C3 Control Strategies

8/12/2019 C3 Control Strategies

1/59

2004,HONGMINHSN

Chng1

Chng1

13/09/2005

Chng2

Chng 3: Cc sch lc iu khini

u khi

n qu trnh


2/59

2

2004,HO

NGM

INH

SN

Chng 3: Cc sch lciu khin 2005 - HMS

HMS

Ni dung chng 3

3.1 Khi nim3.2 iu khin truyn thng

3.3 iu khin phn hi3.4 iu khin cascade3.5 iu khin t l3.6 iu khin la chn3.7 iu khin phn vng

3.8 Cc cu trciu khin h MIMO3.9 Thit kcu trciu khin h MIMO


3/59

3

2004,HO

NGM

INH

SN


HMS

Qu trnh

Nhiu d

Cc bin cniu khin y

Cc biniu khin u

Lu :u, r, y, d

l cc binca m hnh

chun ha G(s)

3.1 Khi ni

m

Bi toniu khin qu trnh: duy tr y r trong khi thayi gi tr t r c tcng ca nhiu d tn ti nhiuo n m hnh qu trnh khng chnh xc


4/59

4

2004,HO

NGM

INH

SN


HMS

nnh h thng Tc png nhanh v cht lngpng tt:

png vi thayi gi tr t png vi nhiu qu trnh t nhy cm vi nhiuo

Gi trbiniu khin thayi chm hoc thayi t

Bn vng: nnh bn vng Cht lng bn vng

Cc mctiuc th ca iu khin


5/59

5

2004,HO

NGM

INH

SN


HMS

Cc vn phc tp

Nhiu qu trnh phc tp, khiu khin (tngtc nhiu chiu, h pha khng cc tiu, gii hn

v gi trv tc thayi ca biniu khin,gii hn v phm vi thayi cho php ca binciu khin,...)

M hnh kh xy dng chnh xc Nhiu kho, kh bit trc Khnng thc thi, cit lutiu khin c gii

hn Trnh hiu bit ca ksvn hnh v l

thuytiu khin hn ch

...


6/59

6

2004,HO

NGM

INH

SN


HMS

Sch lc/cu trciu khin (control strategy/structure):nguyn tc vmt cu trc trong sdng thng tin vcc

bin qu trnh a ra tcngiu khin. Sch lciu khin

iu khin n bin hay a bin? Phi hp sdng cc bin vo no v nhthno iu

khin nhng bin ra no?

Qu trnh

Nhiu d

Cc binoc ym

Cc biniu khin u

Gi trt r

Sch lc iukhin


7/59

7

2004,HO

NGM

INH

SN


HMS

Cc sch lc iukhin c bn

H SISO: iu khin truyn thng (feedforward control) iu khin phn hi (feedback control)

iu khin tng (cascade control) iu khin t l (ratio control) iu khin la chn (selective control)

iu khin phn vng (split-range control) H MIMO:

iu khin tp trung (centralized control)

iu khin tch knh iu khin nhiu chiu iu khin phi tp trung (decentralized control) iu khin phn cp (hierarchical control)


8/59

8

2004,HO

NGM

INH

SN


HMS

3.2 iu khin truyn thng

V d iu khin qu trnh traoi nhit: iu chnh lu lng hi nng vo Fs duy tr nhit du

ra T2 ti gi tr t mong mun


9/59

9

2004,HO

NGM

INH

SN


HMS

Cu trc cbn

Nguyn l: Githit: M hnh chnh xc, nhiu o c o nhiu qu trnh d, tnh ton usao cho y r:

Khng thc hin o y

1

( )( ( ) )

( ) ( )

r d

r

u K s r G s d

K s G s

=

(3.1)


10/59

10

2004,HO

NGM

INH

SN


HMS

Phn tch cht lng

1

1

1

( ) ( )

( )

r

r d d

d d d

K G

u K r G d G r G d

y Gu G d GG r G d G d r

=

= = = + = + =

(3.2)

b) Sai lch m hnhi tng (gisd= 0):

(3.4)

a) iu khin l t ng

1( )

G G G

Gy G G G r r r

G

= +

= + = +

thc

(3.3)

c) Sai lch m hnh nhiu:

thc

( )

d d d

d d d d

G G G

y r G d G G d r G d

= +

= + + = +

sai lchiu khin


11/59

11

2004,HO

NGM

INH

SN


HMS

2 2 2 2d d dy Gu G d G d r G d= + + = +

d) Tn ti nhiu khng o c:

=> H mtn nh khi Gd2 khngn nh

sai lchiu khin(3.5)

e) M hnh cim khng nm na bn phi mt phng phc=> B iu khin l t ng khngn nh, cn xp x!

V d m hnhi tng:

B iu khin l t ng khngn nh => h mtnnh ni!

B iu khin xp x (cho trng thi xc lp):

1( )

1

sG s

s

=

+

1

1

1

( ) ( ) 1rs

K s G s s

+

= =

12 (0) 1rK G

= =


12/59

12

2004,HO

NGM

INH

SN


HMS


13/59

13

2004,HO

NGM

INH

SN


HMS

Phn tch cht lng (tip)

f) M hnh c thi gian tr hoc c bc mu s ln hn bc ts=> B iu khin l t ng khng c tnh nhn qu(non-causal)

V d m hnhi tng:

B iu khin l t ng khng c tnh nhn qu:

=> Ch thc hinc khi b tn hiu ch o bit trc, khngdng cho b nhiu, hoc phi xp xb iu khin

g) Qu trnh khngn nh: B iu khin l t ng trit tiuim cc

khngn nh => H thng khng c tnhn nh ni, ch cn cnhiuu vo r t nh c th lm cho h mtn nh

2

1( )

1

ssG s e

s s

+=

+21

( )1

sr

s sK s e

s

+=

+

( )u d uy G u d G d r Gd= + + = + (3.6)


14/59

14

2004,HO

NGM

INH

SN


HMS

V d: iukhin mc

Nguyn liu khin: Lu lng vo phi bng lu lng ra Vn : Ch cn sai s nh trong gi tro lu lng hoc

sai s nh trong m hnh van iu khin cng c th lm

trn bnh hoc cn bnh


15/59

15

2004,HO

NGM

INH

SN


HMS

Tm lc v iukhin truyn thng

uim: n gin Tcng nhanh (b nhiu kp thi trc khinh hng tiu

ra)

Hn ch: Phit thit bo nhiu Khng loi tr cnh hng ca nhiu khng o c Nhy cm vi sai lch m hnh (m hnh qu trnh v m hnh

nhiu) B iu khin l t ng c th khngn nh hoc khng thc

hinc => phng php xp x Khng c khnngn nh mt qu trnh khngn nh

ng dng chyu: Cc bi ton n gin, qu trnh pha cc tiu, yu cu cht

lng khng cao Kt hp vi K phn hi nhm ci thin tc png ca h

kn: B nhiu o c (chyu l b t nh), lc trc (tin xl)

tn hiu ch o iu khin t l (mc 3.5)


16/59

16

2004,HO

NGM

INH

SN


HMS

Cc bc thit kkhu b tnh

1. Xcnh bin cniu khin, chn biniu khin v cc binnhiu o c.

2. Xy dng m hnhi tng, vit cc phng trnh cn bng vtcht hoc/v phng trnh cn bng nng lngtrng thi xclp.

3. Thay thbinciu khin bng gi tr t, gii phng trnhcn bng cho biniu khin theo gi tr t v cc bin nhiu.

4. Phn tch vnh ginh hng ca sai lch m hnh ti chtlngiu khin.

5. Loi b cc ngun nhiu cnh hng khngng k tit kimchi pht cm bin.

6. Chnhnh li cc tham s ca khu truyn thng choim lmvic quan tm b li sai lch m hnh v cc ngun nhiuloi b.

7. B sung cc b iu khin phn hi trit tiu sai lch tnh, gimtcng ca sai lch m hnh v ca nhiu khng o c.


17/59

17

2004,HO

NGM

INH

SN


HMS

V d: iukhin qu trnh trao i nhit

B qua tn tht nhit, ta cphng trnh cn bng nnglng:

(3.7)

trong:

Cp nhit dung ca du h s nhit ta ra do qutrnh hi nc ngng t.

Thay thT2bng gi tr t (SP):

(3.8)

2 1( )o p sF C T T F =

1( )p

s o

CF F S P T

=


18/59

18

2004,HO

NGM

INH

SN


HMS

V d: iukhin qu trnh trn

Githit:- c1vc2 l hng s

- lu lng wra ty (tchy)

Phng trnh cn bng:

Thay thcbng gi tr t (SP):

1 1 2 2 1 2( )w c w c w w c+ = +

1 12

2

( )w S P cw

c S P

=

(3.9)

(3.10)


19/59

19

2004,HO

NGM

INH

SN


HMS

3.3 iu khin phn hi

V d: iu khin qu trnh trao i nhit

Nguyn liu khin: iu chnh lu lng hi nng (biniukhin) da trn sai lch gia nhit du ra (binc iukhin) v gi tr t (SP)

C


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20

2004,HO

NGM

INH

SN


HMS

Chiu tc ng ca b iu khin phn hi Tcng thun (direct acting, DA): u ra ca biu khin

tng khi bin c iu khin tng v ngc li Tc ng nghch (reverse acting, RA): u ra ca biu

khin gim khi bin c iu khin tng v ngc li

Sla chn chiu tc ng ph thuc: c im ca qu trnh: quan h gia bin iu khin v bin

c iu khin Kiu tc ng ca van iu khin (ch chiu mi tn trn k

hiu van iu khin): ng an ton (fail close, air-to-open), chiu tc ng thun Man ton (fail open, air-to-close), chiu tc ng nghch

Coi i tng iu khin = qu trnh + van iu khin => chiutc ng ph thuc vo du ca h s khuch i tnh ca itng

Trong v d: tc ng nghch Qu trnh: Hi nng nhiu -> nhit tng Van iu khin: ng an ton


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2004,HONGM

INH

SN


HMS

Cuhnhb iu khin phn hi

png vi gi tr t vpng vi nhiu c rng bucvi nhau => khng th thitk iu khinc lp honton theo mun

Thm khnng thit kbiu khin Kr(s) ci thin

png vi thayi gi tr t


22/59

22

2004,HONGM

INH

SN


HMS

Ti sao phi iu khin phn hi?

( ) dy GK r y n G d = +

(1 ) dGK y GKr G d GKn + = +

1 1 1d

dL G L

y r d n Tr G Sd Tn L L L

= + = + + + +

1

1 1 1d

d

G GKe r y r d n Sr G Sd Tn

GK GK GK = = + = +

+ + +

Xt cu hnh b iu khin mt bc tdo:

(3.11)

(3.12)

png h kn:

(3.13)

Sai lchiu khin:

(3.14)


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23

2004,HONGM

INH

SN


HMS

Vai tr ca iukhin phn hi

1. Mt qu trnh khng n nh ch c th n nh (ha) bngcch sdng mch phn hi nhm dch cc im cc sang

bn tri trc o ca mt phng phc (quan sta thc mu

s 1 + GKtrong 3.13 v 3.14)2. Khi nhiu khng o c hoc m hnh p ng nhiu bt

nh th tc ng ca n ch c th trit tiu thng quanguyn l phn hi:

3. M hnh i tng khng chnh xc, do vy vic trit tiu sai

lch tnh ch c th thng qua quan st din bin u ra:

1 01

dGGKGK

+

0, 1 0n GK e


24/59

24

2004,HONGM

INH

SN


HMS

Cc vn ca iu khin phn hi

Mt vng iu khin kn cha mt i tng n nh cngc th trnn mt n nh

iu khin phn hi cn b sung cc cm bin Nhiuo c th nh hng ln ti cht lngiu khin (

s hng cui cng trong biu thc 3.13 v 3.14) => cn cphng php lc nhiu, xl s liu o tt

Kh m c mt biu khin phn hi tt nu nhkhngc mt m hnh tt Vi mt s qu trnh c p ng ngc hoc c tr (h pha

khng cc tiu), mt biu khin phn hic thit k

thiu thn trng thm ch c th lm xu i c tnh png B iu khin phn hipng chm vi nhiu ti v thay

i gi tr t


25/59

25

2004,HONGM

INH

SN


HMS

Kt hp vi sch lc truyn thng V d iu khin mc:

Khu truyn thng: b nhiu Khu phn hi: nnh h thng v trit tiu sai lch tnh

3 4 i khi ( d )


26/59

26

2004,HONGM

INH

SN


HMS

3.4 iu khin tng (cascade)

t vn: Tc ng ca nhiu vi cc qu trnh chm (nhit ,mc v nng ) hoc c tr ln => cc vng iu chnh n khmang li tc p ng nhanh cng nh qu iu chnh nh.

V d tiu biu: Vi cng mvan, thay i p sut dngchy/dng hi nh hng ln ti lu lng

V d i khi b t i hit


27/59

27

2004,HONGM

INH

SN


HMS

V d iu khin bung trao i nhit

Gii php: Trit tiu smnh hng ca nhiu bng cch sdng mt vngiu chnh trong, sdng thm mt i lngo

H i t b


28/59

28

2004,HONGM

INH

SN


HMS

Hai cutrcc bn

Cu trc kinh in (cu trc ni tip): thm mt bino

Cu trc song song: thm mt biniu khin

Phn tch cht lng(cu trc kinh in)


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29

2004,HONGM

INH

SN


HMS

Phn tch cht lng(cu trc kinh in)

p ng h kn:

1 2 22 1 1 2 1 1 1 2 2 2

2 1 2 2 1 2

1 2 2 1 1 21 1 2

2 1 2 2 1 2 2 1 2

1 2 1 1 2 21 22 1 2 1 2 1

( ) , ,1 1

(1 )

1 1 1

(1 1 / ) /1 / 1 1 / 1 1 / 1

dd

d d

d d

K L Gy r G d d L K G L K GL L L L L L

L L L G G Gy r d d

L L L L L L L L L

L L G G G Lr d dL L L L L L

= + = =+ + + +

+= + +

+ + + + + +

+= + ++ + + + + +

Vi trong di tn quan tm (ca L1), ta c:2 1L

1 1 1 21 1 2

1 1 2 11 1 (1 )d dL G G G

y r d dL L L L + ++ + +

nh hng ca d2gimi nhiu!

(3.15)

(3.16)

Khi no s dng sch lc cascade?


30/59

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2004,HONGM

INH

SN


HMS

Khi no sdng sch lc cascade?

Vngiu khin phn hin khng pngc yu cucht lng

C th d dngo c viu khinc mt bin qu

trnh thhai (c lin quan ti bin thnht) Binc iu khin thhai th hin r rtnh hng ca

nhiu kh o c

C mt quan h

nhn qu

gi

a bi

n

iu khi

n v bi

nc iu khin thhai (c th cng l mt bin)

c tnhng hc ca bin thhai phi nhanh hn ctnhng hc ca bin thnht

3 5 iu khin t l (ratio control)


31/59

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2004,H

ONGM

INH

SN


HMS

3.5 iu khin t l (ratio control) iu khin t l l duy tr t l gia hai bin nhm iu khin gin tip

mt bin thba => thc cht l mt dng iu khin truyn thng. V d: iu khin qu trnh trao i nhit


32/59

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2004,H

ONGM

INH

SN


HMS

Hai cu trc thng dng

V d iu khin t l qu trnh trn (kt


33/59

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2004,H

ONGM

INH

SN


HMS

V d iu khin t l qu trnh trn (kthp vi phn hi)

3 6 iu khin la chn


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2004,H

ONGM

INH

SN


HMS

3.6 iu khin la chn

Sdng khu la chn tn hiu: Mt bin iu khin (mtthit b chp hnh)

La chn tn hiu o: iu khin gii hn (limit control)

Mt bin c iu khin Nhiu tn hiu o (o nhiu v tr khc nhau) Mt vng iu chnh

La chn tn hiu iu khin: iu khin ln t (overridecontrol) Hai (nhiu) binc iu khin, hai (nhiu) tn hiu o Hai (nhiu) vngiu chnh

=> m bo an ton

iu khin gii hn


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2004,H

ONGM

INH

SN


HMS

iu khin gii hn

Qu trnh

Khu la chn(max, min,...)

Cu hnh iu khin-

V d: iu khin nhit trong mt l phn ng

FC

100

TT

117

TT

116

TT

115

UC

101

Nc lnh

T

z

t

max

Biuchnh

iu khin ln t


36/59

36

2004,H

ONGM

INH

SN


HMS

Cu hnh iu khin

Qu trnh

BC 2

BC 1

-

-

V d: iu khin ni hiHi nc

LC

101

PC

100

FY

102

ng dng ca iukhin ln t


37/59

37

2004,H

ONGM

INH

SN


HMS

ng dng ca iukhin ln t

Trnh tnh trng trn trong mt thp chng ct bng cchhn chlu lng hi cp nhit hoc lu lng cp liu.

Phng nga tnh trng gi tr mc qu cao hoc qu thptrong mt bnh cha bng cch ginh quyn can thip mnhvo cc van iu chnh (van cp hoc van x).

Phng trnh p sut hoc nhit qu cao trong mt lphn ng bng cch gim lng nhit cp.

Gim lng nhin liu cp cho mt bung t nhm trnhtnh trng hm lng xy qu thp trong kh thi. Trnh trng hp p sut qu cao trong mt ng ng (hi

nc hoc kh) bng cch mvan trn ng trnh (by-pass).

3 7 iu khin phn vng


38/59

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2004,H

ONGM

INH

SN


HMS

3.7 iu khin phn vngSplit-Range-Controller Process+- Mt bin c iu khin

- Nhiu bin iu khin hocnhiu phn tchp hnh

-

V d: iu khin nhit bnh phn ng

mvan

100%TT100

TC100

Nc lnh

Hi nc

Tn hiu iu khin

3 8 Cc cu trc iu khin h MIMO


39/59

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2004,H

ONGM

INH

SN


HMS

3.8 Cc cu trc iu khin h MIMO

iu khin tp trung (centralized control), iu khin abin (multivariable control): Mt biu khin nhiu chiu (nhiu vo/nhiu ra)

Thit ktheo phng php tch knh hoc phng php thitka bin iu khin phi tp trung (decentralized control), iu khin

nhiu vng (multiloop control): Phn chia h thng thnh cc bi ton nh d gii quyt hn

(n bin hoc a bin) Thc hin bi nhiu biu khin c lp

iu khin phn cp (hierarchical control): Phn chia h thng thnh cc vng iu chnh cbn (iu

chnh tng phn,partial control) v cc vng iu chnh phihp (vng iu khin ch, master control)

Sdng ccc biu khin phn tn v cc biu khintp trung

iu khin tp trung


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2004,H

ONGM

INH

SN


HMS

iu khin tp trung

Qu trnh

B iu khin

SP

V d: iu khin bnhtrn Bin c iu khin:

mc v nng ra (c) Bin iu khin: lu

lng vo w1vw2

iu khin tp trung


41/59

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2004,H

ONGM

INH

SN


HMS

iu khin tp trung

V d: Thp chng cthai sn phm Bin cn iu khin:

nng sn phm

nh XDv y XB Bin c iu khin:

Nhit phn tinhct v phn chng

luyn ca thp Bin iu khin: lu

lng hi lu v nhitlng cp

TT

100

TT

101

XD

XB

Hi lu

Nhit cp

Cp liu UYC102

iu khin phi tp trung


42/59

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2004,H

ONGM

INH

SN


HMS


K 3

SP1

K 2

K 1

Qu trnh

SP2

SP3

nh nghaHthng iu khin bao gm

nhiu b iu khin phn hiclp, mi b lin kt mt tp con(khng chia s) cc binu ra ( oc) v gi tr t vi mt tp concc biniu khin.



43/59

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2004,H

ONGM

INH

SN


HMS


TC100

TC

101

XD

XB

Hi lu

Cp liu

Nhit cp

V d: Thp chng cthai sn phm Bin cn iu khin:

nng sn phm

nh XDv y XB Bin c iu khin:

Nhit phn tinhct v phn chng

luyn ca thp Bin iu khin: lu

lng hi lu v nhitlng cp

So snh


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2004,H

ONGM

INH

SN


HMS

iu khin tp trung:+ Cht lng cao (nu m hnh chnh xc)+ Nhiu phng php v cng c thit khin i Xy dng m hnh qu trnh phc tp Thc hin gii php iu khin s phc tp (thiu thvin khi

c sn, chu ktrch mu khc nhau,...) Kh theo dii vi ngi sdng => kh chp nhn tin cy khng cao

iu khin phi tp trung:+ Phng php truyn thng trong cng nghip+ D theo di+ D chnhnh cc tham s iu khin m khng cn m hnh

qu trnh chnh xc+ tin cy cao Thit ksch lc iu khin phc tp (v dvic cp i

vo/ra)

Cht lng thp, khng phi bao gicng thc hin c

3.9 Thit kcu trc phi tp trung


45/59

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2004,H

ONGM

INH

SN


HMS

p p g Cc bc thit k:

La chn cc bin iu khin, cc bin c iu khin v ccbin o

Cp i cc bin iu khin v cc bin c iu khin p dng cc sch lc iu khin cho h SISO

Cc vn t ra: Khi no c thiu khin phi tp trung?

nh gi mc tng tc gia cc knh iu khin nh gi cht lng iu khin c tht c (mc kh

d ca bi ton) Vn la chn cp i bin vo/ra

Mi bin iu khin nh hng khc nhau ti bin c iukhin => chn cp vo/ra c slin kt mnh nht

Trng hp n gin => c tha ra kt lun thng quaphn tch qu trnh vt l

Slng vo/ra ln => s khnng cp i rt ln, cn mtphng php c tnh h thng

Vn nh gi cht lng v tnh n nh ton h thng

3.9.1 Ma trn h s tng tc (RGA)


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2004,H

ONGM

INH

S

N


HMS

3.9.1 Ma trn h stng tc (RGA) Khi nim RGA (Relative Gain Array):

Bristol a ra nm 1966 (AC-11) => ch snh gi mc tng tc gia cc knh vo/ra trong mt h MIMO

Phc v la chn v cp i cc bin vo/ra trong xy dngcu hnh iu khin phi tp trung

C nhiu tnh cht rt hay khc trong nh gi tnh n nh vcht lng ca hiu khin phi tp trung

RGA ca mt ma trn s phc vung mx mkhng suy bin

l mt ma trn s phc vung mx m:

vi k hiu x l php nhn tng phn t(tch Schur, tchHadamard)

V d:

1RGA( ) ( ) ( )TG G G G (3.17)

11 2 0 .4 0 .2 0 .4 0 .6, , ( )3 4 0 .3 0 .1 0 .6 0 .4

G G G = = =

Din gii ngha ma trn RGA qua v d 2x2


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2004,H

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INH

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HMS

Xt h 2x2 trng thi xc lp (s = 0):

1 1 1 2

2 1 2 2

1 1 1 2 1 1 1 1

1 12 1 2 2 1 1 1 1 1 2 2 1 1 1 2 2

(0)

1 1( ) ,

1 1 /

g gG

g g

Gg g g g

=

= = =

(3.19)

=

= 2

1 1 1 10u

y g u

Khi u2 = 0:

Khi u20 giy2=0:

=

= = 2

1 2 2 11 1 1 1 1 1 1 1 1 1 1 10

2 2

( / ) ( )y

g gy g u g u g u

g

(3.20)

(3.21)

Tcng gin tip1 2

1 1 1 2 2 12 1

01 0

0

gg g

gNu

=> Khng c tng tc hai chiu, d iu khin phi tp trung

== =

=

Tng qut ha cho h m n


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11 12 1

21 22

1

( ) ( ) ( )

( ) ( )( ) ( )( )

( ) ( )

m

m m m

g s g s g s

g s g sy s G su s

g s g s

= =

Xt nhy gia bin vo ujv bin ra yica mt vng iuchnh vi hai trng hp:- Khng c cc u vo khc, tc

- C cc u vo khc sao cho ccu ra khcc gic nh, tc

H s t l gia hai gi tr th hin mc lin kt giaujvyi :

0,

[ ]

k

iij ij

ju k j

yg G

u =

=

0,ky k i=

0,ku k j=

1

0,

1/[ ]

k

iij ji

jy k i

yg G

u

=

=

1 1

/ ( ) ( )[ ] [ ]

T

ij ij ij ij jig g G G G G G

=

=

(3.18)

Mt stnh cht ca ma trn RGA


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49

2004,H

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INH

S

N


HMS

Tng cc phn tca mt hng hoc mt ct = 1

Ma trn RGA khng ph thuc vo vic chnh thang (chun ha

m hnh):

Honi hai hng (hai ct) ca G dn ti honi hai hng (haict) ca (G)

(G) l mt ma trn n v nuG l ma trn tam gic trn hocdi (tng tc mt chiu)

G(s) l mt ma trn hm truyn th(G(j))c tnh ton tng

ng vi tng tn s trong di tn quan tm

SRGA l mt ch s cho mc tng tc

ca qu trnh (quan trng nht l xung quanh tn s ct)

1 .0ij iji j

= =

1 2 1 1 2 2( ) ( ), d iag( ), d iag( )i iG D GD D d D d = = =

sum( ) ij

i j

G I g

=

Phng php cp i vo/ra da trn RGA


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Lut 1: Cpi vo/ra (j,i) tngng vi phn t ij c gi tr

gn 1 xung quanh tn s ct mong mun ca h kn, u tins ln hn 1 Di tn m ij 1 cng rng cng tt Trong trng hp n gin c th chn hm truyntrng thi

xc lp (s=0) Lut 2: Trnh chn ij


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2004,H

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HMS

Vi qu trnhG(s)n nh

1. Nu mi vng n n nh khi cc vng khc hmch v matrn(G) = I th ton h cngn nh => Chn cpi saocho(G) Ixung quanh tn s ct

2. Nu cc b iu khin sdng tcng tch phn v cpitngng vi phn tca(G(0)) c gi tr m th:

Ton h mtn nh, hoc

Vng n tngng mtn nh, hoc

Ton h mtn nh khi vng n tngng hmch

3. Nu b iu khin phn hi isdng tcng tch phn vn nh khi cc vng khc hmch, v ch s Niederlinski

th vngiu khin i s mtn nh. Vi n=2 thiu kin

trn l cn v .

1

det (0) 0

(0)n

ii

i

GNI

g=

= thc o khong cch gnhay xa vi "ssuy bin" caAXt chun bc 2 caA:

Din gii ngha:

Vi vector u vo x, ma trnAnh xsang y = Axvi h s khuchi ln nht l v h s khuchi nh nht l H s khuchi ph thuc vo chiu ca vector x

2

2

2

2

20 12

2

20 12

m ax ( ) m ax ( ) ( )

( ) m ax m ax

( ) m in m in

H

i ii i

x x

x x

A A A A

AxA Ax

x

AxA Ax

x

=

=

= =

= =

= =

(3.24)

(3.25)

(3.26)

/

Php phn tch SVD v sph thuc chiu


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HMS

Php phn tch SVD

Nhn tl thuyt h thng, nu coiG(j) l ma trnAvx

l vector tn hiu vo ta s c th a ra mt s din giitng tvi su hn: Cc vector u vo xc chiu trng vi ctu tin caVs

c khuchi nhiu nht => kt qul vector yc chiu

trng vi ctu caU Cc vector u vo xc chiu trng vi ct cui caVs ckhuchi t nht => kt qul vector yc chiu trng vi ctcui caU

(3.27)

1

1 2

1 1

, ,

... , m in( , ), ,

T T T T

k

k

k k

A U V U V U U I V V I

k m nAV U Av u Av u

= = = =

= = =

= = = (3.28)

La chn bin c iukhin


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2004,H

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INH

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N


HMS

V d: chn nhit khay no trong thp chng ct lm binciu khin? (cc biniu khin l lu lng hi lu L vcng sut nhit cp Q)

Theo ch dn tchng 2: La chn binu ra chunh hngmnh nht di tcng ca biniu khin => tngng vi

phn tc gi tr ln nht trong mi ct ca U

9 0.00773271 0.0134723

8 0.2399404 0.2378752

7 2.5041590 2.4223120

6 5.9972530 5.7837800

5 1.6773120 1.6581630

4 0.0217166 0.0259478

3 0.1976678 0.1586702

2 0.1289912 0.1068900

1 0.0646059 0.0538632

Khay T/L T/Q

0.0015968 0.0828981

0.0361514 0.0835548

0.3728142 0.0391486

0.8915611 0.1473784

0.2523673 0.6482796

0.0002581 0.6482796

0.0270092 0.4463671

0.0178741 0.2450451

0.0089766 0.1182182

U

=

0.7191691 0.6948426

0.6948426 0.7191691

TV

=

9.3452 0

0 0.052061

=

Khay th6

S iu kin (condition number) k ( d b )


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HMS

S iu kin (condition number):

Trongi s tuyn tnh, cond(A) ni ln "snhy cm" ca hvisai s trongAhoc trong y, tc khnng tm nghimAx = bmt

cch chnh xc, cond(A) cng ln cng bt li.V d:

NuA12 thayi t0 sang 0.1 s dn tiAsuy bin

Trong l thuyt h thng, cond(G(j)) lin quan nhiu ti khnngiu khin, gii hn cht lngiu khin

S iu kin cng ln th h cng nhy cm vi sai lch tham s mhnh

S iu kin lin quan ti cc ch tiu cht lng (min tn s) c thtc

S iu kin c ph thuc vo cch chnh thang/chun ha m hnh!

(3.29)cond( ) ( ) /A A = =

1 0

10 1

=

A

10.1 0( ) = , cond( ) = 101

0 0.1

A A

Lu : Sph thuc tn s


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2004,HONGM

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N


HMS

V d: M hnh thp chng ct hai sn phm

Loi bt sbin vo/ra


59/59

59

2004,HONGM

INH

S

N


HMS

Da theo (Seborg et. al., 2000): Sau khi chun ha m hnh, phn tch SVD v sp xp cc gi

tr suy bin theo thtnh dn, c th loi bt mt s uvo/ra nu

V d:1 /10i i + C th cn nhc loi bt mt cp vo/ra (u3vy1 hoc y2)

Documents

C3 Control Strategies