dieu khien tu dong - ngan hang de thi
TRANSCRIPT
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7/31/2019 Dieu Khien Tu Dong - Ngan Hang de Thi
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 1
NGN HNG THIMn: CSIU KHIN TNG
Dng cho hHTX, ngnhin t- Vin thngS tn ch: 3
CHNG 1. M T TON HC H THNG IU KHIN TNG /Chohthngiukhincskhinhhnhv,tnhiu l
Tnhiuvo Tnhiura Tnhiuphnhi Tnhiuiukhin /Chohthngiukhincskhinhhnhv,khiCsthhin:
itngiukhin Biukhin Thitbo Khngcvaitrrrng /Hthngtuyntnhlhthngm: Chaikhultuyntnh Cmtkhultuyntnh Ttccctnhiutronghthngltuyntnh Ttccckhutronghthngultuyntnh /Sailchtnhlsailchcahthngtrngthixclp,nghaysai? ng sai /trngthixclp,sailchtnhl: Sailchgiatnhiuchovtnhiuiukhin Sailchgiatnhiuovtnhiucho
HC VIN CNG NGH BU CHNH VIN THNG
Km10 ng Nguyn Tri, H ng-H Ty
Tel: (04).5541221; Fax: (04).5540587Website: http://www.e-ptit.edu.vn; E-mail: [email protected]
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 2
Sailchgiatnhiuovtnhiuiukhin Sailchgiatnhiuchovtnhiuo /NghimathctscaPTTcgilccimkhng(zero)? ng Sai
/NghimathcmuscaPTTcgil? Ccimun Ccimcc Ccimcctr Ccimkhng
/Hthngcmtnhhnhvtngngvitrnghp 1D = khimtntrongkhnggiantrngthi?
ng Sai /Hmtruyntcahthngtronghnhtrn?
( )( )
( )1h
kh
W pW p
W p=
+
( )( )
1
1k
h
W pW p
=+
( )( )
( )21h
k
h
W pW p
W p=
+
( ) ( )( )1
hkh
W pW pW p
=
/Hthngphituyncthpdngnguynlxpchng? ng Sai
/ctnhbintnlogarithmcxcnhtheocngthcnosauyvi ( )A lctnhbintn?
( ) ( )30lgL A =
( ) ( )lgL A =
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 3
( ) ( )20lgL A =
( ) ( )10lgL A =
/Tmhmtruynttngngcagraphtronghnhtrn?
1 2.W W
1 2W W
1 2W W
1 2W W+
/athcctrngcahthngl: Milinhgiatnhiuravtnhiuvocahthng Lmuscahmtruyntcaitngiukhin Muscahmtruynt Tscahmtruynt
/BiniLaplacecahm ( )1 t ? p
21 p
1
1 p
/BiniLaplacecahm ( )t ?
21 p
1 p 1
p
/Hthngcmttrongkhnggiantrngthidng:
Ax Bu
y Cx Du
= +
= +
trong ,x x l: Ccvectorbintrngthi uvo Ccmatrnbintrngthi ura
/Mththngiukhintnggmnhngthnhphncbnno? itngiukhin,thitbiukhinvthitbolng Thitbiukhin,thitbolng itngiukhin,thitbiukhin
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 4
itngiukhin,thitbolng /Tnhiuiukhincamththngiukhintngcphnhiml: Gitrmongmun Gitroc Sailchgiagitrmongmunvgitroc
Tnggiagitrmongmunvgitroc /Hmtruyntcahthngl: TsgiatnhiuravtnhiuvocahthngbiudintheobiniLaplaceviiukinukhngi Tsgiatnhiuravtnhiuvocahthng Tsgiatnhiuravtnhiuvocahthngbiudintheothigian TsgiatnhiuravtnhiuvocahthngbiudintheobiniLaplaceviiukinutrittiu /Scutrctrngthicahlintctronghnhtrncdngbiudinh
thngcmttheophngtrnhtrngthitheodngnosauy?
Ax Bu
y Cx Du= += +
Ax Bu
y Dx Cu
= +
= +
Dx Bu
y Cx Au
= +
= +
Bx Au
y Cx Du
= +
= +
/Graphtnhiunhhnhtrnbiuthhmtruynt ijWbngbaonhiu?
ij i jW X X= +
ij j iW X X=
ij i jW X X=
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 5
ij i jW X X=
/Tmhmtruynttngngcagraphtronghnhtrn?
1 2
1 2
.
1 .
W W
W W+
1
1 21 .
W
W W+
1 2
1 21 .
W W
W W
+
+
2
1 21 .
W
W W+ /Du?tronghnhtrnchmtruynt?
2 3U U
2U
2U
3 2U U
/Hmtruyntcahnhhnhtrn?
1 2 3. .W W W W =
1 2 3W W W W = + +
2
1 2 3
WW
W W W=
+ +
1
2 3
WW
W W=
+
/Hmtruyntcahnhhnhtrn?
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 6
2
1 2 3
WW
W W W=
+ +
1
2 3
WW
W W=
+
1 2 3. .W W W W =
1 2 3
W W W W = + +
/Du?tronghnhtrnlgchngtngngnhau?
1 W
2W
2W
W /ctnhbintn(BT)cahthngcxcnhtheocngthcnodiyvi:
( ) ( ),R I
lnltlphnthc,phnocahmtruyntnscah?
( ) ( ) ( )A R I = +
( ) ( ) ( )2 2A R I =
( ) ( ) ( )A R I =
( ) ( ) ( )2 2A R I = +
/ctnhphatn(PT)cahthngcxcnhtheocngthcnodiyvi:
( ) ( ),R I
lnltlphnthc,phnocahmtruyntnscah?
( ) ( )
( )arg R
I
=
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 7
( )( )( )
argI
R
=
( )( )( )
argI
R
=
( ) ( )
( )arg R
I
=
/Du?tronghnhtrnlgchngtngngnhau?
2
W 2W
W
1 W /Du?tronghnhtrnlgchngtngngnhau?
1 W
W
2W
2
W /Du?tronghnhtrnlgchngtngngnhau?
2W
2
W
1 W
W
/Tmhmtruyntcahthngtronghnhtrn?
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 8
3 1 313
1 21
X W WWX W
= =
3 1 313
1 21
X W WW
X W
+= =
3 1 313
1 21
X W WW
X W= =
3 1 313
1 21
X W WW
X W= =
+
/BiniLaplaceca ( )1 1p p + ?
1t
e
1te+
1t
e
1te
/Hmtruyntcahthngtronghnhtrn?
2 3 4
1 2 5 1 2 3 4
. .
1 . . . . .
W W W
W W W W W W W + +
1 2 3
1 2 5 1 2 3 4
. .
1 . . . . .
W W W
W W W W W W W + +
1 3 4
1 2 5 1 2 3 4
. .
1 . . . . .
W W W
W W W W W W W + +
1 2 3 4
1 2 5 1 2 3 4
. . .
1 . . . . .
W W W W
W W W W W W W + + /Theonhltihn(nutnti)trongbiniLaplace,iunosauylng?
( ) ( )0 lim .
p
x t p X p
= =
( ) ( )0 limp
x t X p
= =
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 9
( ) ( )20 lim .p
x t p X p
= =
( ) ( )0
0 lim .p
x t p X p
= =
/Theonhltihn(nutnti)trongbiniLaplace,iunosauylng?
( ) ( )0
limp
x t X p
= =
( ) ( )0
lim .p
x t p X p
= =
( ) ( )lim .p
x t p X p
= =
( ) ( )2
0
lim .p
x t p X p
= =
/Hmtruyntcahthngtronghnhtrn?
( ) 1 32 3 1 21
W WW p
W W W W =
+ +
( ) 1 2 3
2 3 1 21W W WW p
W W W W = + +
( ) 2 32 3 1 21
W WW p
W W W W =
+ +
( ) 1 22 3 1 21
W WW p
W W W W =
+ +
/ 3 1X X
tronghnhtrnbngbaonhiu?
3 113
1 21
X WW
X W= =
3 1 313
1 21
X W WW
X W= =
+
3 313
1 21
X WW
X W
= =
3 1 313
1 21
X W WW
X W= =
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 11
CHNG 2. C TNH NG HC CA CC KHU CBN
/ctnhtnhcaphntlmiquanhgiatnhiuravtnhiuvocaphnttrngthixclp? Sai ng
/PhngtrnhviphnbiudinkhunguynhmviKlhstruyncaphnt?
y K x=
y x K=
y Kx=
1y Kx=
/Phngtrnhviphnbiudinkhutchphnvi iT lhngsthigiantchphn?
iy T dx=
.iy T x dt=
1
i
y dxT
=
1.
i
y x dtT
=
/Phngtrnhviphnbiudinkhuviphnvi dT lhngsthigianviphn?
2d
dxy T
dt=
1
d
dxy
T dt=
d
dxy T
dt=
2d
dxy T
dt=
/Muntmhmtruynttnscahthnghocphnt,tathaybin p bngbaonhiuvohmtruyntcan?
j
je
j /Khitnhtheodecibel,ctnhbintnlogarithm(BTL)cxcnhtheocngthcno?
( ) ( )10lgL A =
( ) ( )lgL A =
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 12
( ) ( )2lgL A =
( ) ( )20lgL A =
/Cckhunghccbnctnhchtnosauy? Cnhiutnhiuvovnhiutnhiura
Cnhiutnhiuvovmttnhiura Cmttnhiuvovnhiutnhiura Chcmttnhiuvovmttnhiura /Nuhmqucakhukhuchi:
( ) ( ).1h t k t =
thhmtrnglng ( )k t bngbaonhiu? k
( ) ( ).k t k t =
( ) .k t k t =
( ) ( ).1k t k t =
/Tnhiubcthangnvcthcbiudinnhhnhtrn?
Sai ng /Tnhiuxungnv(xungDiract)cthcbiudinnhhnhtrncngkhng?
ng Sai /Vctnhbintnlogarithmbngcchtuyntnhhatngon? ng Sai /Trongkhutchphn,ctnhphatncgitrbngbaonhiu?
2
4
2
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 13
/Hm( )t
?
Lhmxungnvcphttithiim t = Lhmbcthangnvcphttithiim t = Lhmbcthangnvcphttithiim t =
Lhmxungnvcphttithiimt =
/Khutchphnccimg? Ctnhchtnh
Tnhiurasmphahntnhiuvomtgc 2 Cbacimtrn Khuchitnhiuvolnkln
/Nukhudaongbc2chscndu 1 > thnsthhintnhchtgcakhudaong?
Khudaongdaongvibinkhngi Daongrtmnhvbnhthnghsnythng
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 14
/Hmtrnglnglphnngcaphntkhitnhiutcnguvol ( )t ,
nuhmtruyntcaphntl ( )W p thhmquctnhtheocngthcno?
( )
( )
2
1L h t
W p=
( )
( )W pL h t
p=
( ) ( )L h t W p=
( )( )1
L h tW p
=
/Trongkhukhuchi,miquanhvphagiatnhiuvovtnhiural? Haitnhiuvovralngphavinhau Tnhiuvosmphahnsovitnhiuramtgcl
Tnhiuvochmphahnsovitnhiuramtgcl 2 Tnhiuvosmphahnsovitnhiu /Trongkhutchphn,miquanhvphagiatnhiuvovtnhiural? Tnhiuvosmphahnsovitnhiuramtgcl
Tnhiuvochmphahnsovitnhiuramtgcl 2
Tnhiuvosmphahnsovitnhiuramtgcl 2 Haitnhiuvovralngphavinhau
/Trongkhuviphn,miquanhvphagiatnhiuvovtnhiural?
Tnhiuvosmphahnsovitnhiuramtgcl 2 Tnhiuvosmphahnsovitnhiuramtgcl
Tnhiuvochmphahnsovitnhiuramtgcl 2 Haitnhiuvovralngphavinhau /Khivctnhbintnlogarithm,tnsctcxcnhtheocngthcno?
1c T =
21
cT =
cT =
20.logc T =
/ctnhbintnlogarithmcamtkhu ( ) 0L < khino?
( ) 0A
( )A =
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 16
( )3 2
10 4
8 5h
pW p
p p
+=
+ Chobithhgmnhngkhucbnno? Mtkhutchphn,haikhuquntnhbc1vmtkhuviphn Haikhutchphn,haikhuquntnhbc1vmtkhuviphn Haikhutchphn,mtkhuquntnhbc1vhaikhuviphn Haikhutchphn,mtkhuquntnhbc1vmtkhuviphnbc1 /Viiukingthmtkhuquntnhbcnhtlmvicnhmtkhunguynhm?
Tnslmvic c < Tnslmvic 0>
Tnslmvic c >
Tnslmvic c = /Miquanhgiahmquvhmtrnglng? Hmqulcnbc2cahmtrnglng Hmtrnglnglohmcahmqu Hmqulohmcahmtrnglng Hmtrnglnglcnbc2cahmqu
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 17
CHNG 3. KHO ST TNH N NH CA H THNG /HTKTcgilnnhnusaukhibphvtrngthicnbngdotcngcanhiuthhthngsc: Tnhiuradaongvibinkhngi Tnhiuradaongvibintngdn
Tnhiurastiuchnhtrlitrngthicnbng Tnhiuratintivcng
/HTKTskhngnnhnusailch ( )e t thamn:
( )lim
te t
( )lim
te t
hngs
( )lim
te t
daongcbinkhngi
( )lim 0t e t /HTKTcmtbngphngtrnhviphnbc n ,nghimtngqutcaphngtrnhviphnsctrngchoqutrnhnocahthng? Qutrnhhotngcahthng Khngthktlun Qutrnhqu Qutrnhxclp /HTKTcmtbngphngtrnhviphnbc n ,nghimringcaphng
trnhviphnsctrngchoqutrnhxclpcahthng? Sai ng /MunxttnhnnhcamtHTKT,tachphixtqutrnhxclp,nghaysai? ng Sai /Vnggchchotronghnhtrnctrngchovngnocahthng?
Khngcthngtin Khngnnh nnh Bingiinnh /iukincnthitmtHTKTnnhlcchscaphngtrnhctrng? >0
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 18
Cmthsdng =0
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 19
Hkhngnnh /Munxtnnhcahthng,trchttaxt: LpnhthcHurwitz iukinhnnh LpbngRouth
iukincnhnnh /TiuchunRouthcsdngxtnnhcho: Chchohthngcphnhim Hhvhkn Chchohkn Chchohh /TiuchunHurwitzthngcsdngxtnnhchocchthngcphngtrnhctrng: Bcrtcao
Bcthp ( )4n < Chomihthng Bccao /QutrnhqucamtHTKTcmtnhhnhtrn,vyhthngl:
nnh,daong bingiinnh nnh,khngdaong Khngnnh /QutrnhqucamtHTKTcmtnhhnhtrn,ngs4mththngctnhchtg?
nnh,daong bingiinnh Khngnnh,khngdaong Khngnnh,daong
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 20
/TheotiuchunNyquist,nuhhnnhhaybingiinnh( 0k = ),lch
knsnnhnuctnhTBPcahhcquanhnhthnoviim ( )1, 0j Khngbaoquanh iqua Khngcquanhg
Baoquanh /BngRouthcxydngnhsau:
Hs 2b trongbngRouthctnhtheocngthcnosauy?
0 42
1 5
a ab
a a=
0 42
1 5
a aba a
=
0 22
1 3
a ab
a a=
1 32
0 2
a ab
b b=
/PhtbiunosauylngvtnhchtcabngRouth?
CthnhnhocchiaccshngtrncngmtctcabngRouthvimtsdngthktqutnhtonvnkhngthayi CthnhnhocchiaccshngtrncngmthngcabngRouthvimtsdngthktqutnhtonvnkhngthayi CththmmtsdngvomthngbtkcabngRouththktqutnhtonvnkhngthayi CthnhnhocchiaccshngtrncngmthngcabngRouthvimtsmthktqutnhtonvnkhngthayi
/Nu ip nmbntritrconhhnhtrnthgcquaycanquanhgctactnhnhthno?
( )-
arg j ip
=
( )-
arg j ip
=
( )-
arg j 2ip
=
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 21
( )-
arg j 2ip
=
/TheotiuchunMikhailope,nubiuvectorathcctnhnhhnhtrnthhthngnysnnhnuPTTcancbc:
3 2 5 4 /NungcongbaoimM1nhhnhtrnthtaningcongbaoimM1
mtgcbng?
2
2
/dtrnnhl? Gitrphnocanghimsgntrconhtsoviccnghimkhc Gitrphnthccanghimsgntrcthcnhtsoviccnghimkhc Gitrphnocanghimsgntrcthcnhtsoviccnghimkhc Gitrphnthccanghimsgntrconhtsoviccnghimkhc /PhtbiunosauylngvtnhchtcabngRouth? SlniducaccshngtrongctutincabngRouthbngsnghimcaphngtrnhctrngcphnthcbng0
SlniducaccshngtrongctutincabngRouthbngsnghimcaphngtrnhctrngcphnthcm SlniducaccshngtrongctutincabngRouthbngsnghimcaphngtrnhctrngcphnthcdng Khngnilniug /TheotiuchunHurwit,mththngcphngtrnhctnhbc2vicchsdngs: Lunbingiinnh Lunkhngnnh Lunnnh nnhtrongastrnghp
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 23
/TheotiuchunNyquist,nuhthnghcctnhtn-bin-phanhhnhtrnthhthngkntngngcnnhkhng?
C Khng
/Nubiuvector ( )J j baotmtamtgcbng k thbiuvectorca
( )1 J j+
sbaoimnomtgcbng k?
( )0, 0
( )1, 0j
( )1, 1j
( )1, 0j
/Chohthnghchmtruynt:
( )2
1
1hW p
Tp p=
+ + .Vi 2T = thhkntngngcnnhkhng? Khng C /nhthcHurwitzbc n ctnhtheocngthcnodiy?
2 3 5
0 2 4
1 3
0
0
0 0
0 0 0
n
n
a a a
a a a
a a
a
=
1 1 5
0 2 4
3 3
1
1
0 1
0 0 0
n
n
a a a
a a a
a a
a
=
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 24
1 3 5
0 2 4
1 3
0
0
0 0
0 0 0
n
n
a a a
a a a
a a
a
=
0 3 5
0 2 4
1 3
0
0
0 0
0 0 0
n
n
a a a
a a a
a a
a
=
/Hmtruyntcahhcdng:
( )2 1
hk
W p
p p=
+ + .
Viiukinnoca kthhkntngngnnh?
1k <
2k >
1k >
2k < /HTKTchmtruyntdng:
( ) ( )k 4 3 2
3 1W
3 4 2 6 2 1
pp
p p p p p
+=
+ + + +
Hthngl: nnh Khngnnh Khngthxtnnhc bingiinnh /HTKTchmtruyntdng:
( )( )2
k2
2 9 19W
6 8
p pp
p p
+ +=
+ + Xcnhccimcc,imkhngcahthng?
imkhng: 1 25.62; 2z z= = ,imcc: 1 24; 3.38p p= =
imkhng: 1 22; 4z z= = ,imcc: 1 25.62; 3.38p p= =
imkhng: 1 25.62; 4z z= = ,imcc: 1 22; 3.38p p= =
imkhng: 1 25.62; 3.38z z= = ,imcc: 1 22; 4p p= = /Chohthngcitngiukhin:
0 3 2
1
W ( ) 5 8 4p p p p= + + +
vbiukhin CW ( ) P Dp K K p= + (BPD)
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 25
Tmphngtrnhctrngcahthngkn?
3 2( ) 5 (8 ) (4 ) 0D PA p p p K p K= + + + + =
3 2( ) 5 (8 ) (4 ) 0D PA p p p K K= + + + + + =
3 2( ) 5 (8 ) (4 ) 0D PA p p p K p K= + + + + + =
3 2( ) 5 (8 ) (4 ) 0D PA p p p K p K= + + + + =
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 26
CHNG 4. NH GI CHT LNG H THNG IU KHIN TNG
/Saistrngthixclpctnhtheocngthcno( ( )e t lsailchngcntntitrongqutrnhiukhin)?
( ) ( )0lim limt pe t pE p = =
( ) ( )
0lim lim
t pe t pE p
= =
( ) ( )2
0lim lim
t pe t p E p
= =
( ) ( )
0lim lim
t pe t E p
= =
/quiuchnhcaiukhincxcnhtheocngthcno?
max 0% 100y yy
=
max% 100y y
y
=
max% 100y y
y
=
% 100y y
y
=
/BiniLaplacecahm ( )u t kt = ?
k p
kp
2k p
2kp
/Muntmmcnnh,tathaybiuthcnosauyvophngtrnhctrngcahthng?
p j = +
p j = +
p j =
p j =
/NuHTKTcmtnhhnhtrnthmiquanhgia ( )E p v ( )Y p l?
( ) ( ) ( )hY p W p E p= +
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 27
( ) ( ) ( ).hE p W p Y p=
( ) ( ) ( ).hY p W p E p=
( ) ( ) ( )hE p W p Y p= +
/Muntrittiusailchtnhcahthng,thngthngngitasdngthmkhucbnnodiy? Tchphn Viphn Khuchi Khutr
/NunghimcaPTTnmtrongvnggchchonhhnhtrnthcgilg?
dtrnnh Hsnnh dtrdaong Hsdaong
/Vitnhiuvo ( ) ( )1u t t=
,saisxclpctnhtheocngthcno?
( )( )0
1lim
1p hp W p =
+
( )0
1lim
1p hW p =
+
( )0
lim1p h
p
W p =
+
( )( )
1lim
1p hp W p
=
+
/Thigianqu qdtcxcnhbngcchno?
Lthiimmhmqutgitrcci Lthiimmlnutinhmquttrsxclp Lthiimmhthngdaongnhiunht
Lthiimmhmqu ( )y t khngvtrakhibingiicamingiihn quanhtrsxclp /Nuhmtruynthcdng:
( ) 10 11
0 1
... 1
... 1
m mh r n r n r
b p b pkW pp a p a p
+ + +=+ + +
th rcgilg?
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 29
Thigiancquiuchnh Thigianpng /Nuhlkhuquntnhcdng
( )
1
kW p
Tp=
+
thsailchtnhbngbaonhiu,vitnhiuvo ( ) ( )1u t t= ?
1
1k =
2
1
1k =
+
1
1k =
+
1k = +
/Muntrittiusailchtnhtrongkhuquntnh( 0 = )thphimcnitipkhuquntnhvikhuchmtruyntnhthnotothnhhvsaicp1? p
2p
21 p
1 p /Nhntnocnhhnglnnvicxcnhsailchtnhcahthng?
Khutchphn dtrdaong dtrnnh Sailchtnh /DavonghimcaPTT,tacthnhgicphnnochtlngcaqutrnhqu.VynuttcccnghimcaPTTcphnbtrntrcthcthcthkhngnhqutrnhqucahthng: Chtlngqurtkm Cdaong Chtlngqurttt
Khngdaong
/Vitnhiuvo ( )u t kt = ,saisxclpctnhtheocngthcno?
( ) 20
1lim .
1p h
k
W p p =
+
( )0
1lim .
1p h
k
W p p =
+
( )
20
1lim .
1ph
k
W pp
=
+
( )
1lim .
1p h
k
W p p =
+
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 30
/Saisxclpcahthngchmtruynth:
( )h 21
W pp p k
=+ +
khiuvo ( ) ( )1u t t= lbaonhiu?
( )1k k+
( )1 k k+
k
1 k
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 31
CHNG 5. TNG HP H THNG IU KHIN TNG
/Biukhinviphn(D-Derivative)thngcdngtrongthct,nghaysai? Sai ng
/Biukhintl(P-Proportional)ctcdngnhmtkhu Tchphn Viphn Khutr Khuchi /Thayihskhuchicthtrittiusailchtnh? Sai ng
/Khixcnhcccthamstiucabiukhinmhthngiukhinvnkhngthamnccyucutra,chngtaphilmg? Chpnhnktqudkhngththamnyucutra Khngsdnghthngna Sdngbiukhinphctphn Thayicutrchthngiukhintng /Tnhiuiukhintheoquyluttlcxydngtheocngthcno,trongxltnhiura,eltnhiuvo?
px K=
.px K e=
1. .i
i
x K e dt e dtT
= =
x e= /Trongquyluttchphn,tnhiuiukhincxcnhtheobiuthc:
1. .i
i
x K e dt e dtT
= =
(trong 1i iT K= cgilhngsthigiantchphn).Vytisaouimcaquyluttchphnltrittiusailchtnh?
Vkhi iTcgitrrtlnth 0x =
Vgitriukhinx chtcgitrxclp(qutrnhiukhinktthc)khi 0e = Vgitriukhinx chtcgitrxclp(qutrnhiukhinktthc)khi e = Vgitriukhinx thayitheotchphncae
/Trongkhuviphn,tnhiuralunlunsmphahntnhiuvomtgc 2 .iunynilnuimcakhuviphnlctcngnhanh,iunghaysai? ng Sai
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 32
/BiukhinPDthngcdngchonhnghthngccimgnibt? Cnctcngnhanh Cnchnhxccao Khngcnhiutcng Cncnnhbnvng
/NitcngcaquylutPInhanhhnquylutPnhngchmhnquylutIlnghaysai? ng Sai /Khithayit0n thctnhphatncabiukhinPDsthayinhthno?
T 2 n0
Bng 2 ,khngthayi
T 2 n 2 T0n 2 /Trongcngnghip,quyluttl(P)thngcdngchonhnghthngccimg? Yucutcngrtnhanh Chophptntisailchtnh Khngnnh Yucuchnhxccaiukhinphicao
/Nivtcng,quylutPIDcncthnhanhhncquyluttl,iunghaysai? Sai ng /ctnhcakhutchphnltnhiuracanlunchmphasovitnhiuvo
mtgc 2 ,iunynghal: Quyluttchphnctcngnhanh Quyluttchphnctcngchm Quyluttchphnctcngnnh
Khngcnghag /Hskhuychicabiukhintlcnglnthhthng Hthngstinnbingiinnh Cngnnhhn Khngnhhngntnhnnhcahthng Cngmtkhnngnnh /Tcdngcakhutchphntrongbiukhin? Lmtngtccabiukhin Rtngnqutrnhqucahthng Lmgimtccabiukhin Trittiusailchtnh
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 33
/Chcnngcakhuviphntrongbiukhin(nuchnngthngschon)? Hnchtcdngcakhuviphn Lmtngtnhnnhcahthng Cithinqutrnhqu Trittiusailchtnh
/Mcchcaphngphpbnhiuphtillmchohthng Lmtngnhhngcanhiu Btbinvitcng Lmgimnhhngcanhiu Khngcmcchnorrt /cimcahthngiukhinchngtrnh? Tnhiurathayilintc Tnhiuvocgicnh Tnhiuvothayilintc Tnhiuracgicnh
/Trongcutrccahthngiukhintngthngthngcmythitbiukhin? 3 2 5 4 /Kthpquyluttlviquyluttchphntoraquyluttl-tchphn.VybiukhinPIccimgnibt? Ctcngchmnhngtrittiucsailchd
Ctcngnhanhnhngkhngtrittiucsailchd Vactcngnhanh,vatrittiucsailchd Ctcngchmvkhngtrittiucsailchd /Xcnhcchngsthigiantchphn,viphntrongbiukhinPIDctnhiuiukhindng:
1. . . . .p I d P d
i
de dex K e K e dt K K e e dt T
dt T dt
= + + = + +
d p iT K K=
, p d pT K K=
i p iT K K=
, d d pT K K=
i p iT K K=
, d p dT K K=
i i pT K K=
, d d pT K K=
/GclchphagiatnhiuravtnhiuvotrongbiukhinPID? 0
2
2
Nmtrongkhongt2n
2
/Hmtruyntcaquyluttl-vitchphncdng?
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 34
( )1
1 ..
p di
W p K T pT p
= + +
( )1 1
1 ..
pi d
W p K pT p T
= + +
( ) 1 .ip dTW p K T p
p = + +
( )1
1 ..
p id
W p K T pT p
= + +
/Hthngbtbinvinhiuphticxydngnhhnhtrn.Xcnhhm
truyntcakhu ( )bW p ?
( )( ) ( )
( )1 2
3
.b
W p W pW p
W p=
( )( )
( ) ( )3
1 2.b
W pW p
W p W p=
( )( ) ( )
( )1 2
3
.b
W p W pW p
W p=
( )( )
( ) ( )3
1 2.b
W pW p
W p W p=
/Hthngiukhintngnhhnhtrn.itngiukhincathitbiukhin
( )1mW p phicxcnhtheocngthcno?
( )( )
( ) ( )2
12 21 .
md
m
W pW p
W p W p=
+
( )( ) ( )
( )2 1
12
.md
W p W pW p
W p=
( )( ) ( )
( ) ( )2 1
12 2
.
1 .
md
m
W p W pW p
W p W p=
+
( ) ( ) ( )( ) ( )
2 11
2 2
.1 .
md
m
W p W pW pW p W p
=
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 36
/Khitnghphthngiukhintngnhhnhtrn,vnctralmboqutrnhqu
camchvngtrong ( ) ( )( )2 2mW p W p phixyranhthnosovimchvngngoi
(mchvngchnhvithitbiukhin ( )1mW p )?
Nhanhhnrtnhiu Bng Chmhnrtnhiu Khngbrngbuclnnhau /Hthngtuyntnhcmtbiphngtrnhtrngthicp2:
[ ]
1 2 1. .
1 1
1 0 .
x x uk
y x
= +
=
Vigitrnoca kthhthngiukhinchonton? 2k
3k
4k
5k /Hthngtuyntnhcmtbiphngtrnhtrngthicp2:
[ ]
1 2 1. .
1 1
1 0 .
x x u
k
y x
= +
=
Vigitrnoca kthhthngquanstchonton? 2k
1k
3k Mik
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 37
CHNG 6. M T TON HC H RI RC /Nutimtmtxchno,tnhiukhngctruynilintcthhlginon,iunghaysai? ng Sai
/Vicchuyntnhiutlintcthnhginoncgil Tuyntnhhatngon Lngtha Phituynhangcong Rirchatngon /Trongphngphplngthatheothigian,phplngtcthchintheo: Nhngkhongthigianbngnhau Nhngmcbngnhau Nhngkhongthigianthayi
Nhngmcnhtnh,phthucvotnhiuvo /Trongcchthngrircthngthng,ngoiphntxung,ccphntkhccnlitronghthnglccphnt Rirctuyntnh Phituyn Lintctuyntnh Ty /Hnhtrnlphngphplngthatheo
Hnhp Mc Bin Thigian
/Skhicamththngrirccchratrnhnhtrn.Khu ( )LGW p ccimg?
Lngthatnhiutheomc Lngthatnhiutheothigian
LmchogitrhmrircthayitrongkhongthigianT TrongkhongthigianT,gitrhmrirccgikhngi
/Saiphncp1ctnhtheocngthc?
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 38
( ) ( ) ( )1i x i x i = +
( ) ( ) ( )1i x i x i = + +
( ) ( ) ( )1 1x i x i x i = +
( ) ( ) ( )2i x i x i = +
/Qutrnhnghccamththngrirccthcmtbiphngtrnhviphn,nghaysai? ng Sai /Hmtruynttronghrircltsgiatnhiuravtnhiuvocbiudintrongminno? TrongminZviiukinutrittiu TrongminLaplacerircviiukinutintivcng
TrongminLaplaceviiukinutrittiu Trongminthigian
/ViccgitrT (thigianctmu)khcnhauthktquchuynhthngtminlintcsangminrirctngngskhcnhau,nghaysai? ng Sai /iukingphngtrnhsaiphnsaucbcn ?
( ) ( ) ( ) ( ) ( )0 1 11 ... 1n na y i n a y i n a y i a y i u i+ + + + + + + =
0na
0, 0na a
00, 0na a =
00; 0na a=
/Phngtrnhtrngthimthrirchnhtrncdng?
( ) ( ) ( )
( ) ( ) ( )
1 d d
d d
i A x i B u i
y i C x i D u i
+ = +
= +
( ) ( ) ( )
( ) ( ) ( )
1 d d
d d
i C x i B u i
y i A x i D u i
+ = +
= +
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 39
( ) ( ) ( )
( ) ( ) ( )
1 d d
d d
i A x i B u i
y i D x i C u i
+ = +
= +
( ) ( ) ( )
( ) ( ) ( )
1 d d
d d
i B x i A u i
y i C x i D u i
+ = +
= + /Cpcasaiphncaonhtluntrngvicpcaonhtcaphngtrnhsaiphnlnghaysai? Sai ng /Lngthatheomcl: Tnhiurallintc Tnhiuracchiathnhccmcbngnhauphthuctnhiuvo Tnhiuracchiathnhccmckhcnhauphthuctnhiuvo Tnhiurathayikhngngk /Hmtruyntcablugibc0(ZOH)?
( ) ( )-1 1 pLGW p e
p
= +
( ) ( )1 1 pLGW p e
p
= +
( ) ( )-1 1- pLGW p e
p
=
( ) ( )1
1-p
LGW p ep
=
/BiniZ cakhu1 p ?
( )1 1 z
( )11 1 z+
( )11 1 z
( )1
1 1 z
/Trong3phngphpchuynhthngtminlintcsangminrirc(dngbiniLaplace,tnhgnngohmcp1vphngphphnhthang),phngphpnochochnhxccaonht? Phngphphnhthang Tnhgnngohmcp1 Cbachochnhxcnhnhau DngbiniLaplace
/Nutnhiuvocakhu1
zl ( )2y i
+thtnhiuracanlg?
( )3y i +
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 40
( )1y i +
( )2y i +
( )4y i +
/Chohthngxungnhhnhtrn.ulbiuthcngbiudinmiquanhgiacctnhiutronghthng?
( ) ( ) ( ) ( ){ } ( ). .LG LT FHF z Z W p W p W p U z=
( ) ( ) ( ){ } ( ).LT FHF z Z W p W p E z=
( ) ( ) ( ) ( ){ } ( ). .LG LT FHF z Z W p W p W p Y z=
( ) ( ) ( ) ( ){ } ( ). .LG LT FHF z Z W p W p W p E z=
/Hthngcmttrongkhnggiantrngthiviccmatrntrngthitngngl:
0.5 3
2 1
kA
= ;
1
0B
=
; [ ]1 0C = .Vi kbngbaonhiuthhthngtrnliukhinchonton? 0k >
0k <
Migitrca k Khngtntigitrnoca khthngtrniukhinchonton /Miquanhgiaminz vminLaplace?
Tz e=
pz e=
pTz e=
pTz e= /Nuphngtrnhtrngthichchobit:
( ) ( ) ( )1 d dx i A x i B u i+ = +
thtacthxtcctnhgcahthng? Tnhnnh Khngthngtinxtmttrongccctnhcahthng Tnhquanstc Tnhiukhinc
/Nuphngtrnhtrngthichchobit:
( ) ( ) ( )d dy i C x i D u i= + thtacthxtcctnhgcahthng?
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 41
Tnhnnh Khngthngtinxtmttrongccctnhcahthng Tnhquanstc Tnhiukhinc /Cchbiniththnglintcsanghthngrirctrongkhnggiantrngthi
theophngphptnhgnngohmcp1?(TrongI lmatrnnv., , ,A B C D lccmatrntrngthitronghlintcv , , ,d d d d A B C D lccmatrn
trngthitronghrirc)
; ; ;d d d d A I A B TB C C D D= + = = =
; ; ;d d d d A I TA B TB C C D D= = = =
; ; ;d d d d A I TA B TB C C D D= + = = =
; ; ;d d d d A I TA B B C C D D= + = = =
/Cchbiniththnglintcsanghthngrirctrongkhnggiantrngthi
theophngphphnhthang?(TrongI lmatrnnv. , , ,A B C D lccmatrn
trngthitronghlintcv , , ,d d d d A B C D lccmatrntrngthitronghrirc)
1 1
. ; ; ;2 2 2
d d d d TA TA TA
A I I B I C C D D
= + = = =
1 1
. ; . . ; ;2 2 2
d d d d TA TA TA
A I I B I T B C C D D
= + = = =
1
. ; . . ; ;2 2 2d d d d
TA TA TAA I I B I T B C C D D
= + = = =
1
. ; . . ; ;2 2 2
d d d d TA TA TA
A I I B I T B C C D D
= + = = = /NuhthngiukhinxungtuyntnhcmhnhnhhnhtrnthhmtruyntcahhcxcnhtheocngthcnonuhmtruyntcakhuZOHl:
( ) ( )-1 1- pTLGW p e
p=
?
( ) ( ){ } ( )
( ). 1 .
LTLG LT
W p
Z W p W p z Z p
=
( ) ( ){ } ( ) ( ){ }1. 1 .LG LT LTZ W p W p z Z W p=
( ) ( ){ } ( ) ( )1. 1 . LTLG LTW p
Z W p W p z Zp
=
( ) ( ){ } ( ) ( )1. 1 . LTLG LTW p
Z W p W p z Zp
= +
/NuhthngiukhinxungtuyntnhcmhnhnhhnhtrnthhmtruyntcahkncxcnhtheocngthcnonuhmtruyntcakhuZOHl:
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 42
( ) ( )-1 1- pTLGW p e
p=
?
( )( )( )
( ){ }( ) ( ) ( ){ }1 . .
LTk
LG LT FH
Z W pY zW z
U z Z W p W p W p= =
+
( ) ( )( )
( ) ( ){ }( ) ( ){ }.
1 .LG LT
kLG FH
Z W p W pY zW zU z Z W p W p
= =+
( )( )( )
( ) ( ){ }( ) ( ) ( ){ }
.
1 . .
LG LTk
LG LT FH
Z W p W pY zW z
U z Z W p W p W p= =
+
( )( )( )
( ) ( ){ }( ) ( ) ( ){ }
.
1 . .
LG LTk
LG LT FH
Z W p W pY zW z
U z Z W p W p W p= =
/BiniZcakhu
( )1 p a+?
( )1 1 .aTe Z
( )11 1 .aTe Z
( )11 1 .aTe Z
( )11 1 .aTe Z +
/invoccvtr1,2,3,4tronghnhtrntheongthtnmtscu
trctrngthicahrirc?
, , ,d d d d B C A D
, , ,d d d d B C D A
, , ,d d d d B D A C
, , ,d d d d B A C D
/Phngtrnhsaiphnsau:
( ) ( ) ( ) ( )3 22 6 5 0y i y i y i y i + + + =
tngngviphngtrnhnotrong4trnghpdiy?
( ) ( ) ( )2 1 5 0y j y j y j+ = + + =
vi 1j i= +
( ) ( ) ( )2 1 5 0y j y j y j+ + =
vi 1j i= +
( ) ( ) ( )2 1 5 0y j y j y j+ + + =
vi 1j i= +
( ) ( ) ( )2 1 5 0y j y j y j+ + + =
vi 2j i= +
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 43
/Viiukinutrittiu,hmtruyntmatrncbiudindidngno?
( )( )
( )( )
1d d d
Y zW z C ZI A B
U z
= =
( )( )
( ) ( )
12
d d d
Y zW z C ZI A B
U z
= =
( )( )( )
( )d d dY z
W z C ZI A BU z
= =
( )( )( )
( )1
d d
Y zW z C ZI A B
U z
= =
/Chohiukhinlintctuyntnhcbiudindidngphngtrnhtrngthi:
[ ]
1
2
1
2
0.5 1.5 1.2 3 0
1 0 .
x ux
xy
x
= +
=
Vichuklymu ( )0.25T s= ,chuynhthngnysangdngrirctheophngphptnhgnngohmbcnht?
[ ]
1
2
1
2
1.125 0.375 0.25.
0.5 1.75 0
1 0 .
xu
x
xy
x
= +
=
[ ]
1
2
1
2
1.125 0.375 0.25.
0.5 1.75 0
1 0 .
xu
x
xy
x
= +
=
[ ]
1
2
1
2
1.125 0.375 0.25.0.5 1.75 0
1 0 .
x ux
xy
x
= +
=
[ ]
1
2
1
2
1 0.375 0.25.
0.5 1.75 0
1 0 .
xu
x
xy
x
= +
=
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 44
CHNG 7. PHN TCH V THIT K H THNG RI RC /xttnhnnhcamththngrirc,taphilmg? Tmnghimcaphngtrnhviphnbiudinhthng Tmnghimcaphngtrnhsaiphnbiudinhthng Lpmatrnquanstc
Lpmatrniukhinc /Nghimtngqutcaphngtrnhsaiphnctrngcho: Khngthngtinktlun Qutrnhqucahthng Qutrnhxclpcahthng Tnhiukhinccahthng /Tronghrirc,qutrnhxclpnhhngntnhnnhcahthng? ng Sai
/( )cos sinT j T +
luncmodulegiihnbngbaonhiu? 10 -1 1 0
/NuTz e=thvi 0 > tac:
1z >
1z <
1z >
1z =
/HrircsnnhnunghimcaPTTcahthng: Nmngoingtrnnv Nmtrongngtrnnv Nmtrnngtrnnv Nmgcta /Hrircsbingiinnhnu: PTTcmtnghimnmtrnngtrnnvvccnghimcnlinmtrongngtrnnv PTTcmtnghimnmngoingtrnnv TtcccnghimcaPTTnmngoingtrnnv TtcccnghimcaPTTnmtrongngtrnnv /Hrircskhngnnhnu: TtcccnghimcaPTTnmtrongngtrnnv PTTcmtnghimnmngoingtrnnv PTTcttcccnghimnmtrnngtrnnv PTTcmtnghimnmtrnngtrnnvvccnghimcnlinmtrongngtrnnv
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 45
/Mththngcgiliukhincnutacthtmcmtvectoriu
khin ( )u i chuynchthngtmttrngthibanubtk ( )0x nmttrng
thicuibtk ( )n ? Trongmtkhongthigianvhn
Trongmtkhongthigianhuhn
Phichuynvtrngthi ( )0 ngaylptc
Hduytrtrngthiim ( )x n
/Cthdngcctiuchunxtnnhchohlintcxtnnhchohrirc? ng Sai /Hrirctntikhnngnnhvtn.iunyhlintckhngc? Sai ng /iukincnmthrircnnhlcchscaPTTdng,nghaysai? Sai ng /Gishrirccathcctrng:
( ) 10 1 1...
l ll lA z a z a z a z a
= + + + + .
xtiukinnnhcahthngtheotiuchunJurytaphitm ( )1A ,thnghal:
Thay 1z = vo ( )A z
Thay 0z = vo ( )A z
Thay 1z = vo ( )A z
Thay 1l= vo ( )A z /TheotiuchunJury,munxttnhnnhcahrirccPTTdng:
1
0 1 1... 0l l
l la z a z a z a
+ + + + = ,hthngphithamnbaonhiuiukinrngbuc? 4l+
1l+
3l+
2l+
/Theophngphpbinibotonhnhdng,iukin1z >stngngvi
iukinnocav ? Nmbnphitrcotrongmtphngv Nmbntritrcotrongmtphngv
Nmtrntrcotrongmtphngv Nmtrongngtrnnvtrongmtphngv /Nghimringcaphngtrnhsaiphn
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 46
ctrngchoqutrnhqucahthng Khngchothngtinvnlunthayi Dngxttnhnnhcahthng ctrngchoqutrnhxclpcahthng /nhnghatnhiukhincvquanstccahrircgingvihlin
tc? ng Sai
/VipTz e= v
Tz e=thvi 0 > stngngvinghimcaphngtrnhnm
vtrnotrongmtphngz? Nmtrongngtrnnv Nmngoingtrnnv Cthnmbtcutrongmtphngz Nmtrnngtrnnv
/Vi pTz e= vT
z e
= thvi 0 = (nghimnmtrntrco jcamtphngphc)stngngvinghimccimgtrongmtphngz ? Nmgcta Nmbnngoingtrnnv Nmbntrongngtrnnv Nmtrnngtrnnv /GishrirccPTT:
1
0 1 1... 0l l
l la z a z a z a
+ + + + = .Theophngphpbinibotonhnhdng,tatbinph?
1
1
vz
v+=
1
1
vz
v
=
+
1
vz
v=
+
1vz
v
+=
/Mcchcaphngphpbinibotonhnhdng? dngcctiuchunisxtnnhchohlintc tngbccaphngtrnhctrng,lmchohthngnnhhn xtnnhchohrirc PTTcrtgnhn /Nhnxthrirckmnnhhnhlintclnghaysai? Sai ng /Cctiuchdngnhgichtlngqucahlintckhngcpdngchohrirc? Sai ng
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 47
/Nhngtiuchnosauydngnhgihthngtrongminkhnggiantrngthi? Tnhiukhincvquanstc Tnhiukhinc,tnhquanstcvthigianqu Tnhiukhinc,tnhquanstcvtnhnnh
Tnhiukhinc,tnhquanstcvquiuchnhcci /Saisxclpcahrirccxcnhtheocngthcnodiy?
( ) ( ) ( ) ( )1
1lim lim 1i z
e e iT z E z
= =
( ) ( ) ( ) ( )1
1lim lim 1i T z
e e iT z E z
= =
( ) ( ) ( ) ( )1lim lim 1
i T z T e e iT z E z
= =
( ) ( ) ( ) ( )11
lim lim 1
i T z
e e iT z E z
= = +
/Tiuchunnnhtheonguynlgcquaycahthngrirctngngvitiuchunnovxtnnhcahknvhhlintc? Mikhailope Routh Hurwitz Nyquist
/NuPTTcahrirccbc lththeotiuchunJury,taphilpbngJurycshngbngbaonhiu?
2 1l 2 2l
2 3l
2l /GishthngrirccPTTdng:
( ) 10 1 1... 0
l ll lA z a z a z a z a
= + + + + =
ththeotiuchunJury,iukincnkimtrautinbithchocnnhkhngl:
( )1 0A >
( )1 0A
/NuttcccnghimcaPTTphnbgcphntthIvIV(nghimphclunithnhcp)thtnsdaongcahthngnmtrongkhongno?
0 < <
2 0 < <
0 2< <
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 48
2 2 < < /MttrongnhngiukinhthngrirccphngtrnhctrngnnhtheotiuchunJuryl:
( )1 0A =
nu lchnv ( )1 0A < nu ll
( )1 0A > nu lchnv ( )1 0A < nu ll
( )1 0A nu ll
( )1 0A >
nu lchnv ( )1 0A =
nu ll /NunghimcaPTTlim5(nmtrntrcOC)nhhnhtrnthhthngsdaongvitnsbngbaonhiu?
2
2 / ulngbinthincatnhiurakhinghimcaPTTlim6trnhnhdi?
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 50
c b a d
/GishthngcPTTdng:22 3 4 0z z+ + = ,saukhidngphngphpbini
botonhnhdngtacphngtrnhtngngl:
28 4 3 0v v + =
29 4 3 0v v+ + =
29 4 3 0v v + =
29 4 3 0v v =
/iukinhthngcPTTbcnhtdng: 0 1 0a z a+ = nnhtheophngphpbotonhnhdngl?
0 1a a
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 51
/HthngxungcmttrongkhnggiantrngthisiukhinchontonkhivchkhimatrnM chngbngn .MatrnM cxydngthno?
( ) ( )
1 2' . ' . ...
n nd d d d d M A B A B B
=
1 2. ' . ' ... 'n nd d d d d M A B A B B =
1 2. . ... 1
n nd d d d M A B A B
=
1 2. . ...
n nd d d d d M A B A B B
=
/Vitnhiuvo ( ) ( )1u t t= ,saisxclpcahrirccxcnhtheocngthcno?
( ) ( ) ( ) ( ){ }1
1
lim 1 . .z LG LT FHe Z W p W p W p = +
( )( ) ( ) ( ){ }
1lim
1 . .z LG LT FHe
Z W p W p W p =
+
( )( ) ( ) ( ){ }
1lim
1 . .z T LG LT FHe
Z W p W p W p =
+
( )( ) ( ){ }11
lim1 .z LT FH
eZ W p W p
=+
/ HthngxungcmttrongkhnggiantrngthisiukhinchontonkhivchkhimatrnN chngbngn .MatrnN cxydngthno?
( )
1. ... .
nd d d d d N C A C A C
=
( )
1' ' '. ... .
nd d d d d N C A C A C
=
( )
1' '. ... .
n
d d d d d N C A C A C
=
( )
1' ' ' ' '. ... .
n
d d d d d N C A C A C =
/Chohthngcbiudintrongkhnggiantrngthidng:
( )( )
( )( )
( )
( ) [ ]( )( )
1 1
2 2
1
2
1 1 2 1
1 2 1 1
1 0
x i x iu i
x i x i
x iy i
x i
+ = + +
=
Matrniukhincvhngcamatrn?
3 1
1 1M
= , ( )rank 1M =
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Bn cng bcho sinh vini hc txa. Chsdng cho mc ch hc tp. 52
3 1
1 1M
= , ( )rank 2M =
3 1
1 1M
=
, ( )rank 2M =
3 1
1 1M
= , ( )rank 2M =
/Chohthngcbiudintrongkhnggiantrngthidng:
( )( )
( )( )
( )
( ) [ ]( )
( )
1 1
2 2
1
2
1 1 2 1
1 2 1 1
1 0
x i x iu i
x i x i
x iy i
x i
+ = + +
=
Matrnquanstcvhngcamatrn?
1 1
1 2N
= , ( )rank 2N =
1 1
0 2N
= , ( )rank 2N =
1 1
0 2N
= , ( )rank 3N =
1 1
0 2N
=
,
( )rank 2N =
/HmtruyntcabiukhinPIDs?
( )( )
( )
( ). 112 1 .
piPID d
k zk T zW z k
z T z
+= + +
( )( )
( )( )1 . 1
2 1 .
i dPID p
k T z k zW z k
z T z
+ = + +
( )( )
( )
( )1 . 12 1 .
d iPID p
k T z k zW z k
z T z
+ = + +
( )( )
( )( )1 . 1
2 1 .
p dPID i
k T z k zW z k
z T z
+ = + +
/Khitnhiuvo ( )u t t= ,saisxclpcahrirccxcnhtheocngthcno?
( )( ) ( ) ( ) ( ){ }1
lim1 1 . .z LG LT FH
Te
z Z W p W p W p =
+
( ) ( ) ( ) ( ) ( ){ }1
1
lim 1 1 . .z LG LT FHe z Z W p W p W p = +
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( )( ) ( ) ( ){ }1
lim1 . .z LG LT FH
Te
Z W p W p W p =
+
( )( ) ( ) ( ) ( ){ }1
lim1 1 . .z LG LT FH
Te
z Z W p W p W p =
+ +
/Tmhmtruyntcahthngchotronghnhd?
( ) 2 32 3 1 21
W WW p
W W W W =
+ +
( ) 1 22 3 1 21
W WW p
W W W W =
+ +
( ) 1 3
2 3 1 21
W WW p
W W W W =
+ +
( ) 1 2 32 3 1 21
W W WW p
W W W W
=
+ +