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Mn hcMn hc

M HNH HA V NHN DNG H THNGM HNH HA V NHN DNG H THNG

Ging vin: TS. Hunh Thi HongB mn iu Khin T ng Khoa in in TB mn iu Khin T ng, Khoa in in T

i hc Bch Khoa TP.HCMEmail: [email protected],

hthoang hcmut@yahoo [email protected]: http://www4.hcmut.edu.vn/~hthoang/

31 August 2012 H. T. Hong - HBK TPHCM 1

Chng 2Chng 2

M HNH HAM HNH HA


D L S ith I t d ti t D i S t

Ti liu tham kho chng 2Ti liu tham kho chng 2

D. L. Smith, Introduction to Dynamic SystemsModeling for Design, Prentice-Hall, EnglewoodCliffs New Jersey 1994Cliffs, New Jersey, 1994.


Gii thiu

Ni dung chng 2Ni dung chng 2

Gii thiu Phn tch chc nng Phn tch vt l Phn tch vt l Phn tch ton hc Mt s th d


G G Gii thiuGii thiu


M hnh haM hnh ha

M h h h l h h d h h t h M hnh ha l phng php xy dng m hnh ton ca hthng bng cch da vo cc qui lut vt l chi phi hotng ca h thng. g g

Phng php m hnh ha ch c th p dng khi ta bit r cu trc ca h thng v cc qui lut vt l chi phi hot ng ca h thngng ca h thng.

Cc nh lut vt l inin C hc Nhit Lu cht lng Lu cht kh


Cc bc gii bi ton m hnh haCc bc gii bi ton m hnh ha

Ph t h h h t h h th th h khi Phn tch chc nng: phn tch h thng thnh cc khichc nng, trong m hnh ton ca cc khi chc nng bit hoc c th rt ra c da vo cc qui lut vt l. q

Phn tch vt l: rt ra m hnh ton ca cc khi chc nngda vo cc qui lut vt l.

Phn tch ton hc: cc khi chc nng c kt ni tonhc c m hnh ca h thng.



M hnh haM hnh ha

Phn tch chc nng Phn tch vt l Phn tch ton hc

C lp h thngL tng ha

Xy dng h PT

h hC lp h thng

Ph t h HT Quan h gia cc

phn t vt l m t h thng

T t h hPhn tch HT con

Q h h

Quan h gia cc i lng c bn

Tuyn tnh ha

Quan h nhn quCc .lut bo ton

i s s khi


nh gi m hnh

Phn tch chc nngPhn tch chc nng



M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

h hC lp h thng




Q h h


Tuyn tnh ha


i s s khi


nh gi m hnh

Khi nimKhi nim

Ph t h h l h t h h th h h Phn tch chc nng l phn tch h thng cn m hnh ha thnh nhiu h thng con, mi h thng con gm nhiu b phn chc nng (functional component). p g ( p )

Khi phn tch chc nng cn : lin kt vt l (connectivity): cc b phn no ca h

h k i i h ?thng kt ni vi nhau? quan h nhn qu (causality) cc b phn lin kt vi

nhau nh th no?nhau nh th no? Ba bc phn tch chc nng:

C lp h thngp g Phn tch h thng con Xc nh cc quan h nhn qu



M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

h hC lp h thng




Q h h


Tuyn tnh ha


i s s khi


nh gi m hnh

C lp h thng C lp h thng Xc nh cc lin kt ngoiXc nh cc lin kt ngoi

X h ii h h th h h h Xc nh gii hn ca h thng cn m hnh ha Ct kt ni gia h thng kho st vi mi trng ngoi Mi kt i b t th th b t t Mi kt ni b ct c thay th bng mt cng m t s

tng tc gia h thng v mi trng.

bien cua he thong

He thong Moi trngU

He thong Moi trngY


CngCng

C ( t) l t i (t i l) Cng (port) : l mt cp u cui (terminal) m qua nnglng truyn vo hoc ra khi h thng. Mt h thng c thc nhiu cng (multiport system).g ( p y )

Mi cng c th c mt hoc hai ng vo (k hiu l U) vmt hoc hai ng ra (k hiu l Y)

Bn loi cng thng gp: C kh (Structural) in (Electrical) Nhit (Thermal)

L ht (Fl id) Lu cht (Fluid)


Cng c khCng c kh


Cng inCng in


Cng nhitCng nhit


Cng lu chtCng lu cht


Th d: C lp h tay myTh d: C lp h tay my


Th d: C lp h tay my (tt)Th d: C lp h tay my (tt)


Th d: C lp h thng lm mtTh d: C lp h thng lm mt


Th d: C lp h thng lm mt (tt)Th d: C lp h thng lm mt (tt)


TD: C lp b phn trao i nhit trong h thng lm mtTD: C lp b phn trao i nhit trong h thng lm mt


TD: C lp b phn trao i nhit trong h thng lm mt (tt)TD: C lp b phn trao i nhit trong h thng lm mt (tt)


Th d: c lp h thng gim xc Th d: c lp h thng gim xc


Th d: c lp h thng cch nhit Th d: c lp h thng cch nhit



M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

h hC lp h thng




Q h h


Tuyn tnh ha


i s s khi


nh gi m hnh

Phn tch h thng con Phn tch h thng con Xc nh cc lin kt trongXc nh cc lin kt trong

Phn tch h thng sau khi c lp thnh cc h thng con(subsystem), sau tip tc phn tch cc h thng con chitit n cc b phn (component) thay th lin kt gia cctit n cc b phn (component), thay th lin kt gia ccb phn bng cc cng.


Th d: M hnh ho h tay myTh d: M hnh ho h tay my


Th d: M hnh ho h tay my (tt)Th d: M hnh ho h tay my (tt)

C


Cc lin kt ngoi


Cc lin ktCc lin kt trong chi tit n cc h thng con (subsystem)( y )




Cc lin kt trong chi tit n cc b phn (component)


M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

C lp h thng

Q h i


Phn tch HT con


Tuyn tnh ha


i s s khi


nh gi m hnh

Phn tch quan h nhn qu Phn tch quan h nhn qu Xc nh cc bin ca HTXc nh cc bin ca HT

V cng l u cui m qua cng sut (nng lng/n vthi gian) truyn vo ra h thng nn quan h nhn qu cacng c xc nh bi cc bin nh ngha cng sut ticng c xc nh bi cc bin nh ngha cng sut ticng.


Cc bin ca cc loi cngCc bin ca cc loi cng




S khi hon chnh h tay my

Bi tp: Phn tch chc nng h thng thang myBi tp: Phn tch chc nng h thng thang my


Bi tp: Phn tch chc nng h thng lu chtBi tp: Phn tch chc nng h thng lu cht


Bi tp: Phn tch chc nng h thng tn laBi tp: Phn tch chc nng h thng tn la


Phn tch vt lPhn tch vt l



M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

h hC lp h thng




Q h h


Tuyn tnh ha


i s s khi


nh gi m hnh

Cc loi h thng vt lCc loi h thng vt l

H thng vt l c th chia thnh 4 loi: H thng vt l c th chia thnh 4 loi: in (Electrical) C (Machenical)( ) Nhit (Thermal) Lu cht (Fluid)

Mt h thng phc tp c th gm nhiu h thng con thuc 4 loi trn.

Cc phn t c bn (basis element): Cc phn t c bn (basis element): Tr (resistance) Dung (capacitance)Dung (capacitance) Cm (inductance) hay qun tnh (inertia)


Cc bin c bnCc bin c bn

C bi b l ( tit ) th ( t ti l) thi i (ti )

Loi Bin

Cc bin c bn: lng (quantity), th (potential), thi gian (time)

Loi H thng Lng Th Thi gian

in tch in thin in tch(Charge)in th (Voltage) Giy

Khong cch LcC kh Khong cch(Distance)Lc

(Force) Giy

Lu cht Th tch p sut GiLu cht(lng)Th tch(Volume)

p sut(Pressure) Giy

Nhit Nhit nng Nhit Giy


Nhit g(Heat energy)

(Temperature) Giy


M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

h hC lp h thng




Q h h


Tuyn tnh ha


i s s khi


nh gi m hnh

Cc bin khc nh ngha da trn cc bin c bnCc bin khc nh ngha da trn cc bin c bn

C d l bi thi l t t thi Cng dng l bin thin lng trong mt n v thi gian (hay cng dng l tc bin thin lng).

d lngdong o cng dtd

d h Cng sut dongocngthesuatcong


nh ngha phn t trnh ngha phn t tr

Tr l i lng c trng cho kh nng chng li s dch Tr l i lng c trng cho kh nng chng li s dch chuyn c hc hay dng vt cht, nng lng.

Tr c o bng th cn thit chuyn mt n v lngtrong mt n v thi gian (giy).

thedong o cng

thetr


nh ngha phn t dungnh ngha phn t dung

Dung biu din mi quan h gia lng v th Dung biu din mi quan h gia lng v th. Dung c o bng lng cn thit l cho th bin thin

mt n v.

lngdungthe

gdung

dt dong o cngdungthe1

g


nh ngha phn t cmnh ngha phn t cm

Cm hay qun tnh l i lng c trng cho kh nng Cm hay qun tnh l i lng c trng cho kh nng chng li s thay i trng thi chuyn ng c hc ca dng vt cht, nng lng.

Cm c o bng th cn thit lm tc bin thin ca lng thay i mt n v .

thecam d dong ocngdtd

dong o cngcamthedtd


dt


M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

h hC lp h thng




Q h h


Tuyn tnh ha


i s s khi


nh gi m hnh

Cc phng trnh cn bngCc phng trnh cn bng

Cc nh lut bo ton khi lng nng lng v xung Cc nh lut bo ton khi lng, nng lng, v xung lng l cc nh lut c bn c s dng khi m hnh ha.

Phng trnh cn bng c bn c dng tng qut nh sau:radongvaodongluytchdong

Phng trnh cn bng c bn c dng tng qut nh sau:

Nu h thng khng c cc phn t tch tr khi lng, nng lng v xung lng th phng trnh trn tr thnh:

d d 0 radongvaodong 0

Nu h thng c phn t tch tr khi lng, nng lng hay g p g, g g yxung lng th s tch tr ny lm thay i trng thi ca HT:

d d th itbi d


radongvaodongthaitrangbien dt


M hnh haM hnh ha


C lp h thngL tng ha

Xy dng h PT

h hC lp h thng




Q h h


Tuyn tnh ha


i s s khi


nh gi m hnh

L tng ha cc phn t vt lL tng ha cc phn t vt l

Ng n tc th n ha Nguyn tc thun ha Nguyn tc tp trung ha Nguyn tc l tng ha Nguyn tc l tng ha



N t th h h h h t l b hi Nguyn tc thun ha: nhn ra nh hng vt l c bn chi phi hot ng ca i tng v dng cc phn t thun biu dinbiu din.


L tng ha cc phn t vt lL tng ha cc phn t vt l Nguyn tc tp trung ha: cc nh hng vt l thc lun Nguyn tc tp trung ha: cc nh hng vt l thc lun

phn b trong mt min hay khng gian nht nh (d nh). Cc nh hng phn b ny c th l tng ha bng cch

h h h t tm hnh ha tp trung



Ng n tc t n tnh ha tt c cc h thng th c l Nguyn tc tuyn tnh ha: tt c cc h thng thc u l h phi tuyn l tng ha bng cch tuyn tnh ha.


S tng ng ca cc quan h vt lS tng ng ca cc quan h vt l


Ch Ch

Gi h i h h i h t Gia h in v h c c hai cch tng ng Tng ng lc in p Tng ng lc cng dng in Tng ng lc cng dng in

Tng ng lc in p Tng ng lccng d.in

H c H in H c H in

Lc f in p u Lc f Dng in i

Khi lng M in cm L Khi lng M in dung C

H s ma st b in tr R H s ma st b 1/in tr, 1/R

cng l xo k 1/in dung, 1/C cng l xo k 1/in cm, 1/L

Dch chuyn x in lng q Dch chuyn x T thng


Vn tc v Dng in i Vn tc v in p u

Phn tch vt l h thng inPhn tch vt l h thng in

Cc bin c bn: Cc bin c bn: in lng: q [C] in th: u [V]

Cc phn t c bn:

[ ] Cng dng in:i [A]

Cc phn t c bn:

in tr:iuR S

lR i

in dung:uqC d

SC idtCu 1

thetr

u

lngd dt dongocngthe 1 in cm:

dtdiLu

d h d bNrL

2


dong o cngtr

the gdung dt dongocngdungthedt dongocngcamthe dt

d b

Phn tch vt l h thng inPhn tch vt l h thng in

C l i Cc loi ngun: Ngun p l tng Ngun dng l tng Ngun dng l tng

Phng trnh cn bng in nh lut Kirchoff v dng. ut c o d g nh lut Kirchoff v p.

Phng php gii tch mch in Phng php th nh Phng php dng vng


Phn tch vt l h thng cPhn tch vt l h thng c

C bi b ( h th ) Cc bin c bn (chuyn ng thng): Khong cch (lng): x [m] Lc (th): f [N] Lc (th): f [N] Tc (cng dng): v [m/sec]



C h t b Cc phn t c bn Tr:

b: h s ma st nhtf: lc (th)

f

x: dch chuyn (lng)

vfbRM

thetr


dong o cngtr


C h t b Cc phn t c bn Dung: k: cng l xo

f l (th)f: lc (th)x: dch chuyn

(lng)

fx

kCM

1(lng)

vdtCkxf M1

lngd dt dongocngthe 1M


thelngdung dt dongocngdungthe


C h t b Cc phn t c bn Cm (qun tnh)

m: khi lngf: lc (th)

d h h (l )

dvmf

x: dch chuyn (lng)

dtmf

dongocngcamthe d


dongocngcamthedt

Ch th Ch Chuyn ng thng Chuyn ng quayLc MomentKhong cch Gc quayKhong cch Gc quayVn tc Vn tc gcGia tc Gia tc gcG a tc G a tc gcQun tnh Moment qun tnh


Phng trnh cn bng cPhng trnh cn bng c

Ph t h b l h l t N t Phng trnh cn bng lc, nh lut Newton

Phng trnh Euler Lagrange:

qP

qL

qL

dtd

Phng trnh Euler Lagrange:

qqqdt

Trong : UTL U: th nngT: ng nngP: nng lng tiu haoq: ta tng qut: ngoi lc (hay moment)


: ngoi lc (hay moment)

S tng ng gia h thng in v h thng cS tng ng gia h thng in v h thng c


Phn tch vt l h thng nhitPhn tch vt l h thng nhit

C bi b Cc bin c bn Nhit nng (lng): Q [J] Nhit (th): [0C] Nhit (th): [ C] Dng nhit: H [J/sec]

dtdQH

ld d


lngdongocng dtd


C h t b Cc phn t c bn Nhit tr:

kC: h s dn nhitl: chiu di S: tit din ngang

SklRC

T

thetr

S: tit din ngang

RT


dong o cngtrH

RT


C h t b Cc phn t c bn Nhit dung:

c: l nhit dung ring

QCT

c: l nhit dung ringM: l khi lng

McCT .

lngd

CT

dt dongocngthe 1 Hdt131 August 2012 H. T. Hong - HBK TPHCM 72

thelngdung dt dongocngdungthe HdtCT


C h t b Cc phn t c bn Nhit cm (qun tnh nhit): IT

dtdHIT

dongocngcamthe d


dongocngcamthedt

Phng trnh cn bng nhitPhng trnh cn bng nhit

h l t b t l nh lut bo ton nng lng


Phn tch vt l h lu chtPhn tch vt l h lu cht

C bi b Cc bin c bn p sut (th): p [N/m2] Th tch (lng): V [m3] Th tch (lng): V [m3] Lu lng (cng dng): z [m3/sec]

dtdVz dt

ld d


lngdongocng dtd


C h t b Cc phn t c bn Lu tr:

Lu tr ng ng:Lu tr ng ng:

: h s nht ca lu chtl: chiu di ng ng128 l l: chiu di ng ngd: ng knh ng ng(l > 20d)

4128

dlRL

thetrpRL

( )


dong o cngtrz


C h t b Cc phn t c bn Lu tr:

Lu tr van: phi tuynLu tr van: phi tuyn



C h t b Cc phn t c bn Lu dung:

A: tit din ngang: khi lng ring lu chtAC : khi lng ring lu chtg: gia tc trng trngg

CF

pVCL

lngd dt dongocngthe 1 zdtCp L

1


thelngdung dt dongocngdungthe


C h t b Cc phn t c bnQun tnh: IL

la

dzdtdzIp L

tit di d

alIL

a: tit din ngang ng dnl: chiu di ng dn: khi lng ring lu cht

dongocngcamthe d

a : khi lng ring lu cht


dongocngcamthedt

Phng trnh cn bng h lu chtPhng trnh cn bng h lu cht

h l t b t khi l nh lut bo ton khi lng


Cc th d phn tch vt lCc th d phn tch vt l

H i h d bi i Hc vin t c cc th d trong bi ging


Phn tch ton hcPhn tch ton hc


Phn tch ton hcPhn tch ton hc

Kt h tt h h t h t t h Kt hp tt c cc h phng trnh m t c tnh ng ca cc b phn chc nng c h phng trnh m t h thng.g

Tuyn tnh ha quan h phi tuyn c m t ton hc tuyn tnh. i khi Ph h d hi i s s khi Phng php s dng tn hiu v cng thc Mason tm hm truyn tng ng ca h tuyn tnh.y

nh gi s ph hp ca m hnh. Dng m hnh d bo p ng ca h thng i vi tn

hiu vo cho trc.


M hnh tuyn tnh ha h phi tuynM hnh tuyn tnh ha h phi tuyn


im dng ca h phi tuynim dng ca h phi tuyn

Xt h hi t b t bi PTTT hi

))(),(()( ttt uxfx

Xt h phi tuyn bc n c p ng vo, q ng ra m t bi PTTT phituyn:

))(),(()( ttt uxhy

i t thi i l i d h hi t h im trng thi c gi l im dng ca h phi tuyn nu nhh ang trng thi v vi tc ng iu khin c nh, khngi cho trc th h s nm nguyn ti trng thi .

xx u

Nu l im dng ca h phi tuyn th:),( ux

0))(),(( , uuxxuxf tt

i d i l i l i h h hi


im dng cn c gi l im lm vic tnh ca h phi tuyn

Th d im dng ca h phi tuynTh d im dng ca h phi tuyn

)()()( ttt

)(2)(

)().()()(

21

21

2

1

txtxutxtx

txtx

Cho h phi tuyn m t bi PTTT:

Xc nh im dng ca h thng khi 1)( utu

Gii:i d l hi h h

0))(),(( , uutut xxxfim dng l nghim ca phng trnh:

0201.

21

21

xxxx

2

2

2

1

x

x

2

2

2

1

x

x hoc


22x

22

x

Tuyn tnh ha h phi tuyn xung quanh im lm vic tnhTuyn tnh ha h phi tuyn xung quanh im lm vic tnh

Xt h phi tuyn m t bi PTTT phi tuyn:

))(),(()())(),(()(

tttttt

uxhyuxfx

Xt h phi tuyn m t bi PTTT phi tuyn:

))(),(()( ttt uxhy

Khai trin Taylor f(x,u) v h(x,u) xung quanh im lm vic tnhta c th m t h thng bng PTTT tuyn tnh:

)(~)(~)(~ ttt uBxAx (*)

),( ux

xxx )()(~ tt

)(~)(~)(~ ttt uDxCy( )

trong :

yyyuuuxxx

)()(~)()(~)()(

tttttt

))(( uxhy


yyy )()( tt )),(( uxhy

Ma trn trng thi ca h tuyn tnh haMa trn trng thi ca h tuyn tnh ha

222

1

2

1

1

1

f

n

fffxf

xf

xf

222

1

2

1

1

1

f

pfffuf

uf

uf

21)( u,xx

fA

nnn

n

fff

xxx

21

)( u,xufB

nnn

p

fff

uuu

hhh hhh

)(2 u,x nn xxx )(21 u,x puuu

222

1

2

1

1

1

hC

nhhhxh

xh

xh

222

1

2

1

1

1

hD

phhhuh

uh

uh

21)( u,xx

C

qqq

n

xh

xh

xh

xxx

21

)( u,xuD

qqq

p

hhh

uuu


)(21 u,x nxxx )(21 u,x puuu

Tuyn tnh ha h phi tuyn Tuyn tnh ha h phi tuyn Th d 1Th d 1

Thng s h bn cha :

u(t)qin

Thng s h bn cha :

3

22

80/150

100 ,1

CVk

cmAcma

y(t)u(t)

qout 2

3

sec/981

8.0 ,.sec/150

cmg

CVcmk D

PTTT:

))()(()())(),(()(

tuthtytutt

xxfx

))(),(()( tuthty x

)(94650)(35440)()(2

)( 1 ktgxaCDf

trong :

)(9465.0)(3544.0)()(

),( 11 tutxtu

Ak

Ag

u D xf

)())(),(( 1 txtuth x


)())(),(( 1

Tuyn tnh ha h phi tuyn Tuyn tnh ha h phi tuyn Th d 1 (tt)Th d 1 (tt)

Tuyn tnh ha h bn cha quanh im y = 20cm:Tuyn tnh ha h bn cha quanh im y = 20cm:

Xc nh im lm vic tnh:20201 x

05.13544.0),( 1 uxuxf 9465.0u


Tuyn tnh ha h phi tuyn Tuyn tnh ha h phi tuyn Th d 1 (tt)Th d 1 (tt)

Xc nh cc ma trn trng thi ti im lm ic tnh:

0396.02

21

DxA

gaCxfA 5.11

Ak

ufB

Xc nh cc ma trn trng thi ti im lm vic tnh:

2)(1)(1

uu

xAx,x,x )()(

uu Au ,x,x

1 hC 0

hD

)(1 ux ,x )( uu ,x

V PTTT m t h bn cha q anh im lm ic 20cm l: Vy PTTT m t h bn cha quanh im lm vic y=20cm l:

)(~)(~)(~5.1)(~0396.0)(~

tttutt xx

)()(2

),( 1 tuAk

AtgxaC

u D xf )()( tty x


)())(),(( 1 txtuth x

Tuyn tnh ha h phi tuyn Tuyn tnh ha h phi tuyn Th d 2Th d 2

Thng s cnh tay my :Thng s cnh tay my :

2C

02050

1.0,2.0 ,5.0

mkgJkgM

kgmmlml m

l

2sec/81.9 ,005.0

.02.0,5.0

mgB

mkgJkgM

u

PTTT:

))(),(()())(),(()(

tuthtytutt

xxfx

))(),(()( tuthty x

)(2 tx

trong :

)()(

1)()(

)(cos)()(),(

22212 tumlJtx

mlJBtx

mlJgMlmlu Cxf


)())(),(( 1 txtuth x

Tuyen tnh hoa he phi tuyen Tuyen tnh hoa he phi tuyen Th du 2Th du 2 (tt)(tt)

Tuyn tnh ha h tay my quanh im lm vic y = /6 (rad):Tuyn tnh ha h tay my quanh im lm vic y = /6 (rad):

Xc nh im lm vic tnh:

6/1 x

01)()(2

BgMlmlx

uxf 02x0

)(1

)(cos

)()(),(

22212

umlJ

xmlJ

BxmlJ

gMlmlu Cxf 2744.1u

Do im lm vic tnh cn xc nh l:

6/1 xx

02x

x

2744.1u



Xc nh cc ma trn trng thi ti im lm ic tnh: Xc nh cc ma trn trng thi ti im lm vic tnh:

2221

1211

aaaa

A

0)(1

111

uxfa

,x1

)(2

112

uxfa

,x

2221

)(12

)(1

221 )(sin)(

)(

u

C

u

txmlJMlml

xfa

xx

)( u,x

)()( uu ,x,x

)(2

)(2

222 )( mlJ

Bxfa

)(1)()()()(

)(2

BgMlmltx

u Cxf

)()(2 )( uu ,x,x


)()(

1)()(

)(cos)()(),(

22212 tumlJtx

mlJBtx

mlJgMlmlu Cxf



1

bb

B

01fb

2b

0)(

11

uub

,x

1f2

)(

22

1mlJu

fbu

,x

)(1)()()()(

)(2

BgMlmltx

u Cxf


)()(

1)()(

)(cos)()(),(

22212 tumlJtx

mlJBtx

mlJgMlmlu Cxf



11

1

xhc 21 ccC 0

)(22

xhc

)(1 ux ,x )(2 u,x

1dD 0)(

1

uhd

)( uu ,x

Vy phng trnh trng thi cn tm l:

)(~)(~)(~)(~)(~)(~

ttttutt

DCBxAx

)()()( tutty DxC

10

A

0

B 01C 0D

2221 aa

A

2b

B 01C 0D


)(),( 1 txuh x

Mt s th dMt s th d


Cc v dCc v d

M h h h h l M hnh ha h con lc ngc M hnh ha h bng v thanh M hnh ha h tay my y y M hnh ha h bnh li my bay M hnh ha c tnh ng hc xe hi M hnh ha c tnh ng hc tu thy M hnh ha c tnh ng hc tu thy M hnh ha h robot 2 bnh cn bng ...


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