Chuong3 NDHT K2010 Slide

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/

12 October 2010 H. T. Hong - HBK TPHCM 1

Chng 3Chng 3

NHN DNG M HNH KHNG THAM SNHN DNG M HNH KHNG THAM S


Gii thi

Noi dung chng 3Noi dung chng 3

Gii thiu Phn tch p ng qu Phn tch tng quan Phn tch tng quan Phn tch p ng tn s Phn tch Fourier Phn tch ph


Th kh

Noi dung chng 3Noi dung chng 3

Tham kho: [1] L. Ljung (1999), System Identification Theory for the user.

chng 2 v chng 6chng 2 v chng 6.[2] R. Johansson (1994), System Modeling and Identification.

chng 2 v chng 4.g g[3] N. D. Phc v P. X. Minh (2001), Nhn dng h thng iu

khin (chng 2)


Gii thiuGii thiu


Bi ton nhn dng h thngBi ton nhn dng h thng

Nhn dng h thng l xy dng m hnh ton hc ca h thng datrn d liu vo ra quan st c.

( ) (t)He thongu(t)y(t)

tn hiu ratn hiu vo

Ty theo phng php nhn dng m ta chn tn hiu vo thch hp.Tn hiu xung diracTn hiu hm ncTn hiu hnh sinTn hiu ngu nhin


Bi ton nhn dng h thngBi ton nhn dng h thng

v(t)

H thngu(t) y(t)

v(t)

u(k) y(k)

K hiu tp hp N mu d liu quan st c l:

u(k) y(k)

{ })(),(,),1(),1( NuNyuyZ N K=V h h d h h l h V mt ton hc, nhn dng h thng l tm nh x:

khi bit tp d liu Z N)()(: kykuTM a


khi bit tp d liu Z N

H t H t h i l t i bi i Z

H thng tuyn tnh bt binH thng tuyn tnh bt bin

Hm truyn: Hm truyn ca h ri rc l t s gia bin i Z ca tn hiu ra v bin i Z ca tn hiu vo khi iu kin u bng 0

)(zY)()()(

zUzYzG =

+=

=k

kzkyzY )()(

+=

=k

kzkuzU )()(


l h th khi t hi


p ng xung: p ng xung l p ng ca h thng khi tn hiu vo l hm dirac.

1)( =zU)()( zGzY =

{ })()()( 1 zGkgky Z

1)(zU

{ })()()( zGkgky == Zg(k) gi l p ng xung ca h thng


T h h th d


Tnh p ng ca h thng da vo p ng xung:)()()( kukgky =

++=

=l

lkulgky )()()(

i vi h nhn qu: g(k) = 0, k < 0, ta c++=

=0

)()()(l

lkulgky



K hiu q l ton t lm sm 1 chu k ly mu: )1()(. += kukuq

v q1 l ton t lm tr 1 chu k ly mu:)1()(.1 = kukuq

p ng ca h thng trong min thi gian c th vit li l:++=

=0

)()()(l

l kuqlgky

)()()( kuqGky = )()()( kuqGky =k zGqkgqG

+ == )()()(12 October 2010 H. T. Hong - HBK TPHCM 11

qzk

zGqkgqG == )()()(

0


t h t t h t l i l h bit t l bi c tnh tn s: c tnh tn s l i lng cho bit t l v bin v lch pha gia tn hiu ra trng thi xc lp v tn hiu vohnh sin.

jezj zGeG == )()(

kTUku m sin)( =Nu tn hiu vo l:)sin()( += kTYky mv tn hiu ra xc lp l: )()( y mp

)( jm eGY =Th: )(mU

)( jeG=12 October 2010 H. T. Hong - HBK TPHCM 12

)( eG=


v(t)

H thngu(t) y(t)( )

H thng c nhiu: Mi h thng thc u b nh hng bi nhiuu(k) y(k)

g g g(nhiu o lng, nhiu do cc tn hiu vo khng kim sotc,). Gi thit nhiu tc ng vo h thng l nhiu cng. Tnhiu ra ca h thng c nhiu l:hiu ra ca h thng c nhiu l:

)()()()(0

kvlkulgkyl

+=+= +

n gin, gi s nhiu c th m t bi:

trong {e(k)} l nhiu trng (nhiu trng l chui bin ngu nhin

0l= +=

=0

)()()(l

lkelhkv


trong {e(k)} l nhiu trng (nhiu trng l chui bin ngu nhin c lp xc nh bi mt hm mt xc sut no ).

Nhn dng m hnh khng tham sNhn dng m hnh khng tham s

Phng php nhn dng m hnh khng tham s l phng php Phng php nhn dng m hnh khng tham s l phng phpxc nh trc tip p ng xung g(k) hoc c tnh tn s G(ej) cah thng (m khng cn s dng gi thit v cu trc m hnh ca hh )thng).

Cc PP nhn dng m hnh khng tham s c th chia lm 2 nhm: Phng php trong min thi gian (c lng ))( kg Phng php trong min thi gian (c lng ) Phng php phn tch qu (phn tch p ng xung, phn

tch p ng nc)

)(kg

Phng php phn tch tng quan Phng php trong min tn s (c lng )

)( jeG Phng php phn tch p ng tn s Phng php phn tch Fourier Ph h h t h h


Phng php phn tch ph

Qu trnh ngu nhinQu trnh ngu nhin


nh ngha bin ngu nhinnh ngha bin ngu nhin

Bin ngu nhin l bin m gi tr ca n l ngu nhin khng d Bin ngu nhin l bin m gi tr ca n l ngu nhin, khng d on trc c.

Bin ngu nhin X c gi l bin ngu nhin lin tc nu: Tp hp cc gi tr ca X c th lp y mt hay mt s khong

ca trc s, thm ch lp y trc s. X t X h t i t th l l b 0 Xc sut X nhn mt gi tr c th no lun lun bng 0,

ngha l vi mi s a ta c . Hm mt xc sut: Hm s xc nh trn ton b trc s

{ } 0== aXP)(xf X

c gi l hm mt xc sut ca bin ngu nhin lin tc X nu: )(f X

xxf X ,0)(1)( =

+

dxxf X

b


{ } badxxfbXaPa

X

K vngK vng ((EExpectationxpectation) )

nh ngha k vng: Gi tr trung bnh hay k vng ca X k hiu nh ngha k vng: Gi tr trung bnh, hay k vng ca X, k hiu l E(X) c nh ngha nh sau:

+

dxxxfX )()E( Tnh cht k vng:

== dxxxfX X )()E(

Cho X v Y l hai bin ngu nhin v hai s bt k a v b, gi s E(X) v E(Y) tn ti, th th:

)()()( YbEXEbYXE ++ )()()( YbEXaEbYaXE +=+ Nu X l bin ngu nhin lin tc c hm mt phn b xc

sut fX(x) th: +sut fX(x) th:

= dxxfxgXgE X )().()]([

Nu X v Y l hai bin ngu nhin c lp th:


Nu X v Y l hai bin ngu nhin c lp th:)().()( YEXEXYE =

Phng saiPhng sai ((VarVariance)iance)

nh ngha phng sai: Phng sai ca bin ngu nhin X k hiu nh ngha phng sai: Phng sai ca bin ngu nhin X, k hiu Var(X) l:

])[()(Var 2= XEX)(XEtrong :

Tnh cht phng sai:

)(XE=trong :

Nu X l bin ngu nhin c =E(X) v E(X2)

Hip phng saiHip phng sai v h s tng quanv h s tng quan

Hip phng sai (Covariance): Cho X v Y l hai bin ngu nhin Hip phng sai (Covariance): Cho X v Y l hai bin ngu nhin, hip phng sai ca X v Y l:

YXYX XYYXYX == )(E)])([(E),(Cov)( ),( YEXE YX == trong :

YXYX

H s tng quan (Correlation coefficient): H s tng quan ca hai bin ngu nhin X v Y l:

YX

YX

),(Cov=

trong : )(Var ,)(Var YX YX ==

Hai bin ngu nhin X v Y khng tng quan nu 0),(Cov =YX


Hai bin ngu nhin X v Y khng tng quan nu 0),(Cov YX

Qu trnh ngu nhinQu trnh ngu nhin

Qu trnh ngu nhin: Qu trnh ngu nhin: Mt hm x(t)=X(t,) ph thuc vo bin ngu nhin gi l qu

trnh ngu nhin. Vi gi tr t xc nh gi tr hm ch ph thuc vo , do n l bin ngu nhin. Vi gi tr xc nh ca ,

ch ph thuc vo t, do n l hm bin thc thng thng. i vi h ri rc qu trnh ngu nhin l chui {x(k)} i vi h ri rc, qu trnh ngu nhin l chui {x(k)}

Nhiu trng: Nhiu trng: Nhiu trng l chui bin ngu nhin c lp {e(k)} c E[e(k)]=0

v Var[e(k)]= .


Hm hip phng saiHm hip phng sai

Hm t hip phng sai (Auto Covariance Function) Hm t hip phng sai (Auto Covariance Function) Cho {x(k)} l qu trnh ngu nhin, hm t hip phng sai (Auto Covariance Function) ca {x(k)} l:

Nu E[x(k1)]. E[x(k2)]=0 th:)](),([Cov),(Cov),( 212121 kxkxkkkkR xxx ==

)]()([E)( kkkkR )]()([E),( 2121 kxkxkkRx =

Hm hip phng sai cho (Cross Covariance Function) Hm hip phng sai cho (Cross Covariance Function)Cho {x(k)} v {y(k)} l hai qu trnh ngu nhin, hm hip phng sai cho gia {x(k)} v {y(k)} l:

Nu E[x(k1)]. E[y(k2)]=0 th:)](),([Cov),(Cov),( 212121 kykxkkkkR xyxy ==

)]()([E)( kkkkR


)]()([E),( 2121 kykxkkRxy =

Qu trnh ngu nhin dngQu trnh ngu nhin dng

{x(k)} c gi l qu trnh ngu nhin dng (stationary) nu: {x(k)} c gi l qu trnh ngu nhin dng (stationary) nu: E[x(k)] khng ph thuc vo k v Rx(k1,k2) ch ph thuc vo =k1k2x( 1, 2) p 1 2

Khi hm t hip phng sai c k hiu l: )](),([Cov)( = kxkxRx

{x(k)} v {y(k)} c gi l hai qu trnh ngu nhin tng quan dng (stationary corelation) nu: E[x(k)], E[y(k)] khng ph thuc vo k v Rxy(k1,k2) ch ph thuc vo =k1k2hi h hi h i k hi lKhi hm t hip phng sai c k hiu l:

)](),([Cov)( = kykxRxy


Ch : )()( = xx RR )()( = xyxy RR

Qu trnh ngu nhin gn dng (quasiQu trnh ngu nhin gn dng (quasi--stationary)stationary)

{ (k)} i l h hi d {x(k)} c gi l qu trnh ngu nhin gn dng nu: E[x(k)] = mx(k), |mx(k)| C, k E[x(k ) x(k )] = R (k k ) |R (k k )| C v E[x(k1), x(k2)] = Rx(k1,k2), |Rx(k1,k2)| C v

)()]()([E1lim1

xN

kNRkxkx

N=

= 1k=

=

= NkN

kxkxN

kxkx1

)]()([E1lim)]()([E K hiu:

{x(k)} v {y(k)} c gi l hai qu trnh ngu nhin tng quan gn dng (stationary corelation) nu {x(k)} v {y(k)} l hai qu trnh ngu nhin gn dng, ng thi:

)()]()([E Rkykx


= ),()]()([E xyRkykx

Ph cng sutPh cng sut

{ (k)} l hi hi d h { (k)} l {x(k)} l tn hiu ngu nhin gn dng, ph cng sut ca {x(k)} l bin i Fourier ca hm t hip phng sai:

{ } + j{ } =

==

jxxx eRR )()()( F

{x(k)} v {y(k)} hai tn hiu ngu nhin lin kt gn dng, ph cng sut cho ca {x(k)} v {y(k)} l bin i Fourier ca hm hip phng sai cho:

+{ } +=

==

jxyxyxy eRR )()()( F


Phn tch p ng qu Phn tch p ng qu


Phn tch p ng xungPhn tch p ng xung

v(t)

H thngu(t) y(t)

v(t)

gu(t) y(t)

u(k) y(k)

)()()()()()()(0

00 kvlkulgkvkuqGkyl

+=+= +=

Gi s HT m t bi:

)()( kku = Tn hiu vo l hm dirac:)()()()()()( 0

00 kvkgkvlklgky

l+=+=+

= Tn hiu ra:

0l=

)()()(0

kvkykg = p ng xung ng:)(ky


)()( kykg = p ng xung c lng:

Phn tch p ng xungPhn tch p ng xung

)()()(0

kvkykg = p ng xung ng:Kt lun:Kt lun:

)()( kykg = p ng xung c lng:

Nhn xt:Nhn xt: Ph h i

Phng php n gin./ Sai s nhn dng l v(k)/./ Nhiu h thng vt l khng cho php xung tn hiu vo c bin/ Nhiu h thng vt l khng cho php xung tn hiu vo c bin

ln v(k)/ nh./ Ngoi ra tn hiu vo c bin ln c th lm gy ra cc nh


hng phi tuyn lm mo dng m hnh tuyn tnh ca h thng.

Th d nhn dng p ng xung ca ng c DCTh d nhn dng p ng xung ca ng c DC

Gi bi h h ( d h ) Gi s ng c m t bi m hnh ton (s dng m phng):

)(1)()()( tuL

tyL

KtiLR

dttdi b += )(1 =R (H)03.0=L

020=K020KLLLdt)()()( ty

JBti

JK

dttdy m =

02.0=mK02.0=eK)(kg.m 02.0 2=J

(Nms)05.0=B Trong : u(t): in p phn ng (tn hiu vo);

y(t): tc quay ca ng c (tn hiu ra);

(Nms)05.0B

y( ) q y g ( );i(t): dng in phn ng

Dng pp phn tch p ng xung, nhn dng p ng xung ca ng c. Gi s chu k ly mu l T=0.01s, tn hiu o tc b nh

hng bi nhiu cng c gi tr trung bnh l v phng sai l . So snh p ng xung nhn dng c vi p ng xung chnh xc


So snh p ng xung nhn dng c vi p ng xung chnh xc tnh da vo m hnh ton hc.

M phng th nghim thu thp d liuM phng th nghim thu thp d liu

M phng th nghim thu thp d liu ca


p g g png c DC vi tn hiu vo l hm dirac

Kt qu c lng p ng xung ng c DCKt qu c lng p ng xung ng c DC0.08

ghat0.1

h t

0 05

0.06

0.07

ghatg0

0.06

0.08

ghatg0

0.03

0.04

0.05

0

0.02

0.04

0 20 40 60 80 100 120 140 160 180 2000

0.01

0.02

0 20 40 60 80 100 120 140 160 180 200-0.04

-0.02

0

(a) Khng nhiu ( = 0; =0)10

0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200

(b) C nhiu ( = 0; =102)10 = 10 = 10

Nu khng c nhiu nhn dng chnh xc p ng xung C nhiu p ng xung nhn dng khng chnh xc nu tn hiu


C nhiu p ng xung nhn dng khng chnh xc nu tn hiu vo c bin b


h t0.08

ghat

0.06

0.07

0.08

ghatg0

0.05

0.06

0.07

ghatg0

0.03

0.04

0.05

0.02

0.03

0.04

0 20 40 60 80 100 120 140 160 180 2000

0.01

0.02

0 20 40 60 80 100 120 140 160 180 200-0.01

0

0.01

(d) C nhiu ( = 0.5; =102) = 100

0 20 40 60 80 100 120 140 160 180 200

(c) C nhiu ( = 0; =102) = 100

Bin tn hiu vo cng ln nhiu cng t nh hng n p ng xung c lng c


g g Nhiu c mc DC p ng xung nhn dng b sai lch

Th d nhn dng p ng xung ca tay myTh d nhn dng p ng xung ca tay my

K hiu n v Gi trK hiu n v Gi trM kg 3.5m kg 0.6l 1 4l m 1.4lC m 0.5B N.m.s/rad 0.01

/ 2 9 81

M hnh ton hc m t tay my (s dng m phng):)()(sin)()()()( 22 tutgMlmltBtmlMl =++++ &&&

g m/s2 9.81

)()(sin)()()()( tutgMlmltBtmlMl CC =++++ Dng pp phn tch p ng xung, nhn dng p ng xung ca h

thng quanh im lm vic . Gi s chu k ly mu l 4/ =g q yT=0.1s, tn hiu o tc b nh hng bi nhiu cng c gi tr trung bnh l v phng sai l .

So snh p ng xung nhn dng c vi p ng xung chnh xc




S h h hi h h d li hS m phng th nghim thu thp d liu vo ra quanh im vic tnh ca h tay my vi tn hiu vo l hm dirac

uuu =~


D liu dng nhn dng m hnh tuyn tnh: uuu = yyy =~

Kt qu c lng p ng xung h tay my quanh im tnhKt qu c lng p ng xung h tay my quanh im tnh0.015

ghat0.02

ghat

0.005

0.01

ghatg0

0.01

0.015

ghatg0

-0.005

0

0 005

0

0.005

0 20 40 60 80 100 120 140 160 180 200-0.015

-0.01

0 20 40 60 80 100 120 140 160 180 200-0.015

-0.01

-0.005

(a) Khng nhiu ( = 0; =0) = 1

0 20 40 60 80 100 120 140 160 180 200

(b) C nhiu ( = 0; =105) = 1

0 20 40 60 80 100 120 140 160 180 200

1 Nu khng c nhiu nhn dng chnh xc p ng xung C nhiu p ng xung nhn dng khng chnh xc nu tn hiu




ghat0.02

ghat

0.01

0.015g0

0.01

0.015g0

-0.005

0

0.005

-0.005

0

0.005

0 20 40 60 80 100 120 140 160 180 200-0.015

-0.01

0 20 40 60 80 100 120 140 160 180 200-0.015

-0.01

(c) C nhiu ( = 0; =105) = 5

(d) C nhiu ( = 0; =105) = 25

Tng bin tn hiu vo gim nh hng ca nhiu n p ng xung c lng c

Bin tn hiu vo ln qu p ng xung nhn dng b sai lch do


Bin tn hiu vo ln qu p ng xung nhn dng b sai lch do tnh phi tuyn ca i tng

Phn tch p ng ncPhn tch p ng nc

v(t)

H thngu(t) y(t)

v(t)

gu(t) y(t)

u(k) y(k)

)()()()()()()(0

00 kvlkulgkvkuqGkyl

+=+= +=

Gi s HT m t bi:

)(1.)( kku = Tn hiu vo l hm nc:

hi )()()()(1)()( klklklkk+ Tn hiu ra: )()()()(1.)()(1

00

0 kvlgkvlklgkyll

+=+= ==

)1()()()1()( 0 += kvkvkgkyky


)()()()()( 0gyy

Phn tch p ng ncPhn tch p ng nc

Kt lun:Kt lun:

p ng xung ng: )1()()1()()(0

= kvkvkykykg

p ng xung c lng: )1()()( = kykykg

Nhn xt:Nhn xt: Ph h i

Phng php n gin./ Sai s nhn dng l [v(k) v(k 1)] /, loi mc DC ca nhiu/ Nhiu h thng vt l khng cho php tn hiu vo c bin / Nhiu h thng vt l khng cho php tn hiu vo c bin

ln [v(k) v(k 1)] /, nh./ Ngoi ra tn hiu vo c bin ln c th lm gy ra cc nh


hng phi tuyn lm mo dng m hnh tuyn tnh ca h thng.



)(1)()()( tuL

tyL

KtiLR

dttdi b += )(1 =R (H)03.0=L

020=K020KLLLdt)()()( ty

JBti

JK

dttdy m =

02.0=mK02.0=eK)(kg.m 02.0 2=J



(Nms)05.0B


Dng pp phn tch p ng nc, nhn dng p ng xung ca ng c. Gi s chu k ly mu l T=0.01s, tn hiu o tc b nh







p g g png c DC vi tn hiu vo l hm nc

Kt qu c lng p ng xung ng c DCKt qu c lng p ng xung ng c DC

0 08 0 1

0.06

0.07

0.08ghatg0

0.06

0.08

0.1ghatg0

0.03

0.04

0.05

0.02

0.04

0

0.01

0.02

-0 04

-0.02

0

(a) Khng nhiu ( = 0; =0)10

0 20 40 60 80 100 120 140 160 180 2000

(b) C nhiu ( = 0; =102)10

0 20 40 60 80 100 120 140 160 180 200-0.04

Nu khng c nhiu nhn dng chnh xc p ng xung C nhiu p ng xung nhn dng khng chnh xc nu tn hiu

= 10 = 10




ghat0.08

ghat

0.05

0.06

0.07

gg0

0.05

0.06

0.07

ghatg0

0.02

0.03

0.04

0.02

0.03

0.04

0 20 40 60 80 100 120 140 160 180 200-0.01

0

0.01

0 20 40 60 80 100 120 140 160 180 200-0.01

0

0.01

(c) C nhiu ( = 0; =102) = 100

(d) C nhiu ( = 0.5; =102) = 100

Bin tn hiu vo cng ln nhiu cng t nh hng n p ng xung c lng cNhi DC DC kh h h


Nhiu c mc DC mc DC khng nh hng n p ng xung nhn dng c.



/ 2 9 81


g m/s2 9.81

)()(sin)()()()( tutgMlmltBtmlMl CC =++++ Dng pp phn tch p ng nc, nhn dng p ng xung ca h thng

quanh im lm vic . Gi s chu k ly mu l T=0.1s, tn 4/ =q yhiu o tc b nh hng bi nhiu cng c gi tr trung bnh l v phng sai l .





S h h hi h h d li hS m phng th nghim thu thp d liu vo ra quanh im vic tnh ca h tay my vi tn hiu vo l hm nc

uuu =~



Kt qu c lng p ng xung h tay my quanh im tnhKt qu c lng p ng xung h tay my quanh im tnh0.015 0.015

ghat

0.005

0.01

ghatg0

0.005

0.01

ghatg0

-0.005

0

-0.005

0

0 20 40 60 80 100 120 140 160 180 200-0.015

-0.01

0 20 40 60 80 100 120 140 160 180 200-0.015

-0.01

(a) Khng nhiu ( = 0; =0) = 0.2

0 20 40 60 80 100 120 140 160 180 200

(b) Khng nhiu ( = 0; =0) = 1

0 20 40 60 80 100 120 140 160 180 200

Nu khng c nhiu: nhn dng chnh xc p ng xung nu bin tn hiu vo b

1


g p g g kt qu nhn dng p ng xung b sai lch nu bin tn hiu vo ln


h t0.02

0 005

0.01

0.015

ghatg0

0.01

0.015

ghatg0

-0.005

0

0.005

0

0.005

0 20 40 60 80 100 120 140 160 180 200-0.02

-0.015

-0.01

0 20 40 60 80 100 120 140 160 180 200-0.015

-0.01

-0.005

(c) C nhiu ( = 0; =105) = 1

0 20 40 60 80 100 120 140 160 180 200

(d) C nhiu ( = 0; =105) = 5

0 20 40 60 80 100 120 140 160 180 200

C nhiu p ng xung nhn dng khng chnh xc do nh hng ca nhiu

Bin tn hiu vo ln qu p ng xung nhn dng b sai lch do


Bin tn hiu vo ln qu p ng xung nhn dng b sai lch do tnh phi tuyn ca i tng

Phn tch tng quanPhn tch tng quanv(t)

H thngu(t) y(t)u(t) y(t)

u(k) y(k)

)()()()()()()(0

00 kvlkulgkvkuqGkyl

+=+= +=

Gi s HT m t bi:

Tn hiu vo u(k) l chui ngu nhin gn dng: Tn hiu vo u(k) l chui ngu nhin gn dng:kCkmkmku uu = ,)( ),()]([E

)()()]()([E 212121 CkkRkkRkuku = ),( ),,()]()([E 212121 CkkRkkRkuku uu )()]()([E uRkuku = )(),(1lim

1 u

N

kuN

RkkRN

==


v khng tng quan vi nhiu: 0)]()([E =kvku

Phn tch tng quan (tt)Phn tch tng quan (tt)

Th h l 2 2 (Lj 1999 40) Theo nh l 2.2 (Ljung, 1999 trang 40):

+ ==0

0 )()()()]()([El

uyu lRlgRkuky =0l

Nu tn hiu vo c chn l nhiu trng sao cho 0)( =uR p ng xung chnh xc:

)()(0 yuRg =

c lng p ng xung: )()(

NyuRg =

=

= Nk

Nyu kukyN

R

)()(1)(trong :


=k

Phn tch tng quan (tt)Phn tch tng quan (tt)

Kt lun:Kt lun:

Nhn xt:Nhn xt:

Kt lun:Kt lun: p ng xung c lng:

)()(NyuRg =

Nhn xt:Nhn xt: Phng php n gin. Sai s nhn dng l chnh bng sai s c lng , sai s ny)( NyuR Sai s nhn dng l chnh bng sai s c lng , sai s ny

cng gim khi s mu d liu s dng nhn dng cng tng. Bin tn hiu nh hng khng ng k n cht lng nhn

d

)(yuR

dng. Phng php phn tch tng quan c bit thch hp nhn dng

p ng xung trong trng hp h thng c nhiu o lng ngup ng xung trong trng hp h thng c nhiu o lng ngu nhin v bin tn hiu vo gii hn.

Nhn dng tt p ng xung ca h phi tuyn quanh im lm vic


tnh.



)(1)()()( tuL

tyL

KtiLR

dttdi b += )(1 =R (H)03.0=L

020=K020KLLLdt)()()( ty

JBti

JK

dttdy m =

02.0=mK02.0=eK)(kg.m 02.0 2=J



(Nms)05.0B


Dng pp phn tch tng quan, nhn dng p ng xung ca ng c. Gi s chu k ly mu l T=0.01s, tn hiu o tc b nh







p g g png c DC vi tn hiu vo ngu nhin

D liu nhn dng p ng xung dng pp tng quanD liu nhn dng p ng xung dng pp tng quan

0

5

10

a

g

e

0 0 2 0 4 0 6 0 8 1 1 2 1 4 1 6 1 8 2-10

-5

0

V

o

l

t

a

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2

3

1

0

1

S

p

e

e

d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-2

-1

Time (sec)


p ng ca ng c DC vi tn hiu vo ngu nhin


0 08 0 08

0 05

0.06

0.07

0.08ghatg0

0 05

0.06

0.07

0.08ghatg0

0 02

0.03

0.04

0.05

0 02

0.03

0.04

0.05

0 01

0

0.01

0.02

0 01

0

0.01

0.02

(a) C nhiu ( = 0; = =102)1 N 1000

0 20 40 60 80 100 120 140 160 180 200-0.01

(b) C nhiu ( = 0; =102)1 N 10000

0 20 40 60 80 100 120 140 160 180 200-0.01

= 1, N=1000 = 1, N=10000



0 08 0 08

0 05

0.06

0.07

0.08ghatg0

0 05

0.06

0.07

0.08ghatg0

0 02

0.03

0.04

0.05

0 02

0.03

0.04

0.05

0 01

0

0.01

0.02

0 01

0

0.01

0.02

(c) C nhiu ( = 0; = =102)10 N 1000

0 20 40 60 80 100 120 140 160 180 200-0.01

(d) C nhiu ( = 0; =102)1 N 100000

0 20 40 60 80 100 120 140 160 180 200-0.01

= 10, N=1000 = 1, N=100000




/ 2 9 81


g m/s2 9.81

)()(sin)()()()( tutgMlmltBtmlMl CC =++++ Dng pp phn tch tng quan, nhn dng p ng xung ca h thng






S h h hi h h d li hS m phng th nghim thu thp d liu vo ra quanh im vic tnh ca h tay my vi tn hiu ngu nhin

uuu =~



D liu nhn dng p ng xung dng pp tng quanD liu nhn dng p ng xung dng pp tng quan

18

20

22

o

t

I

n

p

u

t

0

2

4

e

a

r

i

z

e

d

M

o

d

e

l

0 100 200 300 400 500 600 700 800 900 100014

16Ro

b

o

0 100 200 300 400 500 600 700 800 900 1000-4

-2

I

n

p

u

t

t

o

L

i

n

e

0 2

uuu =~u

0 7

0.8

0.9

1

R

o

b

o

t

O

u

t

p

u

t

-0 1

0

0.1

0.2

o

f

L

i

n

e

a

r

i

z

e

d

M

o

d

e

l

~0 100 200 300 400 500 600 700 800 900 1000

0.6

0.7

R

Sample

D liu o lng

0 100 200 300 400 500 600 700 800 900 1000-0.2

0.1

O

u

t

p

u

t

Sample

D liu vo/ra m hnh tuyn tnh

yyy =y

p ng ca tay my vi tn hiu vo ngu nhin

D liu o lng D liu vo/ra m hnh tuyn tnh


p ng ca tay my vi tn hiu vo ngu nhin

Kt qu c lng p ng xung h tay my quanh im tnhKt qu c lng p ng xung h tay my quanh im tnh

0.01

0.015

0.02ghatg0

0.01

0.015ghatg0

0

0.005

0

0.005

-0.01

-0.005

-0.01

-0.005

(a) C nhiu ( = 0; =105) = 1 N=1000

0 20 40 60 80 100 120 140 160 180 200-0.015

(b) C nhiu ( = 0; =105) = 1 N=10000

0 20 40 60 80 100 120 140 160 180 200-0.015

= 1, N=1000 = 1, N=10000


Kt qu c lng p ng xung h tay my quanh im tnhKt qu c lng p ng xung h tay my quanh im tnh

0 015

0 005

0.01

0.015ghatg0

0 005

0

0.005

0 015

-0.01

-0.005

(c) C nhiu ( = 0; =105)1 N 100000

0 20 40 60 80 100 120 140 160 180 200-0.015

= 1, N=100000


Phn tch p ng tn sPhn tch p ng tn s


Kim tra sng sinKim tra sng sinv(t)

H thngu(t)=cos(t) y(t)u(t)=cos(t) y(t)u(k)=.coskT y(k)

Tn hiu vo hnh sin: kTku cos)( = Tn hiu vo ra: )()()cos()( kykvkTYky m q+++=

trong thnh phn qu khi .0)( kyq k Nu b qua nhiu, tn hiu ra t.thi xc lp : )cos()( += kTYky m

)( jeG mj YeG )(


= )(0 jeGmjeG =)(0

Kim tra sng sin (tt)Kim tra sng sin (tt)

Kt l n:Kt l n: YKt lun:Kt lun:

= )( jeG

mj YeG =)(

Thc hin th nghim vi thay i trong min tn s quan tm, tas c lng c c tnh tn s trong min tn s ny.)( jeG

Nhn xt:Nhn xt: Phng php n gin./ Phi thc hin nhiu th nghim mt nhiu thi gian./ Nhiu h thng vt l khng cho php tn hiu vo l tn hiu hnh

sin khng p dng c phng php phn tch p ng tn ssin khng p dng c phng php phn tch p ng tn s ny.

/ Ch c lng c trong min tn s quan tm.)( jeG


g g q/ c tnh tn s c lng b nh hng bi nhiu.

)(

Th d nhn dng c tnh tn s ng c DCTh d nhn dng c tnh tn s ng c DC


)(1)()()( tuL

tyL

KtiLR

dttdi b += )(1 =R (H)03.0=L

020=K020KLLLdt)()()( ty

JBti

JK

dttdy m =

02.0=mK02.0=eK)(kg.m 02.0 2=J



(Nms)05.0B


Dng pp kim tra sng sin, nhn dng c tnh tn s ca ng c. Gi s chu k ly mu l T=0.01s, tn hiu o tc khng c

nhiu. So snh c tnh tn s nhn dng c vi c tnh tn s chnh


So snh c tnh tn s nhn dng c vi c tnh tn s chnh xc ca h thng.


M phng th nghim thu thp d liu ca ng c DC vi


p g g p gtn hiu vo hnh sin kTku sin10)( =

D liu nhn dng c tnh tn s dng pp kim tra sng sinD liu nhn dng c tnh tn s dng pp kim tra sng sin

0

5

10

l

t

a

g

e

0

5

10

l

t

a

g

e

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

-5

V

o

15

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

-5

V

o

6

0

5

10

15

S

p

e

e

d

0

2

4

6

S

p

e

e

d

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

-5

Time (sec)

(a) = 22 (rad/sec)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-4

-2

Time (sec)

(b) = 24 (rad/sec)

p ng ca ng c DC vi tn hiu vo hnh sin

(a) 2 2 (rad/sec) (b) 2 4 (rad/sec)


p g g (trng hp khng c nhiu o lng)

D liu nhn dng c tnh tn s dng pp kim tra sng sinD liu nhn dng c tnh tn s dng pp kim tra sng sin

0

5

10

o

l

t

a

g

e

0

5

10

o

l

t

a

g

e

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

-5

V

o

4

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-10

-5

V

o

3

0

2

4

S

p

e

e

d

1

0

1

2

3

S

p

e

e

d

(a) = 26 (rad/sec)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-2

Time (sec)

(a) = 28 (rad/sec)0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

-2

-1

Time (sec)

(a) 2 6 (rad/sec) (a) 2 8 (rad/sec)

p ng ca ng c DC vi tn hiu vo hnh sin


p g g (trng hp khng c nhiu o lng)

c lng c tnh tn sc lng c tnh tn s

V th, ta c c tnh tn s gn ng trong min tn s va kho st.


Phn tch p ng tn s bng phng php tng quanPhn tch p ng tn s bng phng php tng quanv(t)

H thngu(t)= cos(t) y(t)u(t)= cos(t) y(t)u(k)=. coskT y(k)

Tn hiu vo hnh sin: kTku cos)( = Tn hiu vo ra: )()()cos()( kykvkTYky +++= Tn hiu vo ra: )()()cos()( kykvkTYky m q+++=

trong thnh phn qu khi .0)( kyq k Tn hiu ra t thi xc lp : )()cos()( kvkTYky ++= Tn hiu ra t.thi xc lp : )()cos()( kvkTYky m ++=

N kk)(1)( N1 Thnh lp hai i lng:


=

=k

C kTkyNNI

1cos)(1)(

==

kS kTkyN

NI1

sin)(1)(

Phn tch p ng tn s bng phng php tng quanPhn tch p ng tn s bng phng php tng quan

D dng chng minh c: D dng chng minh c:

cos2

)( mCYNI = khi N

sin2

)( mSYNI = khi N

Do , c th tnh c chnh xc bin v lch pha ca tnhiu ra, bt chp tn hiu o c nhiu:

)()(2 22 NINIY )()(2 22 NINIY SCm +=

= )(tan 1 NIS = )(tan NIC

Sau suy ra c tnh tn s theo cch thc hin phng php


Sau suy ra c tnh tn s theo cch thc hin phng phpkim tra sng sin.

Th d nhn dng c tnh tn s ca tay myTh d nhn dng c tnh tn s ca tay my


/ 2 9 81


g m/s2 9.81

)()(sin)()()()( tutgMlmltBtmlMl CC =++++ Dng pp phn tch tng quan, nhn dng c tnh tn s ca h thng


So snh c tnh tn s nhn dng c vi c tnh tn s chnh xc


So snh c tnh tn s nhn dng c vi c tnh tn s chnh xc tnh da vo m hnh ton hc.


M phng th nghim thu thp d liu ca tay my vi


p g g p y ytn hiu vo hnh sin quanh im tnh kTku sin1.0966.17)( +=

p ng ca tay my tn hiu vo hnh sin quanh im tnh

Nhn dng c tnh tn s tay myNhn dng c tnh tn s tay my

p ng ca tay my tn hiu vo hnh sin quanh im tnh

18

18.05

18.1

o

t

I

n

p

u

t

0

0.1

0.2

e

a

r

i

z

e

d

M

o

d

e

l

0 500 1000 1500 2000 2500 300017.85

17.9

17.95

R

o

b

o

0 84

0 500 1000 1500 2000 2500 3000-0.2

-0.1

0

I

n

p

u

t

t

o

L

i

n

e

0.78

0.8

0.82

0.84

R

o

b

o

t

O

u

t

p

u

t

0 02

0

0.02

0.04

o

f

L

i

n

e

a

r

i

z

e

d

M

o

d

e

l

(a) D liu vo ra h tay my

0 500 1000 1500 2000 2500 30000.74

0.76R

Sample

(b) D liu vo ra MH tuyn tnh

0 500 1000 1500 2000 2500 3000-0.04

-0.02

O

u

t

p

u

t

o

Sample

(a) D liu vo ra h tay my (b) D liu vo ra MH tuyn tnh

S dng d liu t mu 1501 tr i (h thng xc lp), tnh c Ym = 0.0256 v = 141.660


m . v . Lp li th nghim ti cc tn s khc )( jeG

Phn tch FourierPhn tch Fourier


Nhc li: Ly mu tn hiuNhc li: Ly mu tn hiu

Ly mu tn hiu lin tc x(t) vi chu k ly T Ly mu tn hiu lin tc x(t) vi chu k lymu Ts (tn s ly mu l fs) ta c tn hiuri rc x(k)=x(kTs). x(t) x(k)

Ts

)2sin()sin()( ftXtXtx mm == Xt x(t) l tn hiu hnh sin

Tn hiu ri rc sau khi ly mu l:)2sin()sin()( k

ffXkTXkTxs

msms ==f s t l tn s chun ha (normalized frequency)sf

ff =f 2= l tn s gc chun ha

)sin()2sin()( kXkfXkx mm ==g

Ch 11 f ff 2


Ch :22

Nhc li: Bin i Fourier tn hiu ri rcNhc li: Bin i Fourier tn hiu ri rc

Cho chui tn hiu ri rc x(k) gm v hn mu (

Nhc li: Ph tn s ca tn hiu ri rcNhc li: Ph tn s ca tn hiu ri rc

)(X

3223 0

)(X

3223 0


Nhc li: Bin i Fourier ri rc (DFT)Nhc li: Bin i Fourier ri rc (DFT)

Cho chui tn hiu ri rc x(k) gm N mu (1kN) Phn tch

N kjk)()( Cho chui tn hiu ri rc x(k) gm N mu (1kN). Phn tch

Fourier ri rc (DFT) tn hiu x(k) l:

=

=k

kjekxX1

)()(

l2t N

l 2= )1,...,0( = Nltrong

)(X

0 2


Nhn dng c tnh tn s dng pp phn tch FourierNhn dng c tnh tn s dng pp phn tch Fourierv(t)


u(k) y(k)

Tn hiu vo u(k) l chui tn hiu ngu nhin, y(k) l tn hiu ra Phn tch Fourier ri rc tn hiu vo v tn hiu ra:

=

=N

k

kjN ekuU

1)()(

==

N

k

kjN ekyY

1)()(

)( Y 2 l)()()(

N

NjN U

YeG = Suy ra: )1,...1,0;2( == NlN

l )( jN eG c gi l hm truyn c lng thc nghim (Emperical


)(N c gi l hm truyn c lng thc nghim (EmpericalTransfer Function Estimate ETFE)

Tnh cht ca hm truyn c lng thc nghimTnh cht ca hm truyn c lng thc nghim

j Hm truyn c lng thc nghim ch xc nh ti cc tn

s: 1,...1,0;2 == NlN

l )( jN eG

N

K vng ca tim cn bng khi N.)( jN eG )(0 jeG

)()()()](E[ 10

N

jjN U

NeGeG +=

NCN 11 )(

)(max.)(21

01 kulkgCl

= =


Tnh cht ca hm truyn c lng thc nghim (tt)Tnh cht ca hm truyn c lng thc nghim (tt)

Phng sai ca tim cn bng t s nhiu trn tn hiu khi N.

)( jN eG

j c lng ti cc tn s khc nhau tim cn khng tng

quan.)( jN eG

jjjj = )]()([)]()(E[ 00 jjNjjN eGeGeGeG

=+ )]()([ 2)(1 2 NN vU neu === 1,1,2)()( )(2 NlN

lNN UU

N neu

CN

CN 22 )(

+212 October 2010 H. T. Hong - HBK TPHCM 79

=

+=l

vRCC )(2

12

Th d nhn dng c tnh tn s ng c DC dng pp phn tch FourierTh d nhn dng c tnh tn s ng c DC dng pp phn tch Fourier


)(1)()()( tuL

tyL

KtiLR

dttdi b += )(1 =R (H)03.0=L

020=K020KLLLdt)()()( ty

JBti

JK

dttdy m =

02.0=mK02.0=eK)(kg.m 02.0 2=J



(Nms)05.0B


Dng pp phn tch Fourier, nhn dng c tnh tn s ca ng c. Gi s chu k ly mu l T=0.01s, tn hiu o tc b nh hng

bi nhiu cng c trung bnh bng 0 v phng sai bng 0.01. So snh c tnh tn s nhn dng c vi c tnh tn s chnh


So snh c tnh tn s nhn dng c vi c tnh tn s chnh xc ca h thng.

c tnh tn s ca ng c DC tnh t m hnh ton hcc tnh tn s ca ng c DC tnh t m hnh ton hc

Bode DiagramBode Diagram

-40

-20

0

20

n

i

t

u

d

e

(

d

B

)

g

-40

-20

0

20

n

i

t

u

d

e

(

d

B

)

-45

0-80

-60

40

M

a

g

n

-80

-60

40

M

a

g

-45

0

270

-225

-180

-135

-90

P

h

a

s

e

(

d

e

g

)

270

-225

-180

-134

-90

P

h

a

s

e

(

d

e

g

)

(a) c tnh tn s tnh t m (b) c tnh tn s tnh t m

10-1

100

101

102

103

-270

Frequency (rad/sec)

10-1

100

101

102

103

-270

Frequency (rad/sec)

(a) c tnh tn s tnh t m hnh ton hc lin tc

(b) c tnh tn s tnh t m hnh ton hc ri rc



M phng th nghim thu thp d liu ca ng c


p g g p gDC vi tn hiu vo ngu nhin

D liu nhn dng c tnh tn s dng pp phn tch FourierD liu nhn dng c tnh tn s dng pp phn tch Fourier

0

5

10

u

0 1 2 3 4 5 6 7 8 9 10-10

-5

2

4

-2

0

y

p ng ca ng c DC i tn hi o ng nhin

0 1 2 3 4 5 6 7 8 9 10-4

Time (sec)


p ng ca ng c DC vi tn hiu vo ngu nhin(chu k ly mu Ts = 0.01 sec, N = 1000 mu d liu)

Kt qu nhn dng c tnh tn s ca ng c DCKt qu nhn dng c tnh tn s ca ng c DC

-20

0

20

u

d

e

(

d

B

)

Bode Diagram

-20

0

20

u

d

e

(

d

B

)

45

0-80

-60

-40

M

a

g

n

i

t

-80

-60

-40

M

a

g

n

i

t

1500

-225

-180

-135

-90

-45

P

h

a

s

e

(

d

e

g

)

-500

0

500

1000

P

h

a

s

e

(

d

e

g

)

(a) c tnh tn s c lng (b) c tnh tn s tnh t m

10-1

100

101

102

103

-270

Frequency (rad/sec)10-1 100 101 102 103

-1000

Frequency (rad/sec)

(a) c tnh tn s c lng dng pp phn tch Fourier


Nhn xt: Do nhiu o lng tp trung min tn s cao nn c tnh


Nhn xt: Do nhiu o lng tp trung min tn s cao nn c tnh tn s nhn dng b sai s kh ln min tn s cao

Kt qu nhn dng c tnh tn s ca ng c DCKt qu nhn dng c tnh tn s ca ng c DC

Bode Diagram

-10

0

10

i

t

u

d

e

(

d

B

)

g

-10

0

10

t

u

d

e

(

d

B

)

0-30

-20

M

a

g

n

i

-30

-20

M

a

g

n

i

0

-135

-90

-45

P

h

a

s

e

(

d

e

g

)

-135

-90

-50

P

h

a

s

e

(

d

e

g

)

(a) c tnh tn s c lng (b) c tnh tn s tnh t m

100

101

-180

Frequency (rad/sec)

100 101-180

Frequency (rad/sec)



Nhn xt: min tn s thp (nh hn tn s ly mu 5-10 ln) c


Nhn xt: min tn s thp (nh hn tn s ly mu 5-10 ln) c tnh tn s nhn dng c kh chnh xc

Th d nhn dng c tnh tn s ca tay my dng pp phn tich FourierTh d nhn dng c tnh tn s ca tay my dng pp phn tich Fourier


/ 2 9 81


g m/s2 9.81

)()(sin)()()()( tutgMlmltBtmlMl CC =++++ Dng pp phn tch phn tch Fourier, nhn dng c tnh tn s ca h

thng quanh im lm vic . Gi s chu k ly mu l 4/ =g q yT=0.01s, tn hiu o tc b nh hng bi nhiu cng c gi tr trung bnh l = 0 v phng sai l = 0.00004.

So snh c tnh tn s nhn dng c vi c tnh tn s chnh xc


So snh c tnh tn s nhn dng c vi c tnh tn s chnh xc tnh da vo m hnh ton hc.

c tnh tn s ca tay my quanh im tnh tnh t MH ton hcc tnh tn s ca tay my quanh im tnh tnh t MH ton hc

Bode Diagram0

Bode Diagram

-60

-40

-20

0

n

i

t

u

d

e

(

d

B

)

g

-60

-40

-20

0

g

n

i

t

u

d

e

(

d

B

)

-100

-80

-60

M

a

g

n

0-100

-80Ma

g

0

270

-180

-90

P

h

a

s

e

(

d

e

g

)

270

-180

-90

P

h

a

s

e

(

d

e

g

)

(a) c tnh tn s tnh t m (b) c tnh tn s tnh t m

10-1

100

101

102

-270

Frequency (rad/sec)

10-1

100

101

102

-270

Frequency (rad/sec)

(a) c tnh tn s tnh t m hnh tuyn tnh lin tc

(b) c tnh tn s tnh t m hnh tuyn tnh ri rc



S h h hi h h d li hS m phng th nghim thu thp d liu vo ra quanh im vic tnh ca h tay my vi tn hiu ngu nhin

uuu =~


D liu dng nhn dng c tnh tn s tuyn tnh: uuu = yyy =~

22

D liu nhn dng c tnh tn s dng pp phn tch FourierD liu nhn dng c tnh tn s dng pp phn tch Fourier

18

20u

0 10 20 30 40 50 60 70 80 90 10014

16

0.85

0.75

0.8

y

0 10 20 30 40 50 60 70 80 90 1000.7

Time (sec)

p ng ca ta m q anh im tnh i tn hi o ng nhin


p ng ca tay my quanh im tnh vi tn hiu vo ngu nhin(chu k ly mu Ts = 0.01 giy, N =10000 mu d liu)

Kt qu nhn dng c tnh tn s quanh im tnh ca tay myKt qu nhn dng c tnh tn s quanh im tnh ca tay my

0Bode Diagram

0

-100

-50

0

t

u

d

e

(

d

B

)

60

-40

-20

0

i

t

u

d

e

(

d

B

)

-200

-150Ma

g

n

i

t

0-100

-80

-60

M

a

g

n

i

5000

-180

-135

-90

-45

P

h

a

s

e

(

d

e

g

)

10000

-5000

0

P

h

a

s

e

(

d

e

g

)

10-1

100

101

102

103

-270

-225

P

Frequency (rad/sec)

10-1 100 101 102 103-15000

-10000P

Frequency (rad/sec)



Nhn xt: Do nhiu o lng tp trung min tn s cao nn c tnh


Nhn xt: Do nhiu o lng tp trung min tn s cao nn c tnh tn s nhn dng b sai s kh ln min tn s cao

Kt qu nhn dng c tnh tn s quanh im tnh ca tay myKt qu nhn dng c tnh tn s quanh im tnh ca tay my

0Bode Diagram

0

-20

-10

0

i

t

u

d

e

(

d

B

)

30

-20

-10

0

i

t

u

d

e

(

d

B

)

-50

-40

-30

M

a

g

n

i

45-50

-40

-30

M

a

g

n

i

45

-90

-45

0

P

h

a

s

e

(

d

e

g

)

-90

-45

0

-45

P

h

a

s

e

(

d

e

g

)

10-1

100

-180

-135

P

Frequency (rad/sec)10-1 100

-180

-135

P

Frequency (rad/sec)



Nhn xt: min tn s thp (khong 0 1-8 rad/sec) c tnh tn s


Nhn xt: min tn s thp (khong 0.1-8 rad/sec) c tnh tn s ca tay my quanh im tnh nhn dng c kh chnh xc

Phn tch phPhn tch ph


Phn tch phPhn tch phv(t)


u(k) y(k)

Tn hiu vo u(k) l chui tn hiu ngu nhin, y(k) l tn hiu ra Bn cht phng php phn tch ph l trn ha c tnh tn s c

t h t h th h d d h t h h

lng thc nghim ETFE (nhc li: ETFE c c bng cch pdng phng php phn tch Fourier.

c tnh tn s ca h thng nhn dng dng p phn tch ph:

)()(

)(

N

Nyuj

N eG =


)()( NuN

Phn tch phPhn tch ph

Trong : Trong :

= jNuNu eRw )()()( =

uu

= jNyuNyu eRw )()()(

= deWw j)()(=

yuyu )()()(

)()( == NjNNu kukuNdeUR 2 )()(1)(21)(

== NjNNNyu kukyNdeUYR )()(1)()(21)( = kNu N 1 )()()(2)(


= kNNyu N 12

Hm ca sHm ca s

2 Bartlett: 22/sin2/sin

21)(

=

W

=1)(w 0

Parzen:4

3 2/sin4/sin)cos2(2)(

+=

W /s

2/0161

2

=

2/,12

2/0,11)( 3

2

w


2/,12

Hm ca sHm ca s

Hamming:

)/(1)/(1)(1)( +++ DDDW )/(8

)/(8

)(4

)( +++= DDDW

)2/1sin( +2/sin)2/1sin()( +=D

= cos12

1)(w )0(


Hm ca sHm ca s

0 80.8BartlettParzenHamming

0.4

)

W

(

0

-3 0 3(rad/s)


Cc ca s tn s ng vi thng s = 5

Hm ca sHm ca s

2

2

2.5=5=10=15

1.5

)

0.5

1

W

(

0

-3 0 3-0.5

(rad/s)

Hm ca s Hamming vi cc thng s khc nhau


Hm ca s Hamming vi cc thng s khc nhau

Th d nhn dng c tnh tn s ng c DC dng pp phn tch phTh d nhn dng c tnh tn s ng c DC dng pp phn tch ph


)(1)()()( tuL

tyL

KtiLR

dttdi b += )(1 =R (H)03.0=L

020=K020KLLLdt)()()( ty

JBti

JK

dttdy m =

02.0=mK02.0=eK)(kg.m 02.0 2=J



(Nms)05.0B


Dng pp phn tch ph, nhn dng c tnh tn s ca ng c. Gi s chu k ly mu l T=0.01s, tn hiu o tc b nh hng bi

nhiu cng c trung bnh bng 0 v phng sai bng 0.01. So snh c tnh tn s nhn dng c vi c tnh tn s c


So snh c tnh tn s nhn dng c vi c tnh tn s c lng thc nghim ETFE v c tnh tn s chnh xc ca h thng.


M phng th nghim thu thp d liu ca ng c


p g g p gDC vi tn hiu vo ngu nhin

D liu nhn dng c tnh tn s dng pp phn tch phD liu nhn dng c tnh tn s dng pp phn tch ph10

0

5u

0 1 2 3 4 5 6 7 8 9 10-10

-5

2

4

4

-2

0

y

p ng ca ng c DC vi tn hiu vo ngu nhin

0 1 2 3 4 5 6 7 8 9 10-4

Time (sec)


p g g g

Nhn dng c tnh tn s ca ng c DCNhn dng c tnh tn s ca ng c DC

F 1 t 1

100

102

i

t

u

d

e

From u1 to y1

100

102

l

i

t

u

d

e

From u1 to y1

10-2 10-1 100 10110-4

10-2

A

m

p

l

10-2 10-1 100 10110-4

10-2

A

m

p

-400

-200

0

e

g

r

e

e

s

)

-2000

0

e

g

r

e

e

s

)

10-2 10-1 100 101-1000

-800

-600

P

h

a

s

e

(

d

e

10-2 10-1 100 101

-6000

-4000

P

h

a

s

e

(

d

e

(a) c tnh tn s c lng dng pp phn tch Fourier(b) c tnh tn s trn c lng dng pp phn tch ph

10 10 10 10Frequency (rad/s)

10 10 10 10Frequency (rad/s)


(b) c tnh tn s trn c lng dng pp phn tch phCh : Kt qu nhn dng (b) ph thuc vo hm ca s v gi tr

Nhn dng c tnh tn s ca ng c DCNhn dng c tnh tn s ca ng c DC

101From u1 to y1

10-1

100

10

m

p

l

i

t

u

d

e

10-1 10010-3

10-2

A

m

-100

0

d

e

g

r

e

e

s

)

10-1 100-300

-200

P

h

a

s

e

(

d

min tn s thp, TTS c lng dng pp phn tch ph (xanh) gn nh trng khp vi TTS chnh xc tnh t MH ton hc ri rc

Frequency (rad/s)


() . Kt qu nhn dng ph thuc vo hm ca s v gi tr

Documents

Chuong3 NDHT K2010 Slide