sổ tay cdt chuong 33-dk nang cao thuy luc

8/6/2019 s tay cdt Chuong 33-Dk Nang Cao Thuy Luc

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33iu khin nng cao cho mt trc thu lc in t

Florin IonescuUniversity of Applied Sciences

Crina VladPoliteknica University of Bucharest

Dragos ArotariteiAalborg University Esbjerg

33.1 Gii thiu chung ...........................................................1

33.2 Tng quan v ROBI_3, robot -cac-t (Cartessian robot) vi ba trcthu lc in t .................................................................. ........2

33.3 M hnh ton hc v m phng cc trc thy lc in t ..........................3

33.4 iu khin trc thu lc in t dng cc b iu khin truyn thng .... .7

33.5 iu khin trc thu lc in t vi b iu khin m 11

33.6 iu khin trc thu lc in t dng k thut n ron 1233.7 iu khin trc thu lc in t dng k thut m-n ron ......................14

33.8 Phn mm ...................................................................19

33.9 Kt lun .............................................................. .......20

33.1 Gii thiu chung

Do s pht trin ca cng ngh trong nhng nm gn y, robot c xem nh l mt h thng c in cao cp, n yucu nhng kin thc v c hc, c cu chp hnh v iu khin thc hin cc nhim v rt phc tp. Nhiu loi h thngservo khc nhau, c bit l thy lc in t c bit n trong cc cp chp hnh ca robot. lm r cho hng iu

khin nng cao, chng ny s cp n vic thc hin nhng b iu khin nng cao bn cnh b iu khin truyn thngci c s dng trong h thng thu lc in t. H thu lc in t c xt y l mt trong nhng trc ca robot.Nhng robot ny c ba trc thu lc in t tr ln chng ging ht nh trc c nghin cu trong chng ny.

Mt trc thu lc in t c m hnh ton hc c miu t trong chng ny c tnh phi tuyn. Nhng b iu khintruyn thng ngy cng tr ln khng ph hp iu khin nhng h thng vi m hnh khng r, s phi tuyn chin ra. Do vy k thut iu khin nng cao nh mng n ron v thut ton m cn c s dng trong vic iu khinnhng h thng ny. Mng n ron c xut u tin bi McCulloch v Pitts, Rosenblantt, Widrow, c nhiu s gii hnlm hn ch phm vi ng dng ca chng. Mt s thay i quan trng din ra nhng trong nm 1980 khi l thuyt caHopfield v mng n ron hi qui c quan tm, mt m hnh t t chc c pht trin bi Kohonen, v nhng mng nron t bo c bt u tr li trong lnh vc nghin cu ny. S pht trin ca nhng thut ton c hiu qu em li nhngcng hin c th v thnh tu ca mng n ron v ng dng ca mng n ron trong iu khin th hin mt phm vi quantm nghin cu trong th gii khoa hc ngy nay.

H thng m, kt hp vi mng n ron gi mt v tr quan trng trong k thut iu khin nng cao. H thng ny cngun gc t l thuyt v tp m c bt u bi L.Zadeh. Mt c im ch yu ca h thng m l s suy lun logic,trong cc bin c miu t thuc mt loi phm cht no . Do nhng kh nng ca h thng m x l nhng thngtin khng chnh xc, chng c xut miu t s hiu bit dng lut ngn ng. Trong cch ny, s hiu bit v hotng ca con ngi l dng ngn ng hoc s c s dng a ra cc tp m qui lut if-then nh l c s cho b iukhin m. Mt mt hn ch chnh ca h thng m l s kh khn thit k chng trn c s mt phng php nghin cuc h thng. khc phc mt hn ch ny, mt th tc hc t mng n ron c ng dng thnh cng iu chnh thams ca hm lin thuc.

S kt hp ca hai lnh vc ny to ra mt s ni bt ca h thng m-n ron, nhng ci c ng dng mang li ktqu y ha hn trong lnh vc iu khin. ci tin tnh linh hot v s th hin tnh ca h thng c c tnh phi tuyn vkhng r, b iu khin m-n ron c s dng.

S phn b ni dng ca chng ny c t chc nh sau. Phn gii thiu v h thng thu lc in t cng vi s nhnmnh v iu khin trn cc thit b c thc hin trong phn 33.2. Phn 33.3 a ra m hnh ton hc ca trc thu lc

in t, v phn tip theo xt vic iu khin cc trc thu lc in t thng qua cc phng php truyn thng. (phn 33.4),h thng m (phn 33.5), mng n ron (33.6), k thut m n ron (phn 33.7). Phn kt lun c a ra phn 33.8.

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S tay C in t

33.2 Tng quan v ROBI_3, robot -cac-t (Cartessian robot) vi ba trc thu lc int

H thng t ng, ci m s dng cc trc thu lc in t c m hnh ton hc c miu t trong phn 33.3 l mtrobot e-cac-t tn l ROBI_3. ROBI_3 c ba trc thu lc in t ging nhau v c lm t nhm [24]. B phn trtc khi ng bi mt c cu chp hnh thy lc. B phn trt di chuyn trong mt ng dn tuyn tnh vi nhng qucu v hai qu o trn khp kn. H thng cung cp nc c t bn di bn robot v c mt h thng iu khin v lm

mt bng kh. Cu trc c kh ca robot c miu t trn hnh 33.1 C ba trc ca ROBI_3 c iu khin ging nhaubng phn mm iu khin c tn l TORCH c chy trn Windows. Phn cng iu khin dSPACE 32 bt c cung cp10 giao din A/D v D/A cm vo my tnh PC v cung cp giao din gia my tnh PC v mi trc.

Trc thu lc in t gm c mt xylanh thy lc v mt van servo (servovalve) v c cu trc tuyn tnh. H thng iukhin ca mt trc gm c:

1. B iu khin l my tnh c nhn c cung cp mt card x l.

2. B bin i thy - in

3. C cu chp hnh (ng c servo thy lc tuyn tnh (linear hydraulic servomotor LHM))

4. Qu trnh c hc c iu khin v c trng bi v tr b phn trt.

5. B chuyn i v tr.

H thng iu khin ca robot ROBI_3 c minh ha trn hnh 33.2, trn miu t ba trc thu lc in t cng vi

cu trc ca tng trc, c th thy cc trc l hon ton ging nhau..M hnh ton hc tng ng cho mi trc, thc hin da trn c s iu khin robot, c miu t trong phn 33.3. Mc

d m phng 3 trc ca robot l m phng s nhng d liu giao din v cu trc c kh cn thit t c.

Qu trnh th nghim s b vi cc bin iu khin: v tr v vn tc c to ra lm thc nghim (hnh 33.2 v 33.3).Biu ca mt h kn iu khin v tr cng vi php o trc tip (c iu chnh bi gi tr trung bnh ca van servo)c th hin trn hnh 33.3 v h kn iu khin v tr vi php o trc tip ti trc quay (c thc hin bng mt vanservo) c th hin trn hnh 33.4.

Hnh 33.1 Robot ROBI_3 vi ba trc quay [21]. (a) Thit k; (b) sn phm c th

Hnh 33.2 H thng iu khin ca robot[21,24]

Hnh 33.3 S ca mt h kn iu khin v tr viphp o trc tip

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iu khin nng cao cho mt trc thu lc in tMt s iu chnh t l th tch Q vi p sut P l hng s (Q thay i, P khng i) c th hin trn hnh 33.5. Mc d,

y l mt m hnh c in, nhng rt c ch trong ng dng, ch c s dng s b a n m phng. Mt trong nhngl do chnh cho vic s dng phng php ny l v chng ta cn mt m hnh ton hc tt vi mt thi nghin cu tt kim tra b iu khin (n ron hoc m n ron).

Hnh 33.4 H kn iu khin v tr vi php o trc tip

Hnh 35.5 iu chnh t l th tch Q vi p sut khng i

33.3 M hnh ton hc v m phng cc trc thy lc in t

Phn 33.3 thc hin vic phn tch tm ra m hnh ton hc (Mathematical Model-MM) ca cc trc thu lc in t,cc phn cu thnh robot ROBI_3. Phng php phn tch ny c thun li v n a ra mt kh nng s dng m hnh tonhc ny cho nhng trc thu lc in t khc, khng quan tm n s b (stage) v cng cho php kim tra th hin nglc hc ca trc trong mt cp thit k.

Trong phn ny, cc vn sau y c thc hin:1. M hnh tnh ca cc thnh phn h thng thu lc in t (van servo, ng c tuyn tnh thu lc)

2. Nhng tham s i hi trong MM, da trn c tnh ch lu lng v cu trc.

3. M hnh ton hc phi tuyn ca mt h thng thu lc in t c xut.

4. Xy dng s cu trc mt trc thu lc m phng cch hot ng ca chng (SIMULINK).

5. Kho st v MM, m bo s n nh ca h thng, v thc t l to ra mt qu trnh n nh nhanh.

Gi tr ca cc tham s c miu t trong MM l mt tp hp da trn c tnh thu lc v tham s cu trc ca h thngc xt.

M hnh ton hc m rng

H thng c nghin cu gm c mt van servo v mt ng c i xng. Trong hu ht trng hp, vic iu khincc trc thu lc in t l iu khin trc tip nhm mc ch iu khin v tr, iu khin vn tc, iu khin p sut hociu khin lc. y chng ta s nghin cu iu khin v tr. iu khin v tr cho h thng xut c minh ho trnhnh 33.6, cng vi tn gi cc dng d liu.

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S tay C in t

Hnh 33.6 S iu khin ca mt h thng servo

M hnh ton hc phi tuyn ca van servo

Nh cp phn trc, van servo s dng cho trc thu lc in t c xut c bn qu o v ba v tr. Vanservo c bn nh iu khin tch cc ti b nc th hai. Ba b c th phn bit vi nhau bi nhng van ny: van thu -c, van in - c v van c - thu (mechanohydraulical). Xt trong h thng ta thy van servo th phc tp vi cc dng phituyn khc nhau c hin ra. S phi tuyn ng v tnh khc nhau nh min cht, nhy qua gc (jump in origin), s boho, cc c im Coulombian v Newtonian vi s tr, v s xut hin i xng trong ba mc ny v cng trong c cuchp hnh ca ng c thu lc in t. Nhng im ny c a vo miu t trong m hnh ca van v cch hot ng caxylanh.

i vi cc van c nghin cu, lu lng cht lng c xem l trc tip t cc bm ti khoang cha A(Q A), v tkhoang cha B ti ngun cp QB. Hnh 33.6 Th hin mt vng iu khin s chuyn i c t trn mt ng phnhi, v mt b iu khin R, v b khuch i A trn mt qu o trc tip. Tn hiu in 10V hoc 300mA c bin

i thnh dch chuyn xv ca van, v cng bng cch ny lu lng Q c truyn ti ng c thu lc tuyn tnh.T quan im v c tnh iu khin, s nh tch cc c xem nh l mt phng php phn loi cc van trt [3]. Mt

van servo vi bn nh iu khin tch cc c xt. Mt m hnh ton hc n gin miu t chc nng ca van c phngtrnh nh sau:

( )( ) ( )

d tu t L R i t

dt= + (33.1)

Trong L(H), l t cm cun dy in, R[W], l in tr dy dn, u(t) [V] l in p iu khin, i(t) [A] l cng dng in.

( ) ( ) ( )v v vm x t d x t c x t F + + = (33.2)

Trong m[kg] l khi lng ca van, d[N/(m)/s], l dc tuyn tnh ho ca ma st cht lng i vi piston ca van;c[N/m], h s n hi ca cht lng; xv [m] l s dch chuyn ca ng cun; [N]F , lc sinh ra, c thc hin trn ngvan.

Hnh 33.7 M hnh ton hc phi tuyn bc nht ca van servo

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iu khin nng cao cho mt trc thu lc in t

2

0 0

* 2 *

0 0

( ) 2 ( ) ( )

( ) 2 ( ) ( ),

v v v v v v

v v v v v v

Fx t D x t x t

m

Fx t k D x t x t k

m

+ + =

= =

&& &

&& &

(33.3)

dch chuyn xv t c da trn nhng phng trnh trn, c thc hin trn SIMULINK s dng s khi trnhnh 33.7. Module ca m hnh ton hc ny bao gm hai tng ca trc thu lc in t: tng thu - in v tng thu - c.

Cc phng trnh trnh tng ng vi bn lu lng i qua van servo l

0 0 max

0 max 0

0 max 0

0 0 max

2( ( )) ( ), [ , ]

2( ( )) ( ) , [ , ]

2( ( )) ( ), [ , ]

2( ( )) ( ) , [ , ]

PA D v v p A v

AT D v v A T v

PB D v v p B v

BT D v v B T v

Q D x x t p p t x x x

Q D x x t p t p x x x

Q D x x t p p t x x x

Q D x x t p t p x x x

= +

=

=

= +

(33.4)

Trong QPA [m3/s], l lu lng ti ng c thu, t bm ti khoang cha A ca ng c; Q AT [m3/s], l lu lng tkhoang cha A ti ngun; QPB [m3/s], l lu lng t bm ti khoang cha B ca ng c; QBT [m3/s], l lu lng t khoangcha B ti ngun; [-]D , l h s x; Dv [m], l ng knh ca ng; x0 [m], l kch c ca lng ng; xv [m] l dchchuyn ca ng; pA [N/m], l p sut cht lng trong khoang A; pB [N/m], l p sut cht lng trong khoang B, [kg/m3] ttrng cht lng. Lu lng truyn ti LHM v i ra l QA v QB c tnh nh sau:

, A PA AT B BT PBQ Q Q Q Q Q= = (33.5)

Lng ca ng c coi nh l bng khng (x0=0), v do vy c tnh tnh l tuyn tnh gn vi gc v cng trong phncn li (also in the rest). Phng trnh lu lng tr thnh

0 0

0 0

, ( )

( ) ,

PA v p A AT v A T

PB v p B BT v B T

Q Q x p p Q Q x p p

Q Q x p p Q Q x p p

= =

= = (33.6)

M hnh ton hc phi tuyn ca ng c thu lc tuyn tnh

Cc phng trnh vi phn trn c s m hnh ton hc ca ng c thu lc tuyn tnh (LHM) c thc hin l:

i. Phng trnh cn bng ng hc ca lc c n gin ti tay n ca ng c, v

ii. Phng trnh dch chuyn v s lin tc ca lu lng.

Hnh 33.8Nguyn tc DAlembert c p dng cho xylanh

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S tay C in t

Hnh 33.9Nguyn tc DAlembert c p dng cho tay n, piston v ti

To m hnh LHM, nhiu dng n gin (phn ln lin quan n ma st Coulombian v Newtonian) c s dng.Nhng lc tc dng ln xylanh ca LHM c miu t trn hnh 33.8.

p dng nguyn tcDAlembert, phng trnh cn bng ng hc ca lc cho xylanh ca LHM l

1 1 2 1 1 2 2 2

2

2

( ) ( ) sgn( ) ( ) B R A k fu z p A p A c x x d x x c N x x d x xxm s

+ + + + =

& & & & & && (33.7)

trong c1 [N/m], n hi; d1 [N/(m/s)], h s tuyn tnh ho ca ma st cht lng (nht) Newtonian trong thnh v xylanhca c cu chp hnh kt ni. c fu [-], h s ma st kh Coulombian trong xylanh v cnh tay n; d z [N/(m/s)], h s ma stNewtonian trong piston v cnh tay n; m2 [kg], khi lng ca xylanh; pA [N/m2], p sut cht lng trong khoang cha ivo A; pB [N/m2], p sut cht lng trong khoang cha i ra B ca c cu chp hnh. A k[m2], phm vi hot ng ca pistontrong khoang cha A; AR [m2], phm vi hot ng ca piston trong khoang cha B; N [N], lc chun xc nh lc ma stgia piston v xylanh; x [m], dch chuyn ca piston; x 1 [m], dch chuyn ca thnh, x2 [m2], dch chuyn caxylanh.

Nhng lc tc dng ln cnh tay n, piston v nguyn l lm vic c minh ho trn hnh 33.9.

Vn tc tng ng vi tay n, piston v khi lng m 3 (thanh trt, ng dn v ti c xem nh l ng cht cng)c suy ra t phng trnh cn bng.

2 2 3 3 1 3 1

3

sgn( ) ( ) sgn( ) ( )( )

A K B R L fu z fu

p T

p A p A F c N x x d x x c N x x d x xxm m m s

=+ +

& & & & & & & &&

(33.8)

trong mp [kg], khi lng ca piston; mT [kg], khi lng ca tay n; m3 [kg], khi lng ca ti (c lm gim ti tayn ca piston); cfu3 [-], h s ma st Coulombian gia ng dn v thanh trt (slade); N3 [N], lc chun gia ti v bn; FL[N], lc ca ti.

Hnh 33.10 Trc thu lc in t c thc hin trn SIMULINK

T nhng phng trnh tng ng, p sut pA v pB c tm ra l

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2 11

0 2

[ ( ) ( )]( )

ers A A K A B

K K

Ep Q A x x a p p

V A x x=

+ & & & (33.9)

2 11 12 0

0 2

[ ( ) ( ) ( ) ]( ) ( )

ers B R A B B B

R R R

Ep A x x a p p a p p Q

V A h A x x= +

+ & & & (33.10)

trong a11, a12 [(N/m2)/(m3/s)], dc ca khe h; V0K,0R [m3], th tch trung bnh ban u tng ng vi khoang cha A vB; Eers [N/m2], sut tng ng ca du (equivalent bulk modulous of oil); p A,B [N/m2], p sut cht lng tng ng trong

khoang cha A v B; v h [m], gp ca tay n piston (the stroke of piston-rod).S hot ng ca LHM da trn nhng phng trnh miu t, (33.7)-(33.10). M hnh ton hc c xut trongphn ny c thc hin trn SIMULINK 2.1/MATLAB 5.1 v c cu trc c miu t trn hnh 33.10.

Biu tng my pht tn hiu t hnh trn pht ra dch chuyn ca thnh x1 c dng hnh sin vi tn s 0.5 Hz v bin 0.0001 m.

Cc h con Ssys1 v Ssys2 c u ra l dch chuyn ca van v lu lng Q A, QB tng ng. Sys3 l mt khi thchin phng trnh 33.9 v h con Ssys4 to m hnh cho phng trnh 33.10. Nhng phng trnh miu t dch chuynca xylanh (wall cylinder) v piston LHM c to m hnh bi h thng ph Ssys5. Tn hiu u vo l step c di gi trtrong khong 0-10V.

33.4 iu khin trc thu lc in t dng cc b iu khin truyn thng

Phn ny c t chc nh sau: phn u tin trnh by nhng nghin cu lin quan n hng truyn thng ca h iukhin, phn th hai bao gm nhng nghin cu v cu trc iu khin c in (PID v cc thut ton iu khin vi b quanst Luenberger) thng qua vic m phng cc trc thu lc in t s dng cc b iu khin ny.

S nghin cu cc m hnh ton hc c thc hin cng vi SIMULIMK v vi mc ch t c cc kt qu thcnghim so snh cc b iu khin c in v cu trc iu khin nng cao c p dng i vi cc trc thu lc in t.

PID, PI, PD vi b lc

Cu trc iu khin truyn thng c s dng trong chng ny l PI (Proportional-Integral), PID (Proportional-Integral-Derivative), v PD (Proportional-Derivative) cng vi h s lc.

Hm truyn ca b iu khin PI l

1( ) 11

( )

T sU s iH K K PI R Rs T sT s ii

+= = + =

(33.11)

KR l h s t l, Ti l hng s thi gian ca thnh phn tch phn.

Hm truyn tng ng vi b iu khin PID c miu t bi phng trnh sau

2 1( ) 11

( )i d i

PID R d R

i i

T T s T sU sH K T s K

s T s T s

+ += = + + =

(33.12)

KR v Ti c cng ngha nh trn, Td l hng s thi gian ca thnh phn vi phn.

Hm truyn ca b iu khin PD vi b lc l

1( )( )

( ) 1d

PDF R

d

T sU sH s K

s T s

+ = =

+ (33.13)

Trong h s c th c gi tr trong khong 0.1-0.125

Ni chung, b iu khin PID c s dng rng ri trong cc h thng iu khin cng nghip, v do vy c cng cvng chc. Tuy nhin, nhng kt qu t c khi s dng b iu khin PID cho cc vng iu khin phc tp th khngthc s tho mn bi v n tn qu nhiu thi gian chnh li b iu chnh. B iu khin PI th ph hp trong cc tnhhung hot ng vi phn khng c s dng thng xuyn.

B quan st trng thi

L thuyt v quan st c bt u bi Luenberger v Ackermann th kh y v hon thin. i vi trc c xt bcca b quan st l (n-m-1) , trong n=5 th hin bc ca h thng v m=1 l s u ra [25]. M hnh iu khin servo cmiu t bi nm bin trng thi: hai trong cho m hnh bc hai ca van servo v ba bin cn li cho c cu chp hnhservo bc ba. S dng b quan st tuyn tnh nh mt m hnh song song t chc li cc bin trng thi ca h thng v

phn phi chng ti b iu khin. Hai kh nng c th sau y: t chc li mt phn hoc ton b. Gii php c chn l tchc li mt phn [12]. H thng hon thin gm c mt h thng vi tnh cht phi tuyn, m hnh bc hai song song cho vanservo, ng c servo tuyn tnh bc ba, mt ma trn hiu chnh cho b quan st v mt b iu khin vi nm vng lp chonm bin trng thi [23,25,26].

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S tay C in t

S khi ca trc thu lc in t c iu khin vi b quan st bc ba th hin trn hnh 33.11, A, b, cT l matrn c trng ca h tuyn tnh (trc thu lc in t), kl ma trn hiu chnh v Rth hin ma trn tng ng ca b iukhin.

S m phng trc thu lc in t c iu khin bi b quan st bc ba nh trong SIMULINK c minh ho trnhnh 33.12

Thut ton c s dng tnh ton ma trn kv r gm c cc bc sau:

i. Hon thin m hnh ton hc cho van servo v c cu chp hnh servo;

ii. Thit lp cc bin trng thi ca qu trnh;

iii. t c b iu khin nh vo ng hc ca h kn;

iv. Tnh ton ma trn hiu chnh bng cch s dng cc im cc mong mun cho b quan st [12].

Hnh 33.11 S khi ca vng iu khin s dng b quan st

Hnh 33.12 Cu trc iu khin cng vi b quan st cho trc thu lc in t s dng SIMULINK

M hnh ton hc tuyn tnh (LMM)

M hnh ton hc tuyn tnh ca van servo v c cu chp hnh servo t c bng cch s dng cc hm truyn xp xHSV, HZ:

2

2 2

( )( )

( ) 2V V V

SV

V V V V

Q s kH s

I s s D s

= =

+ +(33.14)

2

2 2

( )( )

( ) ( 2 )V ZZ

Z

V Z Z Z

kY sH s

Q s s D s s

= =

+ +(33.15)

vi ngha sau y: Qv, lu lng ca van servo; Iv, cng dng in; YZ, v tr ca tay n.

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iu khin nng cao cho mt trc thu lc in tM hnh ton hc tuyn tnh trong khng gian trng thi

Cc bin c s dng l: x1, v tr ca tay n; x2, vn tc ca tay n; x3, gia tc ca tay n; x4, v tr ca ng cun vx5, vn tc ca ng cun.

1 2 2 3 4 5

2 2

3 2 3 4

2 2

5 4 5

( ), ( ), ( )

( ) 2 ( ) ( )

( ) 2 ( ) ( ) Z Z Z Z Z

V V V V V

x x t x x t x x t

x x t D x t k x t

x x t D x t k u t

= = =

= +

= +

& & &

&

&

(33.16)

V vy m hnh ton hc ca trc trong dng khng gian trng thi tr thnh

( ) ( ) ( )x t Ax t bu t = +& (33.17)

( ) ( )Ty t c x t =

2

2

0 1 0 0 0 00 0 1 0 0 0

0 2 0 , 0 (1 0 0 0 0)

00 0 0 0 1

0 0 0 2

T

Z Z Z Z

VV V V

A D k b c

kD

= = =

(33.18)

Thit k b iu khin

a thc c trng t c t ( )det 0Tc csI A b r = , Ac v bc l dng iu khin c ca ma trn A v b. Nu

cA A , s dng ma trn bin i T l thch hp t c A c v bc. V vy1

cA TAT = , v cb Tb= . Ma trn

T

c cF A b r = c dng

0 1 0 2 1

0 1 0

0 1 0

0 0 1

n n

F

a r a r a r

=

(33.19)

a thc c trng ca ma trn F l

1

1 1 2 0 1( ) ( ) ( )n n

n ns a r s a r s a r

+ + + + + + +L (33.20)

Cc im cc c la chn cho h kn xc nh a thc

1 2

1 2 1 0

n n n

n ns p s p s p s p

+ + + + +L (33.21)

a thc 33.20 v 33.21 l ng nht, do vy cc h s ca ma trn TRr l

1 1, 1,...,v v vr p a v n = =

Nu

, T TRA Ac r r = =

cc trng hp khc th

T T

Rr r T= (33.22)

Thit k ma trn hiu chnh

Ma trn F l * T F A Kc= , trong A* l ma trn quan st. Cho F nhng im cc c la chn l s1, s2, sn v

1 2det[ ] ( )( ) ( )nsI F s s s s s s = L (33.23)

1

1 1 0det[ ]n n

nsI F s f s f s f

= + + + +L (32.24)T hai phng trnh trn, tm c cc h s k1, k2, ,kn

Trong trng hp ny (1 0 0)Tc = v ma trn quan st th ba l

9


10/23

S tay C in t

*

2

0 1 0

0 0 1

0 2 Z Z Z

A

D

=

(32.25)

Ma trn hiu chnh nh hng n cch hot ng tc thi, cc im cc ca F cng xa cc im cc ca A * th p ngcng nhanh.

Kt qu m phng trc thu lc in t vi b iu khin truyn thngDa trn c s cc thut ton trn xc nh ma trn hiu chnh v ma trn ca b iu khin, thc hin b quan st

trn SIMULINK vi cc gi tr sau

4

1 2 3

2 1

4 5

19.95854, 0.069481, 7.06024 10

3.158688 10 , 3.451209 10

r r r

r r

= = =

= =

Cho b iu khin, v

2 4 6

1 2 31.67 10 , 3.7028 10 , 6.969698 10 ,k k k= = =

Khi tn hiu u vo l step vi U=10V, kt qu m phng c ch ra trn hnh 33.13 v 33.14.

Hnh 33.13 V tr ca van servo cho m hnh ton hc vi b quan st

Hnh 33.14 V tr ca xylanh

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Hnh 33.15 iu khin trc thu lc in t vi b iu khin m c hai u vo

33.5 iu khin trc thu lc in t vi b iu khin m

Phn 33.5 ny dnh cho vic trnh by v nghin cu v nhng b iu khin khng truyn thng da trn tp m, ci m

c lm theo cch c x ca con ngi trong qu trnh iu khin. Kt qu m phng trc thu lc in t vi b iukhin SUGENO v MAMDANI s c miu t. Vi cng mt s cc lut tc dng c rt ra t c s hiu bit, kt qum phng chng minh rng s th hin ng hc c ci thin cho b iu khin m vi hai u vo.

Biu c thc hin trn SIMULINK iu khin trc thu lc in t cng vi b iu khin m hai u vo vsuy din MAMDANI hoc SUGENO c miu t trn hnh 33.15.

Kt qu th hin s lin quan trong vic m phng trc thu lc cho cng vi mt b iu khin m, da trn suydin MAMDANI [59]. Fuzzy Logic toolbox cho ngi s dng c th to ra h thng m MAMDANI v SUGENO sdng giao din ho. B son tho h thng suy din m FIS (Fuzzy Inference System) Editor, b son tho hm lin thuc(Membership Function Editor), v b son tho lut suy din (Inference Rules Editor) l nhng cng c c sn trnSIMULINK. V d nh l son tho h thng suy din v hm lin thuc ca mi u vo cho b iu khin m c xut y, cng vi suy din MAMDANI v hai u vo c minh ho trn hnh 33.16 v 33.17.

Hnh 33.16 FIS Editor cho h thng m da trn suy din MAMDANI

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S tay C in t

Hnh 33.17 Hm lin thuc kt hp vi u vo

B iu khin m ny c chn hm suy din c la chn, c th hnh dung r hn khi s dng Inference Rules Editor

ca SIMULIMK. Nhiu kt qu ca nhng trc thu lc in t c c cng vi b iu khin m ny nh trn hnh 33.18v 33.19 v miu t v tr v vn tc xylanh bng th.

33.6 iu khin trc thu lc in t dng k thut n ron

Phn 33.6 c cc mc tiu: nhn mnh kh nng s dng cc ti nguyn ca MATLAB thit k h thng iu khinda trn k thut iu khin hin i nh mng n ron; kim tra thng qua cc thut ton n ron ny; thc hin kin trc iukhin n ron c p dng cho trc thu lc in t nghin cu.

C hai hng nghin cu chnh trong iu khin n ron. Th nht l pht trin cc b iu khin t mng n ron. Th hail nhng cc b iu khin vo trong mng n ron [50]. Phn ny thc hin vi vic iu khin trc thu lc in t s dngb iu khin n ron, mng c s dng rng ri l mng perception nhiu lp (MLP).

Hnh 33.18 V tr LHM

Hnh 33.19 Vn tc LHM

K thut iu khin n ron

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13/23

iu khin nng cao cho mt trc thu lc in tVic hc da trn s bt chc

tng n t h thng sinh hc, vic hc bng s bt chc c p dng vo h thng iu khin. Mng n ron cgim st c th bt chc cch hot ng ca ca mt h thng khc. Phng php u tin pht trin mt b iu khinn ron l ti to mt b iu khin con ngi (human controller). B iu khin n ron c gng c x nh hot ng ca conngi. Hun luyn n ron c ngha l hc quan h gia thng tin nhn c t cch hot ng ca con ngi v u vo iukhin (hnh 33.20).

Hc ngc

Mc ch ca iu khin ngc l iu khin h thng s dng ng hc ngc. Trong trng hp ny, mng n ronnhn u ra ca h thng lm u vo v u vo ca h thng lm u ra. H thng lm vic trong h h v phi trongmin m b iu khin hot ng. Hc ngc (hnh 33.21) l mt hng trc tip gim n mc ti thiu sai lch u raca mng thay v sai lch ca ton h thng.

Hc ngc chuyn gia

Theo Psaltis, ngi xut hc ngc chuyn gia nm 1988 th mng n ron ln c hun luyn tp trc tuyn (online) gim n mc ti thiu sai lch iu khin ye r y= (xem hnh 33.22).

Hnh 33.20 S cho vic hc da trn s bt trc

Hnh 33.21 Giai on hun luyn hc ngc

Hnh 33.22 Kin trc iu khin ngc chuyn gia (affter [50])

B iu khin n ron c s dng iu khin v tr ca mt trc thu lc in t l mng n ron nhiu lp thun,thut ton hc ca chng l lan truyn ngc (back-propagation). thch nghi cc trng s, duy tr cc thng tin hc c,hai bc sau y c thc hin: th tc lan truyn thun ca tn hiu c ch v lan truyn ngc ca sai lch. Cu trc iukhin c thc hin trn SIMULINK nh trn hnh 33.23. iu khin n ron ca mt trc thu lc in t v s t ccc tham s iu khin c th hin trc tuyn (online).

Mt mng n ron vi 4 lp, c 2 n ron trn lp th nht, mt n ron lp ngoi cng, v 5 n ron trong mi lp n,

c xut. c tnh th tng ng vi v tr cc trc c c s dng mng n ron c miu t nh trn hnh 33.24.

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S tay C in t

33.7 iu khin trc thu lc in t dng k thut m-n ron

Chng ny cp cc k thut thit k c s h tr ca my tnh ca thut ton iu khin lai. Phn ny s tp trung vocc dng thut ton, v vic thc hin c thng qua vic m phng mt trc thu lc in t vi b iu khin m-n ronth c th snh ngang hoc hn vi cc thut ton khc. Thut ton m-n ron mang n mt s mi l nhng s thiu y trong hp cng c ca SIMULINK dnh cho chng, dn n s nghin cu c nh hng hon thin th vin cachng trnh C++, h tr cho vic s dng SIMULINK trong thit k cc b iu khin. Do vy vic hiu chnh online cc

tham s ca b iu khin m c thc hin. S nghin cu so snh cc thut ton c in v nng cao c thc hin datrn c s sai lch bnh phng tng th c tnh ton t gi tr quan st tc thi.

Hnh 33.23 Cu trc iu khin cho b iu khin c xut

Hnh 33.24 V tr ca trc khi in p u vo U = 8 V

Bi v kh nng ca h thng m l x l cc thng tin khng chnh xc, chng miu t kin thc dng lut ngn ng.Vi cch ny th kin thc ca hot ng con ngi l ngn ng hoc s c s dng pht ra tp lut m nu-th (if-then)nh l c s cho b iu khin m. Mt tr ngi ln ca h thng m l s kh khn thit k chng da trn mt phngphp lun c h thng. vt qua tr ngi ny th tc hc t mng n ron c p dng thnh cng iu chnh tham s

ca hm lin thuc. S lin kt gia mng n ron v logic m to ra nhng b iu khin m - n ron. C th khng nhrng b iu khin m - n ron c c c cc c im c bn ca c h thng m v mng n ron.

B iu khin m - n ron c xut c cu trc da trn phng php Takagi-Sugeto v n c miu t trong hnh33.25.

Th tc hc trong thc t th hin mt vn c lng tham s. Th tc hc cho b iu khin m - n ron c xut l gradient-descendent. Phng php c p dng thit k b iu khin nh vy gi l hc ngc, trong k thutonline c s dng to m hnh ng hc ngc ca i tng. M hnh m n ron t c - ng hc ngc ca itng - c s dng pht ra hot ng iu khin.

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15/23


Hnh 33.25 Cu trc ca mt b iu khin m - n ron.

B iu khin m - n ron l mt h thng nhiu lp ni tip, h thng logic m nhiu u vo v mt u ra. Mng c balp: mt lp u vo vi n x m n v (units), mt lp n vi n n v v mt lp u ra vi mt n v [15]. S phn chiac s dng trong m hnh l s phn chia phn tn [33].

Hnh 33.25 th hin mt trng hp c bit, trong b iu khin m ch c hai u vo v mt u ra. Trong trnghp tng qut, b iu khin m c m u vo v mt u ra.

C s ca lut m gm c mt tp hp vi n lut ngn ng c dng nh sau:Ri: If x1 is A1i and x2 is A2i

and

and xm is Amithen y is wi, i=1,2,n

trong i l ch s ca lut; Aji l mt tp m cho bin ngn ng th j v lut th i v w i l mt s th hin phn kt qu.

Hm lin thuc gn cho mi u vo l hm Gaussian. Tm ca hm lin thuc c la chn sao cho cc hm ny lphn b chun cho mi ngn t.

2 2( ) / 2 j ji jl x a b

ji e = (33.26)

Suy din m bao hm trong b iu khin m - n ron l mt tch v hng T-norm c nh ngha nh l mt hm kt

hp and. bt ca tt c cc lut l

1 2 , 1,...., .i i i miz i n = =K (33.27)

u ra l mt gi tr chnh xc t c nh l mt kt qu ca vic nh gi trng tm.

1 1 21 2

11 1 1 1

nn

i ii nn i in n n n

ii i i ii i i i

z w zz zy w w w z w

z z z z

=

=

= = = =

= = + + + =

L (33.28)

Tham s c c bng cch tm gi tr nh nht ca hm gi tr sau:

21( ) ( ( ) ( ))2 d

J k y k y k = (33.29)

Trong yd(k) l u ra mong mun v y(k) l p ng t c ti thi im k. ti u hm gi tr ny, s dng phng php xp x thng k. Th tc hc c ngha l nh gi tham s v c da

trn thut ton bnh phng nh nht. Tham s c nh gi l

15


16/23

S tay C in t

11 11 1( ,...., , ,..., , ,...., )nm nm np a a b b w w= (33.30)

Phng trnh iu chnh tham s nh sau:

2

11

2

3

11

11

( )( 1) ( ) ( ) ( )

( ( ))

( 1) ( ) ( ) ( )

( 1) ( ) ( )

j jii ji ji a d in

jil

j jii

ji ji b d inji

l

ii i w d n

l

x a t za t a t y y w y

bz

x a t z

b t b t y y w y bz

zw t w t y y

z

=

=

=

+ =

+ =

+ =

(33.31)

Trong cc tha s hc w, ,a b c nh ngha t trc.

Trong qu trnh hc, tham s c th c iu chnh l ( ) ji ji,a b , n miu t hm Gaussian v w i l gi tr kt lun. Nucu trc ca hm lin thuc c thit lp, ch c w i c hiu chnh.

Cu trc iu khin

thit k b iu khin m - n ron c xut trn, phng php hc ngc c p dng. Vic iu khin trcthu lc in t bao hm vic s dng k thut online to m hnh ng hc ngc ca i tng. S khi cho hcngc trc tuyn c miu t trn hnh 33.26.

S ny l mt h h v n cng c tm ra bi phng php sai lch u ra b iu khin (Controller Output ErrorMethod - COEM) [1] iu chnh trc tuyn nhng tham s ca b iu khin m. Phng php ny khng i hi sai lchu ra ca i tng c sinh ra u vo. C mt s rng buc khc l b iu khin phi c kh nng lm n nh itng trc khi bt u hiu chnh. trnh i hi ny, phng php sai lch u ra ca b iu khin sa i (ModifiedCOEM (MCOEM)) c s dng. S khi trong trng hp ny c miu t trn hnh 33.27.

B iu khin phn hi t l P c thm vo v trong trng hp ny u vo ca i tng l tng ca ' ( )u k v ( )pu k .Cc kt qu n t c cho gi tr ban u bng khng v b iu khin P c la chn nh mt cch n nh itng. Cu trc v tham s ca m hnh ngc v ca b iu khin m - n ron c ng nht.

Hnh 33.26 S iu khin da trn hc ngc

Hnh 33.27 S khi ca hc ngc cng vi b iu khin t l

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Hnh 33.28 iu khin v tr cng vi b iu khin m - n ron

C hai giai on trong vic thit k mt b iu khin l: iu khin (control) v hiu chnh (adaptation). Trong giai oniu khin, u ra ca i tng v tn hiu tham chiu (reference signal) xc nh lnh iu khin u(k). u vo ca itng tr thnh u(k), l tng ca u(k) v ( )pu k . Trong giai on hiu chnh, m hnh ngc c u vo l y(k+1) v y(k), to

ra tn hiu ( )u k

u ra. Tn hiu ny c s dng tnh ton sai lch ( )ue k , t xc nh hm gi tr J(k), hm cti thiu ho.

2 21 1 ( ) ( ) ( ( ) ( ))2 2u

J k e k u k u k = = (33.32)

Th tc ny c s dng trong vic iu khin v tr trc thu lc in t, tham s b iu khin c xc nh trctuyn. V tr c cu chp hnh t c khi tn hiu tham chiu thay i t U=4V n U=8V nh miu t trn hnh 33.28.

Bng 33.1

B iu chnh IAE ISE

PID (chng 4) 0.8024 3.4754

PI (chng 4) 0.8006 3.4618

PD (chng 4) 0.7928 3.4537

Neural (chng 6) 0.8027 3.4622

M - n ron (chng 7) 0.7911 3.4501

Hnh 33.29 (a) Hm lin thuc trc khi hc ca bin x1, (b) Hm lin thuc trc khi hc ca bin x2

thc hin vic so snh thut ton iu khin hin i vi cu trc truyn thng, hai tiu chun tch phn: tch phn sai

lch tuyt i (IAE) v tch phn sai lch bnh phng (ISE) c s dng. Kt qu t c khi p dng tiu chun ny thhin bng 33.1.

Tng ng vi nhng kt qu trc , c th suy ra rng b iu khin m - n ron c miu t t ra tt hn so vinhng nhng g t c ca b iu khin n ron da trn MLP, hoc cc b iu khin kinh in (PID, PI, PD) c trnh

17


18/23

S tay C in t

by trong quyn sch ny. Nhng kt qu m phng nhn mnh rng b iu khin m - n ron th hin l mt cng c huch cho cc ng dng c th vi nhiu thnh phn phi tuyn.

Kt qu ti u t c thng qua vic thay i cc tp d liu v s bc lp. kim tra vic th hin ca b iukhin m - n ron c xut, mt hm phi tuyn c cho bi mt phng trnh gii tch xp x. Hm lin thuc cabin u vo x1 v x2 trc khi hc c miu t trn hnh 33.29(a,b). B mt to c sau khi m phng c miu t trnhnh 33.30(c). C th quan st chnh xc ca cu trc xy dng li sau 300 bc hc bng s so snh cc b mt t c.

Nhng tp hp kt qu trung gian t c cng vi cc tp d liu m phng khc nhau c miu t bn di. Cc tp

d liu khc nhau ca s m phng c s dng t c kt qu ti u. Mt vi kt qu trong s c th hin tronghnh 33.30-33.34.

c c nhng s th hin tt t m hnh, 10 hm lin thuc c s dng cho mi u vo. Cc tha s hc

w, ,a b c la chn bng 0.01. Thut ton iu khin c kh nng thc hin vi s thay i trong phm vi hot ng.

Cc kt qu m phng trc thu lc in t cng vi b iu khin c xut t c khi cc u vo thay i. Nhngci ny l trong min thi gian, kt qu c th hin trong hnh 33.35(a,b), tng ng vi in p u vo l 8 v 10V.

Tp th nht: gw = 0.1; ga = 0.05; gb = 0.05; nepoc = 100; nesant = 100; niter = 200; threshold error = 0.001; Vmax =0.04.

Hnh 33.30 (a) B mt t c sau bc lp th nht, (b) Hm lin thuc sau khi hc cho bin x2, (c) B mt t c saukhi m phng

Tp th hai: gw = 0.1; ga = 0.07; gb = 0.05; nepoc = 100; nesant = 21; niter = 200; threshold error = 0.001; Vmax =0.0475.

Hnh 33.31 B mt t c sau bc lp th nht

18


19/23

iu khin nng cao cho mt trc thu lc in tTp th ba: gw = 0.5; ga = 0.07; gb = 0.03; nepoc = 200; nesant = 21; niter = 200; threshold error = 0.001; Vmax =

0.047515.

Hnh 33.32 Hm lin thuc sau khi hc cho bin x2

Hnh 33.33 B mt t c sau khi hc

33.8 Phn mm

M hnh ton hc ca trc thu lc in t c nghin cu trong chng ny c cung cp bi mt h thng vt l phng th nghim c in t ca UAS-Konstanz (xem trn hnh 33.1b). Hai bin th ca m hnh ton hc phi tuyn cthit lp trong phn 33.3 v thm vo tnh phi tuyn ng v tnh l nhng ci pht sinh trong hot ng ca trc thu lcin t [23,58].

M hnh ton hc ca iu khin thu lc c th hin trong cu trc ca ROBI_3 c thc hin trn SIMULINK nghin cu s bin i ng hc ca trc [26,27]. Bin m rng ca m hnh ton hc phi tuyn cc trc thy lc c avo tnh chuyn ng quan h ca cc phn trong servodrive.

B iu khin n ron v m - n ron (Takagi-Sugeno) c pht trin trn Borland C++ v thc hin trn SIMULINKcho vic iu khin cc trc thu lc in t. SIMULINK h tr ngi s dng mt th vin logic m, n cho php thit kv to m hnh h thng suy din m SUGENO v MAMDANI. S thiu vng mt phn mm dnh cho thit k b iukhin m - n ron c khp phc bng vic thc hin mt b iu khin trn C++ v bin i vic s dng n trongSIMULINK [26,27,28].

Vi s h tr vic m phng bng SIMULINK 2.1 v MATLAB 5.2 (di mi trng Window), a n mt gii phpthc hin b iu khin ca chng ta nh mt m un v tng ng vi cc biu tng trong toolbox. Trong qu trnh thcnghim, chng ti s dng nhng kh nng c tr gip bi S-function v C Mex kt hp vi Borland C++ 5.0 bindch chng. Chng ti la chn C S-function bi v s cn thit v tc x l thng tin trong khi thc hin b iukhin. Khi thc hin b iu khin c hai u vo (thm ch c th c ba u vo mc d vic x l hiu chnh s phc tphn) v mt u ra.

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S tay C in t

Hnh 33.34 (a) B mt t c sau bc lp th nht, (b) Hm lin thuc sau khi hc cho bin x1, (c) Hm lin thuc saukhi hc cho bin x2, (d) B mt sau khi hc

Hnh 33.35 (a) iu khin v tr vi b iu khin m - n ron (U=8V), (b) iu khin v tr vi b iu khin m - n ron(U=10V)

Tham s hiu chnh (trng s, tm, phm vi ca hm Gaussian) phi lin tc. Khai bo ton cc, tnh hoc s dng khnggian lm vic cha nhng k thut c ch hon thnh nhim v.

Phin bn mi nht ca SIMULINK cung cp nhng kh nng vit gi hm S-funccion, s dng gi li cc hm v

nh mt bin i ADA hoc ngn ng lp trnh Portran.

Hnh 33.36 Robot 3 trc Cartesian c to m hnh, iu khin, m phng trn SDS [21,24]

33.9 Kt lun

Nghin cu c thc hin trong chng ny ng nh mc ch t ra, s pht trin ca cu trc iu khin ci tinda trn k thut iu khin hin i (n ron v m) c s quan h vi cu trc iu khin truyn thng. Cc trc thu lc

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21/23

iu khin nng cao cho mt trc thu lc in tin t c nghin cu l mt thnh phn ca robot Cartesian ROBI_3 c thc hin trong phng th nghim C in tca UAS-Constance. M phng 3D vi ng hc ngc, cng vi vic thc hin b iu khin bng cch s dng SDS-Modelling v mt phn mm m phng h thng thc [21,23,25,28]. M hnh v kt qu m phng c minh ha trn hnh33.36.

Mt cch tng qut, phn 33.1 a ra gii thiu ca chng ny. Trong phn 33.2, kha cnh quan trng nht ca iukhin h thng thu lc in t v tnh cht phi tuyn ca h thng c ch ra. Robot ROBI_3 c trnh by vi c thnhphn v h thng iu khin.

M hnh ton hc cc trc thu lc in t ca ROBI_3 c miu t trong phn 33.3. M hnh ton hc phi tuyn c

hon thnh da trn d liu k thut ca cc thnh phn h thng. Kt qu m phng m hnh ton hc phi tuyn t trongvng lp v tr c c s dng phn mm SIMULINK/MATLAB. Mt ch quan trng l tt c cc vn c m phngtrong chng ny c hon thnh s dng MATLAB/SIMULINK, trong cc thut ton iu khin hin i (n ron vm - n ron) c pht trin trn Borland C++ 5.0.

Phn 33.4 bao gm mt ci nhn tng quan ngn gn v l thuyt cc b iu khin truyn thng PID, PD, PI v b quanst, cng vi cc kt qu m phng trc thu lc in t c cu trc iu khin trn.

Phn 33.5 nhc li v l thuyt h thng m v trnh by s m phng cc trc thu lc in t vi b iu khin m. Lthuyt h thng m gp phn quan trng vo vic nh m hnh h thng v s pht trin mt khung l thuyt ph hp vivic thc hin nhng ch tiu cht lng ca con ngi. Lp lun ny th rt hu ch nh m hnh cho cc h thng phctp c tnh phi tuyn v thng tin khng r rng. Cc kt qu m phng trc thu lc in t t c s dng b iu khinm SUGENO v MAMDANI.

Mt s gii thiu ngn gn v l thuyt mng n ron, cu trc n ron ph bin nht v cc k thut iu khin n ron

c trnh by trong phn u ca mc 33.6. Nu logic m c c mt suy lun da trn cc thng tin khng r rng, thmng n ron hc bng cch hun luyn v sau cng, mng lm vic c xp x bng mt hm mong mun. S phn tch ccmng n ron c hun luyn gp nhiu kh khn v kt qu l cc lut thng khng c rt ra t cc mng ny. Kt qum phng trong phn 33.6 t c s dng mng n ron nhiu lp.

H thng m - n ron gi c c tnh ca c h thng m v n ron v c s dng thnh cng trong lnh vc iukhin nhng nm gn y. Ton b phn 33.7 trnh by v l thuyt h thng m - n ron, b iu khin m - n ron cthc hin trn Borland C++ v p dng trong SIMULINK cho cc trc thu lc in t vi mt s kt qu m phng cthc hin trong phn ny v mt s so snh gia b iu khin hin i v truyn thng.

Phn 33.8 bao gm mt s trnh by ngn gn ca chng ny v mt s kt qu chnh trong phm vi ch , cng nhtrin vng ca hng nghin cu ny trong tng lai.

Khng c nh che du, sau y l mt danh sch cc hng nghin cu c th v trin vng pht trin trong tng lai:

ng dng cc b iu khin c thc hin trn SIMULINK khng ch iu khin cc trc thu lc in t

tho lun m cn i vi cc h thng c cu trc rt phc tp trong mt h thy lc ln, cung cp cho ngi sdng mt th vin b iu khin m - n ron.

Thc hin trn phn cng ca b iu khin m - n ron.

Nghin cu c tip tc cng vi s pht trin ca b iu khin ti u (thng qua s nghin cu su hn v tnhn nh s dng s thay i ca ma trn tuyn tnh).

S tch hp cc b iu khin trnh by trong mt gi phn mm dnh cho lnh vc thu kh.

S pht trin ca k thut thit k b iu khin thc y vic thc hin cc b iu khin ny nh l s cngsinh tt hn gia phng php hin i v c in (m - n ron v thut ton di truyn).

S m rng phm vi nghin cu v iu khin vn tc, gia tc, p sut, lu lng, lc, m men v cng sut.

Ti liu tham kho

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