chn cng c ngha l qu

o trng thi ca h cng b chn. Mt khc nu tn ti tn hiu(t)E vimi tth x x (t, ) do x (t, ) khng gim dn i vi . Nh vyvi Gi thit 1, h sai s khng ch l php o cht lng ca h vng kn m

cn cho bit c tnh b chn i vi cc trng thi ca h.

Ngoi ra vi phng trnh ng hc (2-14) v h sai s c chn tha mnGi thit 1, ta c th s dng ng hc ca h thng tnh ng hc h sai s

nh sau:


31/173

E (t, x) = + x = +

E( t, x )= k e= k E ,1 e= k Ed

E+vi kT = kTE,1 , kTE = [k1,, kn1] , d E = x1 2 r,, xn1 r(n2) ,r, x

E = kE E + f(x) r (n) + g(x)u = (t, x) + (x)uTvi (t, x) = kE E + f(x) r (n) v (x) = g (x) .T

- 22 -

Et

E

x

E

t

Ex f(x) g(x)u (t, x) (x)u . (2-15)

Phn tip theo cho thy gii quyt bi ton ca h (2-6), ta lun lp ch sai s thch hp tha mn Gi thit 1 m khng cn phi a thm bt c

iu kin rng buc no khc.

Trng hp 1p dng phng php lp h sai s ([57]) trong gii bi ton ca h (2-6)

trong trng hp f(x) , g(x) xc nh dn n phng php gii sau y. nh

ngha h sai s:

T T (2-16)

e x r v sn1 kn1sn2 k1 l Hurwitz. Lu rng E y l i

lng v hng thay v dng vecte nh phng php gii trnh by trong

phn trc. Gi s h sai s (2-16) tha mn Gi thit 1, khi ng hc ca h

sai s c dng:

d

d

Chn hm Lyapunov V 12 E 2 v s dng lut iu khin:

u1(x) (t, x) E

(2-17)

(2-18)

vi 0 s cho kt qu V E (t, x) (x)u E 2 2V nn E 0 lim cn bng n nh theo hm m (exponentially stable) ca h sai s. B

di y (tng hp t cc kt qu trong [57]) cho thy h sai s c nh ngha

nh trn (im cn bng n nh) th cng tha mn Gi thit 1.


32/173

f

V(t, E) ( E ) vi ( E ) K(hm thuc lp K ) thlim E 1 ( m2 m1 ) .

V(0) + m2 2 m1t

V(0) + m2 2 m1t

chn ca h sai s c pht biu nh sau: Nu V(t, E) : + l hm

- 23 -

B 1 : H sai s nh ngha bi (2-16) cho bi ton bm ca h (2-6) thamn Gi thit 1.

Chng minh b trn c trnh by trong Ph lc mc 5.2 trang 136.

C th thy trong trng hp ny, cc lut iu khin phn hi (2-10) v(2-18) trong hai phng php v c bn l ging nhau do thnh phn phn hi

trong c hai phng php u tuyn tnh. Tuy nhin vi phng php thit k

da trn h sai s c th a thnh phn phn hi phi tuyn vo h sai s

nng tnh bn vng ca h vng kn nh s thy phn sau ca lun n ny.

Trng hp 2Trc tin ta xem li B 2.1 trong ti liu [57] dng phn tch tnh b

n

s xc nh dng v V m1V m2 vi m1 0 , m2 0 l cc hng s b chn

th V(t, E) mm1 m1 vi mi t 0 .

Chng minh b bng cch gi m1 m2 v chn (0) V(0) 0th (t) m

m1 m1 , mt khc t V (hay V lun gim nhanhhn hoc bng so vi ) v V(0) (0) suy ra V(t, E) (t) vit 0 .

Lu l b trn cng cho bit Vm2 m1 khi t v nut

Trng hp f(x) , g (x) c cha cc thnh phn khng r, gi thit rng t

s liu o v hiu bit v h thng ta c th tm c cc hm s

(x) f(x)f(x) , g (x) g (x) g (x) tnh gn ng c xn nh sau:


33/173

x

E = k E E n r(n)d + x

d + x = k E E n dxn r(n)

= k E E dxn r(n) + f(x) + g(x)ud

hay vi k hiu (t, x) = kE E r(n) + f(x) , (x) = g(x) th:T

x x

( f(x) E= g (x) kE E + r1 T (n)

vi > 0 v zT = t, xT l vct o c th phng trnh ng hc ca h sai

- 24 -

n f(x) g(x)u(z)f(x) g(x)u(z) xndxn (x, u)

(2-19)

vidxn n xn f gu l sai s gia tn hiu xp x n vi tn hiu xnvdxnW , W 0 cho trc vi mi x , u trong min hp lx n vu . Tip tc nh ngha h sai s nh (2-16) trong Trng hp 1, khi o hm ca h sai s theo thi gian s l:

T

T

T

d

E (t, x)(x)u dxn (x, u)S dng lut iu khin phn hi:

(2-20)

u(z)1(x) (t, x) Ed

(2-21)

s tr thnh:

E E dxn (x, u) . (2-22)Lu l z trong lut iu khin phn hi (2-21) ch chat xut hin r

trong trng hp r(t) c o hm l hm s c cha t.

Chn hm Lyapunov xc nh dng V (E) 12 E 2 v tnh o hm ca Vtheo (2-22) ta c:


34/173

W 2 W t W 2V + V (0) e =

2 2 2

W

lim VH = = = V , lim EH = = = E

0 khi V = V WW2 = V ( E ) h a yE = = E ,

- 25 -

V EE E2dxn E V

12

E2 W E

VW2

2 1

2 W E2(2-23)

V W22

p dng B 2.1 ([57]) vi m1 , m2

Ecng b chn:

W2

2 dn n Vb chn v do

2 2 22

1 e t V (0)e t V H

E W22 1 et E2 (0)et EH. (2-24)

Kt qu (2-23) cho thy V 0 khi V 222 v t (2-24):

m2t m1 2 2 t m1 (2-25)

do vy nu ln th c th xc nhEHtrong ch xc lp nh ty .Ngoi ra nu php xp x xn cng chnh xc bao nhiu (sai s xp xWcng

nh) trong min hp l ca x v u th E hay gii hn EHkhi t ca hsai s cng nh by nhiu.

Bit rng V2 2

2m2 W m1

do ta cn c th suy lun nh sau: VV EE E V 0 .

Nh vy nu V0 V E v iV0 V(0) l Vban u ti t 0 th

0 V V E v i m it 0 do V l hm s xc nh dng nn khng th


35/173

- 26 -

tng ln hn V E . T r n g h pV0 V E t h r r ngV 0 cho n khiV V E . Tm l i k t qu (2 -24) cn c th v i t nh sau :

0 V maxV0 ,V E

E max E0 , E(2-26)

vi mi t 0 , E0 E (0) l gi tr ban u ca h sai s ti t 0 v V0 12

E02

.

Cc kt qu trn cho thy vi lut iu khin phn hi (2-21) cht lng ca

h vng kn ch ph thuc vo sai s xp x xn v khng nht thit phi xc

nh c chnh xc cc hm f (x) , g (x) c cha cc thnh phn khng r. Ni

cch khc thay v phi xp x gn ng tng hm f (x) , g(x) vi sai s cn

thit hoc s dng cc m hnh xp x nh trong nhiu phng php khc ([40],

[52], [53], [54], [56], [60], [61], [62], [63], [72], [73], [75], [92], [94], [95], [98],[103], [104], [105]), ta c th xp x f (x) , g(x) vi sai s ty min sao sai s

xp x xn tha mndxnWtrong min hp l ca x x v u u (lu l iu kin sai s xp x khng cn p ng ngoi min hp l).

Ngoi ra vi mi W 0 cho trc v vi u uu : uuM , uM 0lun tn ti cc cp hm trng thi f (x) , g(x) lin tc b chn p ng iu

kin xp x v d nh trng hp cc hm thay th tha mn:

g WuM

, 0 f W guM (2-27)

do khi dxn f gu f guM W.Tuy nhin ngay c trng hp khng xc nh c cp hm thay th tha

mn hay cp hm thay th khng p ng iu kin sai s xp x (2-27) nu trn

ta vn c th p dng c phng php nu nh b c sai s xp x do php


36/173

W

kE E + E=T ki ( xi r) + k e = ki ( xi + 1 r+ 1) + ki + 1ei + 1 + k1e1

(ki ik+ 1)ei + 1 1 1 1 1 2 ,, kn1 + ] e+ k e = [ k , k+ k

= k+ e = e

- 27 -

c lng cc thnh phn khng r gy nn. Trong thc t c nhiu cch xcnh cp hm thay th t s liu bit v h thng v d nh ta c th nh

ngha trc hm f(x) v g(x) 0 da trn cc thnh phn bit v tm cch

b sai s xp x do cc thnh phn khng r gy nn thng qua lut iu khin

phn hi sao cho o hm ca V theo (2-22) tha mn (2-23) hay

V V 22

trong min hp l ca x v u . Nh vy bi ton iu khin

h vng kn n nh trong trng hp ny tr thnh bi ton xp x xn vi

chnh xc cn thit v vn m bo cc iu kin v trng thi v u votrong min hp l. Phng php gii quyt cc vn ny s c trnh by chi

tit trong Chng 3.

Do c im ca phng php l xp x xn khng nht thit phi xp x

ring tng hm trng thi vi sai s cn thit m c th thay th bng cp hm

c lng nh phn tch m trong lun n ny phng php c gi l

phng php thay th c lng hm trng thi. Phn sau ca lun n s phntch phng php thay th c lng cc hm trng thi s dng iu khin m

nron nhm thch nghi vi cc thay i khng r trong h sai s.

Tnh cht b chn ti hn u ca h sai sGi s tm c cp hm trng thi thay th iu kin xp x xn c

tha mn, khi tip tc bin i biu thc:

d

n1 n1 n1

i 1 i 1 i 1

n1

i 1

T

TT

kE ta c th biu din li lut iu khin phn hi (2-21) nh sau:


37/173

u =u = g1 (x ) ( r (n ) e (x )

vi = [ k1 1 2,, kn1 + ] ., k+ k

Do xn = f(x) + g(x)u = r(n) e nn:x en

,1e1, e1,e(n)

E1(s) = n 1

=

- 28 -

T

T

dxn x, u n xn

T (2-28)

T

T 1

T (2-29)

dxn (e1)

hay dxn cng l hm ca e1 . Mt khc t php chnkTk1, ,kn1,1 athc sn1 kn1sn2 k1 l Hurwitz nn cc s hng ca

T,1 1, , n ,1 c n g l p t h n h a t h c H u r w i t z:12s n s n1 s n k1 (k1 k2 )s ( kn1 )s n1 s n

( s )(k1 k2s s n1).

Biu din quan h (2-29) qua php bin i Laplace:

(2-30)

1E(s)

(k1 k2s s )

1(s )(k1 k2s s n1)

dxn (s)(2-31)

vi E1(s) , E(s) vdxn (s) tng ng l bin i Laplace ca e1(t, x) , E(t, x)vdxn (e1) suy ra:


38/173

lim e1 = lim E= lim dxn

lim e1 = lim dxn

lim dxn

nghim ca a thc Hurwitz (2-30). Ngoi ra do xn = r(n) e nn iu kin

dxn = r(n) e xn W

r(n) e xn W

- 29 -

t1 1k1 tk1 t

t1 W

k1 tk1(2-32)

lim Et

1 t

W

hay vi lut iu khin phn hi (2-28), gii hn sai s bm u ra e1 y r

trong ch xc lp b chn ph thuc vo cc gi tr , k1, Wc chntrong thit k. Lu l

k1 si chnh l gi tr tuyt i ca tch ton b ccT

xp x cn c th vit di dng:

T (2-33)

Nh vy trong bi ton bm ca h phi tuyn (2-6) trng hp 2, bngphng php lp h sai s (2-16) v s dng lut iu khin phn hi (2-21),

nu ta coi E l trng thi ca h sai s th kt hp cc kt qu trn, dn n pht

biu ca nh l 1 di y v tnh cht b chn ca nghim ca phng trnh

ng hc h sai s (2-20) trong phng php thay th c lng hm trng thi.

nh l 1 : Phng trnh ng hc h sai s (2-20) c nghim b chn ti hnu (uniformly ultimately bounded) theo (2-26) v gii hn sai s bm u ra

trong ch xc lp theo (2-32), nu xc nh c cc hm s lin tc, b

chn g(x) 0 vf(x) vi lut iu khin phn hi tnh (2-28) th iu kin:

T

lun tha mn vi mi x x n , u u v W 0 cho trc.(2-34)


39/173

VE 3( E)

( E) V+ = V (1 ) V+ W2 2

(E) ( E) (1 ) V+ W. V ( E) ( E) cn thit V2

V

- 30 -

Chng minhTheo nh l v iu kin b chn ti hn u ([51], [57]), vic chng minh

nghim ca phng trnh ng hc (2-20) vi lut iu khin phn hi (2-28) bchn ti hn u (hay b chn cui ng u) thc cht l phi ch ra c cc

hm s1( E), 2 ( E)K (hm lp K ) v 3 ( E) K(hm lp K ) xcnh trn0 , th a m n :

1( E)V(E) 2 ( E)V (E) E (2-35)

vi E Rv V(E) l hm s kh vi lin tc xc nh trn E R.

Chn1( E) 2 ( E) V( E) 12 E 2 l cc hm lp K , ta cn tm

3 ( E)Ktha mn (2-35) khi E R . T (2-23) c th bin i tip nh sau:W2 2

V

1( E) (1 )V W22

vi 0 1 nn nu chn 3 ( E)1( E) th3 3

2 W2

2(1 ) 2hay khi E W

1 R .R rng cc hm1( E), 2 ( E), 3( E), V(E) c chn nh trn lun

tha mn iu kin (2-35) nn nh l 1 c chng minh.


40/173

W

Kt qu di y cho thy nu tn ti hm (x,u) : + tha mn

u= u+ uc vi u=

g 1 (x

trong (t, x) = kE E r(n) + f (x) = e E r(n) + f (x) , (x) g%(x) dnT T

- 31 -

2.2.2. Tnh bn vng ca h vng kn trong phng php

Nng cao tnh bn vng ca h vng knPhng php thay th c lng hm trng thi nu trn xut pht t gi

thit thnh phn sai sdxnWb chn vi W 0 cho trc, t s dnglut iu khin phn hi trng thi tnh (2-28) V V 2

2v do h

vng kn c sai s Ecng b chn theo (2-26). Ngoi ra quan h (2-32) cho

thy lun tn ti sai s u ra c quan h t l thun vi sai s xp x trong ch xc lp. Nhm tm cch b tr nh hng ca sai s xp x, sau y tip tc

phn tch phng php theo hng nng cao tnh bn vng ca h vng kn

gii quyt vn ny.

n1

iu kindxn (x, u) vix x , u u th v l thuyt c th loi trhon ton nh hng ca sai s xp x

dxn trong phng trnh ng hc sai s(2-20) bng cch a thm thnh phn b uc vo lut iu khin phn hi, hay

T T k1, k1 k2 ,, kn1 l thnh phn phn hi theo (2-28).

T phng trnh ng hc ca h sai s:

E (t, x) (x)u ucd x n(t, x) (x)u (x)ucdxn (2-36) E (x)ucdxn

d

n o hm ca hm Lyapunov theo (2-36) s l:

V EE E2 E (x)uc Edxn


41/173

nh v loi tr c gii hn sai s bm u ra lim e1 trong (2-32). T bt

sign( E) = 0 E= 0 lun p ng c yu cu ny do:

u= u + u c=

g 1(x

u=

g 1(x

- 32 -

R rng nu xc nh c uc V 0 viE0 th h vng kn s nt

ng thc trn suy ra uc E (x,u)sign(E)

(x) vi v 1 E 01 E 0

V E 2 E (x)uc E (x, u)( ) E 2 E sign( E) E( ) E 2 0E0.

Khi vi thnh phn b uc nu trn, lut phn hi (2-28) tr thnh:

(2-37)

T

hay khi

0 c th biu din gn li di dng:

(2-38)

T (2-39)Tuy nhin kt qu (2-39) c cha thnh phn sign(E ) khng lin tc nn nu

(x, u) l hm lin tc th c th thay th gn ng sign(E ) bng mt hm lin

tc tn hiu iu khin l lin tc. Sau y xut v phn tch s dng hm

xchma lng cc:

bsig( , E) 21 eE 1

1 eE1 e E

(2-40)

trong phng php vi 0 l h s gc ti im un E 0 ca hm. Dosign( E) lim bsig( , E) nn vi thnh phn b:

uc (x,u) (x ) bsig( , E) (2-41)

lut iu khin phn hi s lin tc v c dng:


42/173

u =

g 1( x)

- 33 -

T

Nu k hiu:( ,E) 1 sign( E) bsig( , E)

( , E) E ( , E)

th 0 1 (Hnh 1) v:V E2 Esign(E) bsig(, E) E

E2 E( , E)

E2 ( , E)

(2-42)

(2-43)

(2-44)

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

( ,E) = 1 - sign( E)bsig( ,E)

=50.2

= 100.1

0

= 100

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

E

Hnh 1 : Hm ( , E) 1 sign(E)bsig( , E)Bit rng hm xchma lng cc bsig( , E) bsig( ,E) l hm l nn

suy ra ( , E) l hm chn khng m v do ( , E) ( ,E) cng l hmchn khng m (Hnh 2). Nh vy tm cc i ca hm ( , E ) ta ch cn xthm (, E ) ( , E ) vi E0, v 0 tm (cc) im cc tr cahm , t suy ra (cc) im cc tr cn li ca ( , E ) i xng qua trcta tung v xc nh gi tr cc i.


43/173

=5 = 10 = 100

(1 + e )

- 34 -

(,E) =E. (,E)0.12

0.1114

0.1

0.08

0.060.0557

0.04

0.02

0.0056

0-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

E

Hnh 2 : Hm ( , E) E( , E)

T ( ,E) E1 b sig ( , E) 2 Ee

E1 eE , tnh o hm ca theo Eta

c dd E

( , E) 2e E E 2 1E e E hay hm c cc tr (cng l

cc i) ti E Em l nghim ca phng trnh:

E1 e E. gii phng trnh (2-45), ta dng B 2 sau:

(2-45)

B 2 : Nghim ca phng trnh x b a x vi a 0 l

x bwab l n ( a )

ln(a) v iw( x) l hm Lambert v ln(a) l logarit c s t

nhin ca a .


44/173

w(

x)

Em =

- 35 -

C th chng minh B 2 t nh ngha hm Lambert ([85]) vi

x ab ln(a) v lu e a1/ln(a) .

p dng B 2 vi a 1/ e , b 1 thu c nghim ca phng trnh

(2-45) lEm 1 w(1 / e) vi w(1 / e) l hm Lambert ca 1 / e (Hnh 3) v:1 w(1 /e)

( , Em ) 2

1.2785

Eme Em1 e Em 2 Em

e1w(1/ e)

1 e1w(1/ e) 0.5569

(2-46)

Lambert WFunction

1.5

1

w(x)e w(x) =x

0.5

0.2785

0

-0.5

-1-1 -1/e 0 1/e 1 2 e 3 4 5

x

Hnh 3: Hm Lambertw(x)e

w (x) x

Nh vy ( , E ) nhn gi tr cc i ti cc im E E m . V d gi tr cci ca hm ( , E ) trong cc trng hp minh ha trn Hnh 2 tng ng s l

(5, 0 .2557) 0.1114 , (10, 0.1278) 0.0557 v (100, 0.0128) 0.0056 .Thay (2-46) vo (2-44) thu c:

V E2 ( ,Em ) 2 V0 .5569

. (2-47)


45/173

*

E* = lim EH*

u=

E*

E EH

- 36 -

Kt qu (2-47) cho thy V 0 khi V 0.55692 hayE 0.5569 v p

dng B 2.1 ([57]) vim1 2 , m2 0 .5569 dn n:V 0.5569

2

1 e2 t V 2 ( 0 ) e2 t

E0.5569

1 e2 t

E2 ( 0 ) e2 t

E

H (2-48)

t0.5569

lim.t

Tm li, cc kt qu trn cho thy nu xc nh c hm (x, u) sao cho

dxn (x, u) (x, u) 0.5569

E 2 vi x x , u u th h vng kn s nnh; nu (x, u)

0.5569E 2 th nghim ca h sai s lun b chn theo (2-48).

Trng hp (x, u) W, lut iu khin phn hi v gii hn nghim ca h

sai s s l:

T

E * limt EH*

0 . 5 5 6 9

W. (2-49)

Khi t cc kt qu (2-25), (2-49) dn n:

0.5569

lim

E tEH

E

0.5569 W

(2-50)


46/173

thnh phn b ( E < E ) nu h s gc c chn tha mn:

(x) : l hm lin tc khng m b chn bit, khi s dng lut

- 37 -

hay vi lut iu khin phn hi (2-49) c cha thnh phn b b chn, gii hnca h sai s trong ch xc lp lun nh hn so vi trng hp khng c

*

0.5569 W

0.5569

E . (2-51)

Tnh bn vng ca h vng kn i vi c tnh khng r trong h sai sCc kt qu (2-48), (2-50) cho thy bng cch a thm thnh phn b phn

hi trong h vng kn c th b tr nh hng ca sai s xp x do php clng gy nn. Nh vy phng php ny cng c th p dng i vi thnh

phn khng r xut hin trong phng trnh ng hc ca h sai s c dng:

E (t, x) (x) uu (t, x)dxn (t, x) (x)u dxn (x)u (t, x)

(2-52)

viu (t, x) l thnh phn khng r.Trng hp thnh phn khng ru (t, x) 0, cc kt qu (2-23), (2-47)

trn cho thy lun tn ti lut iu khin phn hi u u h vng kn n nh

c nghim b chn nh phng php phn tch s dng hm Lyapunov xc nh

dng V 12 E2 o hm theo qu o ng hc (2-52) ca h sai s tha

mn V m1V m2 vi m1 0, m20 .Gi thit rngu (t, x) (x) vi 0 l hng s cha bit b chn v

n

iu khin phn hi trng thi:

u u u vi u l thnh phn b dn n:

E (t, x) (x)udxn (x)u (t, x) u

(2-53)


47/173

= m 1V+ m 2 + E ( 1 sig n (

V2

- 38 -

V EEEEu E dxn Eu u m1V m2 Eu u (2-54)

m1V m2 E EuKt qu (2-54) cho thy nu bit trc, th tng t nh phng php

trnh by trn, vi thnh phn b u (x)sign(E ) c th loi tr honton tc ng ca thnh phn khng ru (t , x) do:

V m1V m2E E sign(E )2

m 1V m2.

Trng hp s dng thnh phn b lin tc:

u (x) bsig( , E)vi 0 l h s gc ca hm bsig( , E) ti E 0 , o hm:

V m1V m2E Esign(E) bsig( , E)m1V m2 E1 sign(E) bsig( , E)m1V m2 ( , E)

vi ( , E) E( , E) nh (2-43). p dng kt qu (2-46) cho thy:

V m1V m2 ( ,Em )

(2-55)

(2-56)

(2-57)

m1V m2 0.5569 (2-58)

hay nu chncng ln th c th gim c tng ng mc tc ng cathnh phn khng r.

Tuy nhin do khng bit nn bng phng php s dng thnh phn b

u E vi 0 nh xut trong [57] dn n:


48/173

= m1V+ m2 E +

= m1 2 + E .sign(E) bsig( , E)

V m1 2 + + E( 1)V+ m

m1 2 + V+ m

- 39 -

V m1V m2E 2E22

22

2

4 (2-59)

m1V m2 24 .

Kt qu (2-59) cho bit c th gim tc ng ca thnh phn khng r bng

cch chonhn gi tr ln, tuy nhin phng php ny kh p dng trong thct v thnh phn b to dao ng ln trong tn hiu iu khin khi Ei du.

Sau y lun n xut s dng thnh phn b c dng:

u bsig( , E )nh trnh by trong phn trn, khi :

V m1V m2E Eum1V m2 E Esign(E) bsig( , E)

V m

(2-60)

t 0 v:

E( , , E) E sign(E)bsig( , E) (2-61)dn n E ( , , E) E ( 1)

0.5569 E ( 1) hay nu tm c 1 th khng nhng c th gim c tc ng ca thnh phnkhng r m sai s do thnh phn khng r gy nn b chn khng ph thuc

vo do:

0.5569

0.5569

(2-62)


49/173

E _ max ( , ) = E m ) > 0 , Em 0( , ,

- 40 -

Ngoi ra c th tnh ton chnh xc gi tr ln nht ca hm E( , , E)bng phng php gii trn MATLAB nh B 3 sau:

B 3 : Hm E( , , E) nh ngha nh (2-61) vi 01, 0 c gitr ln nht bng E _ max ( , ) 0 ti hai im i xngEm (,) xc nhbi:

xm (2-63)vi xm l nghim duy nht ca phng trnh

( 1)e2x 2( x)e x1 0 .

Chng minhPhng php chng minh v chng trnh tnh ton gi tr ln nht trn

MATLAB c tc gi trnh by trong mc 5.3 trang 139 phn Ph lc.

Lu l vi1 th E(1, , E) ( , E) theo (2-43) nn kt qu (2-46) ltrng hp ring ca B 3 v ( , 1 . 2 7 8 5

) E(1 , , 1 . 2 7 8 5

) 0.5569

.

Ngoi ra xEv vi mi gi trxc nh trong khong(0, 1] v 0 ,hm E( , , E) t cc i v cng l ln nht bng E _ max ( , ) ti ccimEm ( , ) l cc hm s cav .

Hnh 4 biu din hm E( , , E) trong cc trng hp 5 , 10 v gi

tr c chn trong mi trng hp l 1, 0.9 v 0.5. Kt qu tnh trong cctrng hp trn Hnh 4 nh sau:

E(1.0, 5, 0.2557) 0.1114 E(1.0, 10, 0.1278 ) 0.0557

E(0.9, 5, 0.2154) 0.0879

E(0.5, 5, 0.1046) 0.0256

E(0.9, 10, 0.1077 ) 0.0440

E(0.5, 10, 0.0523 ) 0.0128

(2-64)


50/173

- 41 -

0.12

0.1114

0.1

0.0879

0.08

= 50.06

0.0557

0.05

0.0440

0.04

= 10

=10.06

0.04

0.0256

0.02

0

-0.02

-0.04

0.03

0.02

0.0128

0.01

0

-0.01

-0.02

=0.9

=0.5

-1 -0.5 0 0.5 1 -0.5 -0.25 0 0.25 0.5

E

Hnh 4 : Hm E(,, E) E

E

sign(E)bsig( , E)


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=1 =0.9 =0.5

E E

1.4

=10.4

=1

1.2785

1.2

1.07690.3

1

0.2557

0.8

Em

0.2

E m

0.6

0.5569

0.5229

0.4396

0.4

0.1278

0.1114

0.1

E_max

0.2

0.1278

0

E_max0.0557

00 0.2 0.4 0.5 0.6 0.8 0.9 1 0 5 10 15 20

Hnh 5 : Hm Em ( , ) v E _ max ( , ) E( , ,Em )


52/173

v (x) : l hm lin tc khng m b chn cho trc, dn n pht

nu V m1 2 vi V = 12 E 2 , m1 2 0 khi u = 0 v .

VE 3( E)

- 42 -

Hnh 5 biu din th ca E_ max trong cc trng hp c bit 1 v1. Ngoi ra c th c lng ta im cc i t th bn tri trnHnh 5 ( 1). V d tnh im cc i ca hm vi 0.9 v 5 , t th Hnh 5 bn tri suy ra:

Em (0.9,5) Em (0.9,1) 1.0769

5

0.2154

E_ m a x E_ m ax

0.4396

5 Nh vy so vi (2-62) ta thu c kt qu mnh hn nh sau:

V m1V m2E _ max ( , ) . (2-65)Tng hp cc kt qu trn, trong trng hp h sai s (2-52) c cha thnh

phn khng r b chnu (t, x) (x) vi 0 l hng s b chn cha bitn

biu ca B 4 di y.

B 4 : Nghim ca phng trnh ng hc h sai s (2-52) b chn ti hn

u (uniformly ultimately bounded) bi lut iu khin phn hi u u u viu l thnh phn b lin tc theo (2-60) vu l thnh phn iu khin n nh

V m 0, m

Chng minh chng minh nghim ca h sai s vng kn b chn ti hn u ta cn ch

ra cc hm s1( E), 2 ( E)K v 3 (E ) K xc nh trn0, t hamn:

1( E)V(E) 2 ( E)V (E) E

(2-66)


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Sau y chn 1 2 ( E ) = V ( E) = 12 E

2( m + )R = 11 E _ max

(1 )m1

- 43 -

vi ER v V (E) l hm s kh vi lin tc xc nh trn ER .

( E )2

l cc hm lp K v t(2-65) bin i tip nh sau:

V ( E ) m1V m2 E _ max m1V (1 )m1V m2 E _ max m11( E ) (1 )m1V m2 E _ max

vi 0 1. t3 ( E )m11( E )Ksuy ra V ( E ) 3 ( E ) khi ERvi R

2 m2 E _ m a x(1 )m1

v B 4 c chng minh.

Ngoi ra lu l trng hp V (E) tng qut ta c

2

.


54/173

- 44 -

2.3. iu khin n nh cc h thng kh tuyn tnh ha phn hi vo-ra

bng phng php thay thc lng hm trng thi2.3.1. Bi ton iu khin v c s ton hc

Trong phn trc, mc 2.2 trnh by v phn tch phng php thay thc lng hm trng thi trong iu khin cc h kh tuyn tnh ha phn hi

trng thi (khng c thnh phn h con phi tuyn ni ng hc q ). Sau y lun

n phn tch kh nng p dng phng php thay th c lng hm trng thi

trong iu khin n nh cc h thng kh tuyn tnh ha phn hi vo-ra cphng trnh ng hc v u ra bin i c v dng chun tc (2-3) vi Gi

thit 2 nh sau:

Gi thit 2: H (2-3) c:

1) bc tng i n v h con q (x, q) l n nh u vo-trng thi

(ISS) vi x l u vo;

2) f (x, q) , g (x, q) l cc hm s thc b chn v g (x, q) 0 vi mi (x, q)

trong min hp l ng xq nd ;

3) cc trng thi (x, q) ca h o c.

Bi ton t ra l cn iu khin n nh (2-3) sao cho u ra ca h bm

theo tn hiu mu r (t ) vi gi thit r (t ) v cc o hm ca tn hiu mu n

bc n b chn v o c. Vn l mc d h con q khng c tc ng tiu ra ca h, tuy nhin cho d xc nh c b iu khin n nh ng hc

ca h con tuyn tnh ha x th vn c th xy ra q nu ng hc ca h

con (phi tuyn) q (x, q) khng n nh. Nh vy gii quyt bi ton, cn

thit phi bit c c tnh ng hc ca h con phi tuyn. Nhm n gin ha

tnh ton m khng lm mt i tnh thc t nn phng php gii trong phn

ny lun gi thit rng h con phi tuyn q (x, q) l n nh u vo-trngthi vi x l u vo.


55/173

Theo nh ngha, h x = f(t, x, u) vi f: [0, ) , n , n lin tc phn

x(t) ( x(t0 0 ) + sup u( ) .

) , t t0

hay = k x trong (2-5) c chn sao cho (A bkT ) l Hurwitz th c th

- 45 -

m

on (piecewise continuous) i vi t v Lipschitz cc b i vi x vu cgi l n nh u vo-trng thi nu tn ti hm KL (hm lp KL) v K (hm lpK) vi bt k trng thi ban u x0 x(t0 ) v u vo bchn u(t) no, lun tn ti nghim x(t) vi mi t t0 v tha mn:

(2-67)

Bt ng thc (2-67) cho thy nu h l ISS th lun m bo rng vi bt ku vo u(t) b chn no, trng thi x(t) ca h cng b chn. Ngoi ra khi t

tng dn th trng thi x(t) s b chn cui (ti hn) bi hmKdo khi

x(t0) ,t t00 v nu u(t) hi t v 0 khi t th x(t) cng hi t v0 . Mt tnh cht khc ca h ISS l khiu(t)0 th do bt ng thc (2-67) rtgn thnh x(t) x0 ,t t0 n n s u y r a h k h n g c n g b cx f(t, x, 0) cgc ta l n nh tim cn u.

Cc B 13.1 v 13.2 trong [50] cho bit trong trng hp h con x c th

n nh c (dng lut iu khin phn hi trng thi) v dng x (A bkT)x

T

kt lun c c tnh n nh i vi im gc ta x;q 0 c a h ( 2 - 3 )tng ng nh sau: Gc ta ca h (2-3) l n nh tim cn nu gc ca hcon q (0, q) (im q 0 ) n nh tim cn v gc ca h (2-3) l n nh

tim cn ton cc nu h con q (x, q) l n nh u vo-trng thi (ISS) vi

x l u vo. Ngoi ra cc kt qu trn cn xut pht t tnh cht ca cc h

lin kt tng (cascade) c trnh by trong [50], [51] v c tng hp li nh

di y:

H lin kt tng phi t tr (nonautonomous):


56/173

vi f1 : [0, ) m v f2 : [0, ) n l lin tc phn on

- 46 -

1 : q f1(t,q, x) 2 : x f2 (t, x) (2-68)

m n n

i vi tv Lipschitz cc b i viq; x . N u h 1 vi x l u vo ln nh u vo-trng thi v im gc ca h2 l n nh tim cn u toncc (globally uniformly asymtotically stable) th gc ta ca h lin kt tng

(2-68) cng n nh tim cn u ton cc.

i vi trng hp h lin kt tng t tr (autonomous):1 : q f1(q, x)

2 : x f2 (x,u)(2-69)

nu h 1 vi x l u vo l n nh u vo - trng thi (cc b/ton cc)

v im gc ca h2 l n nh tim cn (cc b/ton cc) th gc ta ca

h lin kt tng (2-69) cng l n nh tim cn (cc b/ton cc).

Do phng php xy dng trong lun n da trn c s lp h sai s tha

mn Gi thit 1 vi cc thnh phn khng r nn c th dng nh l 6.1 trong

[57] chng minh cc kt qu ca lun n. Pht biu ca nh l ny nh sau:

Gi E(t, x) l h sai s tha mn Gi thit 1. Gi thit rng tn ti b iu

khin u v(z) v hm Lyapunov V (E) sao cho E ( E )V(E) viEK vV 0 theo qu o (2-3) khi V Vrvi mi qd, xn v t . Nu hcon q (x, q) vi u vo x l n nh u vo-trng thi (ISS) th b iu

khin u v(z) m bo rng x v q b chn u.

Lu rng nu h con q l n nh u vo-trng thi (ISS) cng c ngha

l tn ti hm xc nh dng Vq :

q1( q )

Vq (q)

q2 ( q )Vq q3 ( q ), q ( x ) (2-70)


57/173

Trng hp f(x, q) , g(x, q) xc nh, t e = x rvi r = r, r,, r(n1)

= Ae + b f(x, q) + g(x, q)u r(n)

u = g1(

x , q)

( f(x ,q

)+ r (

n) ke

- 47 -

viq1,q2K , q3, K.nh l 6.1 ([57]) cho bit nu b iu khin c thit k n nh ng

hc x th ng hc q cng s n nh nu tha mn iu kin (2-70). Ngoi ra

t nh l 6.1 ([57]) c th suy ra h qu mnh hn ca nh l trong trng

hp V kVth E 0 l im cn bng n nh theo hm s m trong khi c

th q ch b chn. Lu l khix 0 th iu kin i viVq trong (2-70) tr

thnh Vq q3 ( q ) vi mi q dn n nghim ca ng hc khng

q (0, q) l n nh tim cn ton cc v h l pha cc tiu (minimum phase).Vi cc c s ton hc nh trnh by trn, phn tip theo ca lun n

cho thy bng phng php lp h sai s v thay th c lng hm trng thi

i vi cc thnh phn khng r tng t nh trong trng hp h kh tuyn

tnh phn hi u vo-trng thi (mc 2.2) v vi gi thit h con phi tuyn l

ISS th vn iu khin trong trng hp ny lun gii quyt c.

2.3.2. iu khin n nh bng phng php thay th c lng hm trng

thi

Trng hp 1

th t phng trnh (2-4) suy ra:

e x r Ax b f(x, q) g(x, q)u r

T

Ae Ar r b f(x, q) g(x, q)u

nn nu chn lut iu khin phn hi tnh theo [50]:

(2-71)

T

(2-72)

vi k c chn sao cho (A bkT) l Hurwitz th h vng kn tr thnh:


58/173

y = cT .

E (t, x, q) = ke = k E ,1 e= kEd

E +vi kT = kTE,1 , kTE = [k1,, kn1] , d E = x1 2 r,, xn1 r(n2) ,r, x

vi (t, x,q) = kE E r(n) + f(x,q) , (x, q) = g(x, q) .T

- 48 -

q (e r, q)

e ( A bkT)e (2-73)

e r q

p dng tnh cht ca h lin kt tng v do gi thit ban u h con

q (x, q) l n nh u vo-trng thi (ISS) vi x e r l u vo b chn

do r r M b chn suy ra im gc ta ca (2-73) l n nh ton cc.

Ngoi ra bng phng php lp h sai s c th gii quyt bi ton nh sau

([57]). nh ngha h sai s:

T T (2-74)

e x r v sn1 kn1sn2 k1 l Hurwitz. Khi h sai s (2-74) tha

mn Gi thit 1 v phng trnh ng hc ca h sai s c dng:

E (t, x, q)(x, q)u (2-75)d

Chn hm Lyapunov V 12 E2 v s dng lut iu khin phn hi tnh:

u1(x, q) (t, x, q) E (2-76)vi 0 dn n E E v V E2 . Do gi thit h con q (x, q) l nnh u vo-trng thi (ISS) vi x l u vo nn p dng h qu ca nh l

6.1 ([57]) suy ra E 0 l im cn bng n nh theo hm m ca h sai s.

Trng hp 2Trng hp f(x, q) , g(x, q) c cha cc thnh phn khng r, gi thit rng

t s liu o v hiu bit v h thng ta c th tm c cc hm s


59/173

f

x f x

vi (t, x,q) = kE E r(n) + f(x,q) , (x, q) = g(x, q) .T

= g

1 ( x , q)( kE E

+ r (n)

(x , q ) ET

vi zT = t, xT ,qT n+d + 1 v > 0 th phng trnh ng hc ca h sai s

V+

Whay V < 0 khi V

> =Vr. Khi theo nh l 6.1 ([57]) ta cx , q b chn

- 49 -

(x, q) f(x, q) f(x, q) , g(x, q) g(x, q) g(x, q) thay th f(x, q) ,g(x, q) tnh gn ng c xn nh sau:

n ( x, q) g(x, q)u(z) xndxn (x, q, u) (2-77)

vidxn (x, q, u) n xn f(x, q) g(x, q)u(z) l sai s gia tn hiu xpx xn vi tn hiu xn vdxn W , W 0 cho trc vi mi x, q trong min

hp lx,q ndv u u .nh ngha h sai s nh (2-74) khi :

E(t, x, q)(x, q)u dxnd

S dng lut iu khin phn hi trng thi tnh:

(2-78)

u(z) u1(x, q) (t, x, q) Ed

(2-79)

vng kn tr thnh:

E Edxn (x, q, u) .

Dng hm Lyapunov V 12 E 2 dn n:

V EE E2dxn E

(2-80)

V

W2

2

W2

2

1

2 W E2 (2-81)

2

2 2u v tng t nh trong trng hp h l kh tuyn tnh ha phn hi u


60/173

( )W2 W t W2 1 e t + V(0)e t = VH eV + V2 2 2 2 2 2

(1 e t ) + E2 (0)e t = EH.W

vi E0 = E(0) , E = lim EH =

Lu l do e = kE E+ E vi T = [ k1 1 2 ,, kn1 + ] n n l u t, k+ kd

u =u = g1 ( x ,q ) ( r (n ) e ( x ,q )

dxn = r(n) e xn W

- 50 -

vo-trng thi, p dng B 2.1 ([57]) vi m1 , m2

chn v do E cng b chn theo biu thc sau:

W2

2 dn n V b

hay:

E

2

2

2

0V max V0 ,V EE max E0 , E

(2-82)

(2-83)

tW

v V0

1

2

2E0 .

T T

iu khin (2-79) c th vit nh sau:T (2-84)

v iu kin sai s xp x chung cn c th biu din di dng:

T (2-85)

Kt qu trn cho thy nh hng ca sai s xp x do php thay th c

lng cc hm trng thi gy nn trong trng hp h kh tuyn tnh ha phnhi vo-ra tha mn Gi thit 2 cng c th gim tr c bng cch a thm

thnh phn b phn hi vo h vng kn ging nh trng hp h kh tuyn

tnh phn hi u vo-trng thi nhng vi iu kin h con phi tuyn l ISS.

Phn tip theo cho thy cng vi gi thit ny phng php hon ton p dng

tng t c trong trng hp h c cha thnh phn khng r trn u vo

ca phng trnh ng hc.


61/173

l hng s cha bit b chn, (x, q ) : + l hm khng m bit.

- 51 -

2.3.3. Tnh bn vng ca h vng kn i vi thnh phn khng r trong

phng trnh ng hc

Xt h c phng trnh ng hc v u ra sau:

q (x, q)

x1 x2xn1 xn

xn f(x, q) g(x, q)uu (t, x, q)(2-86)

y

x1

trong u (t, x, q) l thnh phn khng r vu (t, x, q) (x, q ) vi 0n

H con q (x, q) l ISS vi x l u vo, cc hm f(x, q) , g(x, q) c cha

cc thnh phn khng r b chn v g(x, q) 0 vi mi (x, q) trong min iu

khin cxq nd nh Gi thit 2.Trng hp thnh phn khng r u (t, x, q) 0, tip tc vi gi thit rng t

s liu o ta c th tm c cc hm thay th c lng tnh gn ng c

xn nh (2-77) th bng phng php lp h sai s (2-74) v s dng lut iu

khin phn hi u u nh (2-84) dn n x , q b chn u nh phng php

phn tch s dng hm Lyapunov xc nh dng V 12 E2 o hm theo

qu o ng hc (2-80) ca h sai s tha mn V m1V m2 vi

m1 0, m2 0 .

Vi thnh phn khng ru (t, x, q) tha mn gi thit nu trn, tng tnh trnh by trong phn trc ta c th s dng thnh phn b u a vou iu khin u u u n nh h sai s trong :

u (x, q ) bsig( , E) (2-87)


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= m1 2 + E sign(E) bsig( , E)

u=

g 1 (x,q )

- 52 -

vi bsig( , E) l hm xchma lng cc nh ngha nh (2-40), 0 v 0l h s gc ca hm bsig( , E) ti E 0 .

Khi ng hc ca h sai s s l:

E(t, x, q)(x, q)udxn (x, q)u (t, x, q) u (2-88)v o hm ca hm Lyapunov theo qu o ng hc ca h sai s phn tchc thnh:

V EEEEu Edxn Eu u m1V m2 E u um1V m2 E Esign(E) bsig( , E)

V m

m1V m2 E ( , , E)m1V m2 E_max ( , ).

(2-89)

v i 1

0 v E ( , , E) nh ngha nh (2-61) t gi tr ln nht bng

E_max ( , ) c th xc nh nh B 3 trang 40 hay nu tm c ththeo nh l 6.1 ([57]) ta c x , q b chn u v sai s do thnh phn khng r

gy nn b chn khng ph thuc vo . Nh vy trong trng hp ny kt qu

(2-89) cng c dng ging nh kt qu (2-65) trong trng hp h tuyn tnh

ha phn hi trng thi.

Tng hp li dn n pht biu tng qut ca nh l 2 nh sau:

nh l 2 : H (2-86) c x v q b chn u (uniformly bounded) bi lut iu

khin phn hi u u u vi u v u c nh ngha nh (2-84) v (2-87)hay:

T (2-90)


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r(n) e xn Wvi mi ( x,q) x q n+d , u u v W> 0 cho trc.

- 53 -

nu trong g(x, q) 0 ,f(x, q) l cc hm lin tc b chn tha mnT

Chng minhChng minh nh l 2 t cc kt qu nu trn v nh l 6.1 ([57]).

Sau y chn1( E) V(E) 12 E 2 l hm lp K th t (2-89) bin itng t nh trong chng minh 0 s cho kt qu:

V(E) m11( E) (1 )m1V m2 E_ maxvi 0 1 nn suy ra o hm ca hm Lyapunov V( E) m11( E) khiE Rvi R

2 m2 E_ m a x(1 ) m1

.

Kt qu trn tng ng V 0 khi V Vr V( R) vi mi

x,q xq nd nn theo nh l 6.1 ([57]), vi gi thit h conq (x, q) l n nh u vo-trng thi (ISS) vi x l u vo suy ra lut iu

khin (2-90) m bo rng x v q b chn u v nh l 2 c chng minh.

Mt im cn lu l cc kt qu trn ca phng php xut pht t gi

thit ton b trng thi ca h o c. Tuy nhin cng c th p dng phng

php trong cc trng hp c bit khi mt s trng thi ca h khng o c

nh v d sau. Xt h c phng trnh ng hc v u ra:

q (x, q)

x1 x2xn1 xn

xn

f(x) g(x) uu (t, x, q)y x1

(2-91)


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- 54 -

trong q (x, q) l ISPS (Input-to-State Practically Stable) vi x l u vo,

u (t , x, q) l thnh phn khng r c iu kin rng buc nh trong nh l 2v(x, q ) khng gim dn i vi q , ngoi ra gi thit rng ch cc trng thix ca h l o c, cc trng thi q khng o c.

Tip tc p dng phng php trn vi gi thit t s liu o ta c th thay

th c cc hm s f(x) , g (x) tnh gn ng xn vi sai sdxn (x, u)Wvi mi x x n , u u v W 0 cho trc. Khi vi h sai s nhngha nh (2-74), nu x , q o c v nu tm c th theo nh l 2h (2-91) c x , q b chn u. Tuy nhin do gi thit trng thiq ca h khng

o c nn ta cn xc nh u khng ph thuc vo q .Bit rng h con phi tuyn q (x, q) l ISPS vi x l u vo nn theo

iu kin cn v ca h ISPS ([51], [57]) tn ti hm xc nh dng Vq (q)

:

q1( q )Vq (q) q2 ( q ) Vqq (x,q) cVq ( x ) d

(2-92)

viq1,q 2 ,K v c 0 , d0 .T (2-92) nh ngha c( x ) d v chn (0) Vq (0) V q th

qq1 (Vq ) q1 () . Do vy nu chn u x, q1 ( ) bsig( , E) vs dng lut phn hi u u u th bin i nh trn cng dn nV m1V m2 E _ max nn suy ra x v q b chn u.


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r(n) e xn Wvi mi x trong min ng x v u u . Trng

- 55 -

2.4. Tng hp thit k b iu khin tnh n nh

Tm li, cc kt qu trnh by trong chng c th tng hp li thnh ccbc tng hp b iu khin tnh n nh theo phng php thay th c lng

hm trng thi nh sau:

1. Biu din phng trnh ng hc v u ra ca h dng tuyn tnh haphn hi trng thi phng trnh (2-6) hoc tuyn tnh ha phn hi

vo-ra phng trnh (2-3). Xc nh cc thnh phn khng r v cc

gii hn.

2. Xc nh tn hiu mu cn bm, nh ngha h sai s v chn hmLyapunov V. S dng lut iu khin phn hi tnh theo (2-28) hoc

(2-84) V m1V m2 . Xc nh gi tr W 0 cn t cht lng

h vng kn tha mn yu cu thit k.

3. T cc d liu o v hiu bit v h thng tm cch xc nh cp hm

thay th fv g ph hp sao cho sai s xp xxn

tha mnT

hp iu kin sai s xp x khng tha mn th c th s dng thnh phnb m nron trong phng php thay th c lng (chi tit trnh by

trong Chng 3) b sai s do php thay th c lng gy nn.

4. Thit k thnh phn b lin tc u bsig( , E ) a thm vo uiu khin nhm nng cao tnh bn vng ca h i vi cc thnh phnkhng r (nu c) xut hin trn u vo ca h. S dng cc cng thc

(2-51), (2-65) v B 3 (trang 40) tnh ton cc tham s thnh phn

b lin tc p ng sai lch cho php theo yu cu thit k.


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- 56 -

2.5. Kt lun

Chng 2 trnh by cc c s ton hc hnh thnh phng php mi tnghp b iu khin n nh tnh (khng thch nghi) cc h thng kh tuyn tnh

ha phn hi trng thi dng (2-6) v kh tuyn tnh ha phn hi vo-ra dng

(2-3) c cha cc thnh phn khng r b chn trong cc hm trng thi fv g

ca phng trnh ng hc.

gii quyt bi ton bm theo tn hiu mu cho trc, khng nh cc

phng php tm cch xp x gn ng cc hm trng thi fv gcha bit,phng php mi xut xy dng trn c s gi nh rng c th tm c cp

hm fv g thay th c lng (khng cn chnh xc) cc hm trng thi cha

bit sao cho sai s xp x xn tha mn iu kin sai s trong min trng thi hp

l (Chng tip theo ca lun n s gii quyt vn khi iu kin xp x khng

tha mn). Khi bng cch lp h sai s thch hp (B 1 trang 23) v s

dng lut iu khin phn hi cha cp hm thay th tm c s m bo

nghim ca h sai s c lp b chn ti hn u v do sai s bm u ra

cng nh trng thi ca h b chn (nh l 1 trang 29).

Mt khc nhm phn tch tnh bn vng ca h vng kn trong phng phpi vi thnh phn khng r b chn xut hin trn u vo ca h (nh sai s

xp x, nhiu u vo, ...), phng php ch ra rng bng cch a thm thnh

phn b lin tc da trn hm xchma lng cc (2-40) vo lut iu khin phn

hi ( tn hiu iu khin cng lin tc) c th gim tr c tc ng cathnh phn khng r gy nn. Vi c s ton hc c tc gi xy dng v

chng minh l B 3 (trang 40) dng xc nh chnh xc gi tr ln nht

ca hm E(,, E) (nh ngha nh (2-61)) bng phng php gii trn

MATLAB, tc gi ch ra cng thc tnh ton tc ng ny ln h sai s v t

cho php xc nh c tc ng ln sai s bm u ra (B 4 trang 42 v

nh l 2 trang 52). Cc kt qu ny c ngha quan trng trong thit k b


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- 57 -

iu khin p dng trong thc t v l c s gii quyt vn b sai s khiiu kin xp x khng c tha mn trong cc chng tip theo.

Tm li Chng 2 a ra c s ton hc v xut mt phng php mithit k b iu khin n nh tnh cc h thng kh tuyn tnh ha phn hi

trng thi v kh tuyn tnh ha phn hi vo-ra c cc thnh phn khng r

trong phng trnh ng hc cho lp bi ton iu khin bm tn hiu mu l

dng bi ton thng dng trong cc ng dng cng nghip. Cc bc tng

hp b iu khin n nh tnh theo phng php c trnh by trong mc 2.4.

Mc tiu ca phng php hng ti n gin ha qu trnh thit k v tmcch trnh c nhng vn thng gp trong cc phng php hin nay cng

nh c th p dng trn cc h thng iu khin cng nghip (PLC, IPC).

Tuy nhin phng php c tnh ng dng cng nh c phn tch y, trong chng tip theo tc gi tip tc pht trin phng php gii quyt

cc vn trong thit k lut iu khin phn hi tnh khi iu kin xp x

khng c tha mn trong min hp l ca x v u cng nh phn tch, xc

nh tham s iu khin p ng cc iu kin rng buc i vi qu otrng thi v u vo iu khin ca h phi tuyn. tng ca phng php l

xy dng thm thnh phn b phi tuyn trong lut iu khin phn hi sao cho

vi lut iu khin phn hi mi, h sai s b chn nh trong trng hp iu

kin xp x c tha mn (hay tng ng nh khi xc nh c cc hm

thay th tha mn). thc hin tng ny phng php c xy dng theo

hng ng dng iu khin m nron do nhng u im ca h m v mng

nron trong nhn dng c tnh phi tuyn ca i tng.


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- 58 -

CHNG 3

PHNG PHP THAY TH C LNG HM TRNGTHI DNG B XP X M NRON

3.1. t vn v c s l thuyt xy dng phng php

3.1.1. Gii thiu chung

Mt trong nhng vn ca phng php thay th c lng hm trng thi

l t s liu o v hiu bit v h thng phi xc nh c cc hm s clng thay th sao cho sai s xp x x n lun p ng yu cu thit k. Cc kt

qu trong nh l 1 (trang 29) v nh l 2 (trang 52) u gi thit rng c th

tm c cc hm s lin tc, b chn fv g 0 sao cho sai s xp x x n tha

mndxnWvix x , u u . Tuy nhin nu iu kin xp x khngc p ng hay ni cch khc nu khng tm c cc hm c lng thay

th tha mn yu cu th r rng khng th p dng phng php.Ngoi ra mt vn khc cn xem xt l vic xc nh tham s iu khin

(nu tn ti) b iu khin n nh tnh p ng c cc iu kin rng

buc i vi qu o trng thi v u vo trong sut qu trnh hot ng, v d

nh cn gi x v u tng ng lun nm trong min hp lx vu . Vn

ny c ngha quan trng nu xt gc ng dng tr li cho cu hi l

nu ch xc nh c cc hm s thay th tha mn iu kin xp x trong mt

min no khng bao ph min hp l th c th thit k b iu khin n

nh tnh tha mn yu cu thit k hay khng.

Nh vy m rng phm vi ng dng v pht trin phng php, cc vn trn cn c xem xt v gii quyt. y cng l mc tiu t ra trong

Chng 3 ny ca lun n.

Nh nu, do nhng u im ca h m v mng nron trong nhn dng

c tnh phi tuyn ca i tng m phng php c xy dng theo hngng dng iu khin m nron xy dng thnh phn b phi tuyn trong lut


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- 59 -

iu khin phn hi tnh. Phn sau ca lun n s cho thy vn ny c giiquyt nh cc b xp x vn nng (universal approximators) trong l thuyt xp

x hm s. Lu l cc nghin cu v xut trong chng ny ch yu tptrung gii quyt tip cc vn cn tn ti ca phng php trong thit k b

iu khin n nh tnh. Vn xy dng lut iu khin phn hi ng (hay

thch nghi) s c pht trin trong chng tip theo.

3.1.2. B xp x vn nng

Sau y k hiu F(x, ) l b xp x vi p l vect tham s chnh nhc vF p l tp hp ca ton b cc gi tr tham s hp l ca b xpx. Nu gi F(x, ) : F p , p 0 l l p h m c h

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