Digital Control (Bachelor)

7/28/2019 Digital Control (Bachelor)

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21 August 2011 Hon.-Prof. Prof. Dr.-Ing. habil. Nguyn Phng QuangElectrical Engineering - Automatic Control

1

iu khin s(Digital Control Systems)

Phn A:

Mn hc truyn t cc kin thc phc vphntch, thit k cc h thng iu khin t ng sdng vi x l (P, C, DSP).Phn A bao gm cc ni dung thuc chng

trnh dnh cho i hc.(Version 6, 8/2011)


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2

iu khin sChng 1: M hnh tn hiu v h thng

1. Cu trc csca h thng K s2. M hnh tn hiu trn min nh z3. M hnh h thng trn min nh z

Chng 2:iu khin c phn hi u ra1. Xt n nh ca h thng s2. Thit k trn min thi gian xp x lin tc

3. Thit k trn min thi gian gin on4. Mt s dng mrng


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3

iu khin s

Chng 3: iu khin c phn hi trng thi1. n li cc kin thc cs

2. M hnh tr ng thi gin on3. Tnh Kc, QS c v c c dng chun4. Cu trc cbn ca h thng K s trn khng

gian trng thi5. Mt s dng mrng

Chng 4: Thc hin k thut h thng K s1. nh hng ca s ha (lng t ha) bin 2. Thit k h thng bng my tnh (MATLAB)

3. Thit k h thng vi iu khin


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4

iu khin sTi liu tham kho:[1] Isermann R.:Digitale Regelsysteme. Bd. I und II, Springer-Verlag, 2.

Auflage, 1987-1988[2] Franklin G.F., Powell J.D., Workman M.L.:Digital Control of DynamicSystems. Addison Wesley, 2nd 1994

[3] Quang Ng.Ph.:MATLAB & Simulink dnh cho ks iu khin t ng.Nh xut bn KH&KT, 2004

[4] Quang Ng.Ph., Dittrich A.-J.: Vector Control of Three-Phase ACMachines. Springer, Berlin Heidelberg, 2008

Ch : Gio trnh ny s dng dy c c lp i hc vi thi

lng 45 tit, bao gm l thuyt v v d. Vi c c lp 60tit, s dy ging nh lp 45 tit nhng c thm bi tp ln12-15 tit.


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5

1. M hnh tn hiu v h thng1.1 Cu trc csca h thng K s

1 1 0

0 1 1

k k k

k k k

p u p u p u

q e q e q e

+ + + =

+ + +

( )( )( )

110 1

C 1 10 1

Q zq q z q zG z

p p z p z z

+ + += =

+ + +

Khu iu chnh:1. Pt. Sai phn

2. Hm truyn t trnmin nh z


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6


Khu C: s dng vi xl (microprocessor: P),

vi iu khin (microcontroller: C) hoc vi xltn hiu (digital signal processor: DSP) Khu DAC: c th khng tn ti mt cch tng

minh, m n di dng thit b c chc nng DA.V d: khu iu chvectorin p (khi iukhin digital ng cba pha)

Khu ADC: thng s dng khi o c gi tr thc ca i lng ra (v d: o dng). i khi tnti di dng khc nh: o tc quay bng IE


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7


Khu ADC v qu

trnh trch mu o

( ) ( ) ( ) ( )

[ ] [ ]0 1 2

0 , 1 , 2 , hay

, , ,k

u k u u u

u u u u

= =

( ) ( ) ( )

( ) ( )

*

0

0

k

k

u t u kT t kT

u t t kT

=

=

=

=

Sau khi trch mu ( l tng)

bng ADC ta thu c chuigi tr s:

kho st tn hiu gin onbng cng c Laplace (hayphn tch ph), ng thi toiu kin m t hn hp vi cckhu lin tc, ta nhn chui vihm (t) v thu c dy xung:


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8


Khu DAC v qu trnh

lu gi (nh) khi xut

( ) ( ) ( ){ }0

1 1 1kk

u t u t kT t k T

=

= +

( )0

1 sT skTk

k

eU s u e

s

=

=

( )( )

( )*1 sT

H

U s eG s

sU s

= =

M hnh tn hiu c dng bc thang trn

min thi gian:

Chuyn sang min nh Laplace:

T thu c hm truyn t ca khugi chm:


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9

1. M hnh tn hiu v h thng1.2 M hnh tn hiu trn min nh z

( ) ( ) ( ) ( )* *

0 0

skTk

k k

u t u kT t kT U s u e

= =

= =

Chuyn phng trnh m t dy xung u*(t) sang min nh Laplace:

Thay: ta thu c:Tz e= ( ) ( )*0

sT

kke z

k

U s U z u z

==

= =

V d: Mt tn hiu gin on v thi gian cho trc bi0 0

0k k

ku

a k


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10

1. M hnh tn hiu v h thng1.3 M hnh h thng trn min nh z

H thng K s bao gm2 loi khu cbn:

1.Khu c bn cht ginon: Cc tn hiu vo/ra/trng thi u gin onv thi gian v v mc.Khu m t cc thit b

K digital.2.Khu c bn cht lintc: M t i tngiukhin. Khi gin on has a n m hnh nhhnh bn. Vic gin onha xut pht t m hnhtrng thi lin tc ca itng.


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11


1.3.1 M hnh khu c bn cht gin on

Quy lut tnh ton (c gi l thutton) xc nh c tnh truyn t cakhu.

a) M tbng phng trnh sai phn

1k k ku u u+ =

1k k ku u u = 2

1

2 12k k k

k k k

u u u

u u u+

+ +

=

= +

( )

1 11

0

1

n n nk k k

nn

k n

u u u

nu

+

+ =

=

=

*Sai phn bc nht:

Sai phn tin:

Sai phn li

*Sai phn bc 2:

*Sai phn bc n:

Mt phng trnh sai phn c t nht 2 gitr uk+n v ukc gi l p hng trnhsai phn bc n.


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12



a) M tbng phng trnh sai phn

0 1 1 0 1 1k n n k n k k m m k m k a x a x a x b u b u b u+ + + ++ + + = + + +

0 1 1 0 1 1k k n k n k k m k ma x a x a x b u b u b u + + + = + + +

*Pt. sai phn bc n s dng sai phn tin:

*Pt. sai phn bc n s dng sai phn li:

Gii pt. sai phn bng phng php tnh truy hi (recursive method)

Gi s ta xut pht tpt. sai phn li vi a0=1

0 1 1 1 1 2 2k k k m k m k k n k nx b u b u b u a x a x a x = + + +

Qu trnh tnh xkc bt u t k=0, ln lt nng thm 1:0 0 0

1 0 1 1 0 1 0

0

1

k x b u

k x b u b u a x

= =

= = +


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13



a) M tbng phng trnh sai phn Gii pt. sai phn trn min nh z

{ } { }0 1 1 0 1 1k n n k n k k m m k m k a x a x a x b u b u b u+ + + + + + + = + + +

* Bc 1: Chuyn ng thi 2 v ca pt. sai phn sang min nh z:

* Bc 2: Gi thit cc gi trban u x0,x1,, u0, u1, bng 0, ta c:

( ) ( )1

0 11

0 1

m mm

n nn

b z b z bz U z

a z a z a

+ + +=

+ + +

* Bc 3: p dng bin i ngc tm xk

Ch : C th gii pt. sai phn trn min nh z, xut pht t pt. sai phn tinhoc li, kt qu thu c bao gi cng l duy nht.


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14



b) M tbng hm truyn t trn min nh z

Vi: ( ) { } ( ) { };k kX z x U z u= = l nh z ca chui gi tr (tn hiu digital) u r a / u vo, ta s chm truyn t sau:

( )( )

( )

10 1

10 1

;m

mn

n

X z b b z b zG z m n

U z a a z a z

+ + += = =

+ + +

Tng t h lin tc, hm truyn t G(z) c th c coi l nh zca hm trng lng gin on [gk] (chui trng lng). Vy:

( ){ }10

k

k k k i ii

g G z x g u =

= =

( )( )

( )

( )

[ ] ( )

4

1

1 4 4

1 1

4 11 1

1 14 1 1 4

1 1 1 1, , , ,0,0,4 4 4 4

k kk

k

X z zG z

U z zz z

g zz z

g

= =

= =

=

V d: Khi uk=1kta c:1 2 1 0

0 0

1 1 0

2 2 1 0

3 3 2 1 0

4 4 3 2 1 0

0,25

0,5

0,75

1

1

k k k k x g g g g g

x g

x g g

x g g g

x g g g g

x g g g g g

= + + + + +

= == + == + + == + + + == + + + + =

Ch : Trn cscc

phng trnh vector saiphn, c th m t khutruyn t gin on nhiuchiu tuyn tnh bi:

( ) ( ) ( )z z z=X G U

Trong G(z) l ma trntruyn t gin on.


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15



c) M tbng m hnh trng thi gin on

* *

+1

* *

+

+

k k k

k k k

q A q B u

x C q D u

= =

* *

+1

* *

+

+

k k k

k k k

u

x d u

q A q b

c q

= =

H MIMO:

H SISO:

M hnh thu c tphng trnh sai phn, hay hm truyn t (trn min nh z) m tthut ton m khu thc hin (thut ton C, lc s vv).

C th thc hin bin i sang cc dng chun tc (chun K, chun QS) thng dng m t hoc tnh ton.


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16


1.3.2 M hnh khu c bn cht lin tc v tn hiu vo dng bc thang

a) c im ca qu trnh nh

(xem trang 7)

( )

( )( )*

0

1

H

sTskT

kkG s

U s

eU s u e

s

=

=

( )( )

( )*1 sT

H

U s eG s

sU s

= =

Dng bc thang ca tn hiu vo doqu trnh nhto nn. Trn minnh Laplace c dng:

Kt lun: Khi xt TK khng bao gi c php qunkhu gi chm (c trng cho qu trnh nh)

b) M tbng hm truyn t

( ) ( ) ( )*s G s U s=Vi X(s) l nh Laplace ca bin ra, U*(s)l nh Laplace ca chui xung u vo

Gi nh Laplace ca p ng bc nhy

n v (ca hm qu h(t))l H(s) ta c:( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

1

1

sT sT

sT

H

G s H s e H s e H s

eG s G s G s

s

= =

= =


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17




( ) ( ) ( )z G z U z=Vi c tnh theo mt trong hai cchm t hnh bn

( )G z

V d: i tng K l mt khu qun tnh

bc nht. Theo cch i thuc nhnh bn tri:( ) ( )

( )( ) ( ) ( )1

1 1

1 11 1

1 1= = =

+ +t TG s H s h t e t

sT s sT

11 kT TkTkh e=

( )11 T T

z zH z

z z e=

( )1

1

1

11

1

T T

T T

T T

zG zz e

e

z e

=

=

*Chui sau gin on ha:

*Chuyn sang nh z:

*Hm truyn t cai tng trn minnh z:


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18




Lu , khi hm truyn t c dng phn thc hu ts c kh nng tch thnh cc phn thc ti gin nh sau:

( ) ( )( ) ( ) ( )( )B s B sG s H sA s s A s

= =

a)H(s) c cc cc sbt k, khc nhau:

b)H(s) c cc s lp li m ln:

1s T

z

s s e

=

( ) ( )

1

11 1

1 !

m

m m s T z

m s es s

=

Tip tc v d trang trc bng cch i theo nhnh bn phi:

*Tch H(s) thnh cc phn thc ti gin: ( )

( )

1

1 1

1 1 1

+1 T +1 T

TH s

s s s s

= =

( ){ } ( )11 T T

z zH s H z

z z e = =

*Tm H(z) nhtm nh ca cc phn thc ti gin:

*Hm truyn t ca i tng trn min nh z: ( )1

1

1T T

T T

eG z

z e

=


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19



c) M tbng m hnh trng thi gin on

( ) ( ( )t t t

= +q Aq Bu

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

0

0

0

0 0 0 0 0, 1, 2,

= +

= + =

ttt t

t

t e t e d

t t t t t t k

AAq q Bu

q u

( ) ( ) ( )

( ) ( )

1 1 1

1

k k k k k k k

T T

k k k

t t t t t t t

T T

+ + +

+

= +

= +

q q u

q q u

( ) ( )1T T = H A I B

Cho trc i tng MIMO:

Nghim tng qut vi t> t0 v :

Vi t0=tkv chn t=tk+1 ta c:

Vi:

u im: D dng tm c m hnhgin on ca cc i tng MIMO

( )= tt eA


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21 August 2011 Hon.-Prof. Prof. Dr.-Ing. habil. Nguyn Phng QuangElectrical Engineering - Automatic Control 20



d) Quan h gia m hnh trng thi v m hnh truyn t

M hnh y ca i tng MIMO c dng:( ) ( )1+ = + = +

k k k

k k k

T Tq q u

x Cq Duvi phng trnh c tnh: [ ]det 0 =z I

Ma trn truyn t G(z) trn min nh z ca i tng MIMO:

( ) ( ) ( )( ) ( ) ( )

( )

( )( )

1

det

= + = = +

z z T Tz z z adj z T

Tz T

G C I H Dx G u I

C H DI

( ) ( ) ( )( )

( )( )

1

det

= =

z z T Tadj z T

Tz T

G C I HI

C HI

Khuqun tnh

Hm truyn t G(z) trn min nh z ca i tng SISO:

( )( )

( )

( ) ( ) ( )

( )

( )( )

1

det

= + = = +

T

T

G z z T T d x z

G z adj z T u z T dz T

c I h

Ic h

I

( ) ( ) ( )

( )

( )( )

1

det

= =

T

T

G z z T T

adj z T T

z T

c I h

Ic h

I

Khuqun tnh


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1.3.3 M t h trong khong gia hai thi im trch mu

c im khng tng minh

ca php bin i z ngc

Gia 2 thi im

trch mu:( ) ; 0 1t k T = +

Chn s lng ln,ta c th m t x(t) bi:

( )( ) kx k T x + +

Bin i z m rng { } ( )

( ) ( )

0

,

,

0, 1, 2, , 0 1

kk k

k

x X z x z

G z U z

k

+ +=

= =

=

=

Hai trng hp c bit c t h dng kim tra:

( ) { } ( )

( ) { } ( )1 0

0 ,0

1 ,1

k

k

X z Z x X z

X z Z x z X z x

+

= = =

= = =


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1.3.4 M t h gin on c tr (tn hiu vo dng bc thang)

M hnh c trTd u vo

( ) ; 1, 2, ; 0 1d d dT d T d = =


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1. M hnh tn hiu v h thng

Ch chng 1: Sinh vin phi nm vng chng 1 v thnhtho cc phng php gn lin vi cc v d sau y

1. V d 1.3.3, 1.3.4, 1.3.5: M t khu c bn cht lin tcvi tn hiu vo bc thang bng hm truyn t (b tham s

ca ng cDC trong v d 1.3.5 sc s dng nhtqun trong nhiu v d tip theo)2. V d 1.3.6, 1.3.7: M t khu c bn cht lin tc vi tn

hiu vo bc thang bng m hnh trng thi gin on


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2.K c hi tip i lng ra2.1 Xt n nh ca h thng K s

2.1.1 n nh truyn t

( )( )

( )

adj

detT zG z d

z

= +

Ic h

I

( )( )

( )

adj

det

zz

z

= +

IG C H D

I

( )

( )

( )

( ( ) ( ) 11 2det

ni

in i

B z B z c z

z z z z z z z z z== = I H SISO:

H MIMO:

V cbn, khi h c qun tnh (d= 0, D = 0), haicu trc u c dng phn thc nh sau:

1 1 2 2 ; 0, 1, 2,k k k

k n ng c z c z c z k= + + + = Bin i z ngc

Theo nh ngha v n nh truyn t, dy gk ch c gi tr hn ch khi |zi|


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2.K c phn hi u ra2.1 Xt n nh ca h thng K s

2.1.2 Tiu chun i s

1. ng vi mi im bt k thuc min nh z: z u jv= +

ta thu c mt im mi trn min nh w:2 2

2 2 2 2

1 1 2

1 1 2 1 2

z u v vw j

z u v u u v u

+ + = =

+ + + + 2. ng trn n v , bin gii n

nh trn min nh z trthnh ng thng:

2 2 1u v+ =

1

vw j

u

=

3. Trck h i s dng tiu chun ROUTH hay HURWITZ ta phi chuyn a thc c tnh:

( ) ' ' ' 2 '0 1 2n

nN z a a z a z a z= + + + + sang min w:

( )2

' ' ' 20 1 2 0 1 2

1 10

1 1

+ + = + + + = + + + =

w wN w a a a h h w h w

w w

Nghim ca a thcc tnh N(z) ch nmtrong ng trnn v khi v ch khitt c nghim caN(w) u c phnthc m.

a) S dng php bin i tng ng (tip):


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2.K c phn hi u ra

2.1 Xt n nh ca h thng K s

( ) ( )

( )

( )

110 1 1

0 2 2

0

det ; det ; 1, 2, ,

0 0

;

0 0 0 0

k k k k k k

n nn kk

k nn k

k k

n

C D k n

a a aa a a

a a a a

a a

= + = =

= =

A B A B

A B

2.1.2 Tiu chun i s

a) S dng php bin i tng ng(tip):

b) S dng tiu chun Schur-Cohn-Jury: Tng t tiuchun HURWITZ, ta sphi thit lp cc nh thc tcc h s ca a thc c tnhN(z)

1. Tnh cc nh thc Ck,Dk:

2. iu kin cn v nghim caN(z) nm trong ng trn n v s l v

ng thi phi tha mn:

( )2 1

0 1 2 1

= + + + + +n n

n nN z a a z a z a z a z

2 2

4 4

6 6

0; 0

0; 0

0; 0

C D

C D

C D

< >< > ( ) ( )1 1 0n N >


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2.K c phn hi u ra

2.1 Xt n nh ca h thng K s2.1.2 Tiu chun i s

Ch mc 2.1.2:1. V d 2.1.1: S dng php bin i tng ng kho st n nh2. Sinh vin phi t to v d kim chng kh nng s dng tiu

chun Schur-Cohn-Jury trn cst thit lp a thc c tnh c

nghim nm trong ng trn n v.


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2.1.3 S dng qu o im cc

Hm truynt vng h

Qu o im cctrn min z

Phng trnhc tnh

01

1K

z z

101

Dz zK z z

0 1

0 1

0z K z

z K z

+ =

= +

( )0 1 1

1 0 1

0

0

1

D

D

K z z z z

z K zz

K

+ =

+=+


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Hm truynt vng h

Qu o im cctrn min z

Phng trnhc tnh

( )( )0 1 2

1K

z z z z

( )( )1

01 2

Dz z

K z z z z

( )2 1 2 1 2 02

1 2 1 2, 0

0

2 2

a b

z z z z z z K

z z z zz K

+ + + =

+ = +

( )2 1 2 0 1 2 0 1 0Dz z z z K z z K z + + =

( )2 2 2

r jc z r + =

( )

1

21 2 1 1 2 1

;r j D

D D

z z j z c z

r z z z z z z

= + =

= + +

Pt. ng trn:

Vi:


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Hm truynt vng h

Qu o im cctrn min z

Phng trnhc tnh

( )( )

( )( )1 1

01 2

D Dz z zK z z z z

( ) ( )2 0 1 2 0 1 2

1 2 0 1 2

1

0

D D

D D

z K z z z K z z

z z K z z

+ + + + + + =

( )2 2 2

r jz c z r + =

( ) ( )

( ) ( )

( ) ( )

1 2 1 2

1 2 1 2

1 2 1 2 1 2 1 22

1 2 1 2

r j

D D

D D

D D D D

D D

z z j zz z z z

cz z z z

z z z z z z z zr c

z z z z

= +

=+ +

+ += +

+ +

Pt. ng trn:Vi:

Khi kho st n nh, b tham s h thng ti giao im ca ng trn n v viqu o im cc s l b tham s cn c kho st k. Khi tn ti nhiu giaoim, phi tm ra v tr ca im bt li nht.


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2.1.4 D bo c tnh ca h thngK s

a) D bo qu trnh qu trn c s v trim cc

( ) ( ) ( ) ( ) ( )( )

( )( )

00

01R w

X z G zG z G z G z G zW z G z

= = =+

( ) 0N z =

Xt h c hm truyn t sau:

vi phng trnh c tnh:

a thc N(z) l bc 1:

( ) 1N z z z= vi im cc thc: 1z=

Tn hiu r a c dng:

vi gi tr ban u:

( ) 11

kk

zz x z

z z= =

01x =

11 0 :z < > h = t f ( [ 1 - 0. 5] , [ 1 1 - 2] , 0. 01)

Tr ansf er f unct i on:z - 0. 5

- - - - - - - - - - -

z 2 + z - 2Sampl i ng t i me: 0. 01

M hnh ZPK:>> h = zpk ( 0. 5, [ - 2 1] , 1, 0. 01)Zer o/ pol e/ gai n:

( z- 0. 5)- - - - - - - - - - -( z+2) ( z- 1)Sampl i ng t i me: 0. 01

V d:

a) M phng bng cc lnh trc tip tToolboxca MATLAB:

) M h b l h t ti t T lb

4. Thc hin k thut h thngK s4.2 Thit k h thng bng my tnh


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21 August 2011 Hon.-Prof. Prof. Dr.-Ing. habil. Nguyn Phng Quang

Electrical Engineering - Automatic Control

97

4.2.2 M phng bng MATLAB & Simulink a) M phng bng cc lnh trc tip tToolboxca MATLAB (tip):

Phng php gin on ha: zoh , f oh , t ust i n , pr ewarp , mat ched

methodThay i c h u k trch mud2d(sys, TsChuyn h gin on thnh h lin tcd2c(sysd, methodChuyn h lin tc thnh h gin onc2d(sysc, Ts, method)

Chuyn i gia hai h LTI lin tc v gin on

Nhm lnh chuyn i gia hai loi m hnh gin on v lin tc (thuc Control Toolbox)V d:>> sysc = t f ( 1, [ 1 1] )

Tr ansf er f unct i on:1

- - - - -s + 1>> sysd = c2d ( sysc, 2)

Tr ansf er f unct i on:

0. 8647- - - - - - - - - -z - 0. 1353Sampl i ng t i me: 2>> sysdd =d2d ( sysd, 0. 7)

Tr ansf er f unct i on:

0. 5034- - - - - - - - - -z - 0. 4966Sampl i ng t i me: 0. 7>> st ep ( sysc, ' r - ' , sysd, ' c- ' , sysdd, ' g- - ' )

4 2 2 M h b MATLAB & Si li k a) M phng bng cc lnh trc tip t Toolbox



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98


Nhm lnh lc sFIR (Finite Impulse Response, thuc Signal Processing Toolbox)

V d:% To tp s liu x c chiu dI% length(x)=101>> t = 0: 0. 005: 0. 5;>> x = 5 + 8*si n( 2*pi *8*t ) + 4*cos( 2*pi *33*t ) ;% Thit k b lc FIR

>> Bw = f i r 1( 20, 0. 2, hammi ng( 20+1) ) ;% Dng Bw lc x theo 2 cch: filter% v filtfilt>> x_f = f i l t er ( Bw, 1, x) ;>> x_f f = f i l t f i l t ( Bw, 1, x) ;

( )

( )

( )

( )

( )

( ) ( ) ( ) ( )

( ) ( )

1 1

1

1 1

1 21 2 3 1

1 21 2 3 1

1 1 2 1

2 1

1

1

+

+

+

+

= =

+ + + +=

+ + + +

= + + +

mm

nn

m

n

y z B z

H z x z A z

b b z b z b z

a a z a z a z

a y k b x k b x k b x k m

a y k a y k n

p ng tn s ginon

f r eqz( num, den, points, samplingfreq)

Lc s liu c h iuchnh pha

f i l t f i l t ( num, den, data)Lc s liuf i l t er ( num, den, data)

Thit kb lc FIR(lc thng thp)

f i r 1( order, limitfrequency, window)

B lc FIR v hm ca sCng thc tng qut:

4 2 2 M h b MATLAB & Si li k a) M phng bng cc lnh trc tip t Toolbox



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Nhm lnh lc sIIR (Infinite Impulse Response, thuc Signal Processing Toolbox)

V d:>> t = 0. 01: 0. 01: 1;>> x = 5 + 8*si n( 2*pi *8*t ) + 4*cos( 2*pi *40*t ) ;>> [ B, A] = but t er ( 4, 20/ 50) ; %Thit k b lc IIR>> x_f = f i l t er ( B, A, x) ; %Lc tn hiu x>> x_f f = f i l t f i l t ( B, A, x) ; %Lc tn hiu x c b pha>> pl ot ( t , x, ' g- ' , t , x_f , ' r - ' , t , x_f f , ' b: ' ) ;>> axi s( [ 0 0. 5 - 10 30] ) ;>> t i t l e( ' Di scret e Fi l t er ' , ' FontSi ze' , 12) ;>> xl abel ( ' Ti me [ s] ' , ' Font Si ze' , 12) ;>> l egend( ' non- f i l t er ed' , ' I I R f i l t er ' , ' I I R f i l t f i l t ' ) ;

( ) ( ) ( )

( )1 1 2

1

2 +1

1

0+

= + +

+

= = =

m

n

a y k b x k b x k

b x k m

a a

Lc TschebyscheffTyp 1cheby1( order, ripple, limitfreq)Lc TschebyscheffTyp 2cheby2( order, ripple, limitfreq)Lc Elliptic (Cauer)el l i p( order, ripple, attenuation, limitfreq)

p ng tn s gin onf r eqz( num, den, points, samplingfreq)Lc s liuch iu chnh phaf i l t f i l t ( num, den, data)Lc s liuf i l t er ( num, den, data)

Lc Butterworthbutter( order, limitfreq)B lc IIR

Cng thc tng qut:

4 2 2 M phng bng MATLAB & Simulink b) M h b t Si li k



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100

4.2.2 M phng bng MATLAB & Simulink b) M phng bng s cu trc ca Simulink:

Khi Discrete Transfer Function c c im ging khi Discrete Filterv c m tbi hm

truyn t bn:

Cc h s ca hai a thc t s v mu s c khai bo theo trnh t s m ca z gim dn, btu t m (t s) v n (mu s).

Discrete Transfer Function (scalar)

Khi Discrete Filterm t mt khulc s c hm truyn t nhbn:

Cc h s ca a thc t s v mu s c khai bo theo trnh t s m ca z gim dn, bt ut h s ca z0.

Discrete Filter (scalar)

Khi Discrete-Time Integrator(tch phn gin on) v cbn cng ging nh khi Integrator(tch phn) lin tc. Bn cnh chu k trch mu ta cn phi chnchomi khi thut ton tch

phn (tch phn Euler tin, tch phn Euler li hay tch phn hnh thang). Sau khi chn thutton tch phn, biu tng (Icon) ca khi li thay i tng ng.

Discrete-Time Integrator

Khi Unit Delay c tc dng trch mu tn hiuvovct gi gi tr thu c trong mt c h u k trch mu. V vy, khi c c im nh mt phn t cbn cacch gin on. Khi c t h

c s dng nh mt khu qu t tn s trch mu thp sang tn s trch mu cao.

Unit Delay

( ) ( )( )

1 21 2 3 1

1 21 2 3 1

+

+

+ + + += =+ + + +

m m mm

n n nn

B z b z b z b z bH zA z a z a z a z a

( ) ( )( )

( )( )

1 1 1 21 1 2 3 1

1 21 11 2 3 1

+

+

+ + + += = =

+ + + +

mm

nn

y z B z b b z b z b zH z

a a z a z a zx z A z

4 2 2 M phng bng MATLAB & Simulink b) M phng bng s cu trc ca Simulink



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101

4.2.2 M phng bng MATLAB & Simulink b) M phng bng s cu trc ca Simulink(tip):

Khi Zero-Order Holdtrch mu tn hiu u vo v gi gi tr thu c n thi im trch mutip theo. Nn s dng khi Zero-Order Holdtrong cc h trch mu cha c mt trong cc khigin on c m t trn (tc lnhng khi c sn khu gi chm bc 0). Khi chn buctch phn cng, c th s dng khi Zero-Order Holdti c cv tr chuyn t tn s trch mu caosang tn s trch mu thp hn.

Zero-Order Hold

Khi Discrete State Space m t mt h thng gin on bng m hnh trng thi. Khic c im s dng ging nh khi State Space cacch lin tc.

Discrete State Space

Trong khi Discrete Zero-Pole, thay v phi khai bo cc h s, ta khai bo im cc - im khngca hm truyn t v mt h s khuch i.

Discrete Zero-Pole (scalar)

Ch : Mt h thng s k thut thng s dng nhiu chu k trch mu khc nhau (gi l hc chu k hn hp), v cn phi c lu c bit khi m phng.H lai l cc h c chac hai thnh phn lin tc v gin on.

4 2 2 M phng bng MATLAB & Simulink


b) M phng bng s cu trc ca Simulink


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102

4.2.2 M phng bng MATLAB & Simulink b) M phng bng s cu trc ca Simulink(tip):

V d:M phng khu C 2 chiu (2-dimensional, khu MIMO) dng C vector dng statoris cang cxoay chiu 3 pha.

S cu trckhu C digital

S m hnhSimulink

4. Thc hin k thut h thngK s4.3 Thit k h thng vi iu khin

4 3 1 Phn loi vi x l l t t ( C P U )


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103

4.3.1 Phn loi vi x l

n v s

h c v l g i c( A L U )

n v x l t r u n g t m ( C P U )K h u i u k h i nK h u t n h t o n

K h u m

B u s t r n ph i n

T h a n h g h is l i u

T h a n h g h i a c h

G i i m l n h

m c h - n gt r n h

m B u ss l i u m B u s i u k h i n m B u s a c h

Ch vi trong khi nim trn c ci ngunt ch micro, k hiu l , c ngha l

mt phn triu hoc rt nh. Vi x l(Microprocessor) c ngha l b x l rtnh, k hiu l P.Khu tnh ton: gm c n v shc vlgic (Arithmetic Logic Unit: ALU), cc

thanh ghi sliu va ch.Khu iu khin: gm c b gii m lnhv b m chng trnh.Khu m: vi cc bm (thng l batrng thi: Tri-State), ghp ni Bus trnphin ca P vi cc Bus iu khin, sliu v a ch nm bn ngoi.

a) Khi nim vi xl

Ch : s dng trong cc h thng K s, P sphi c b sung thm cc phn t ngoi vi, phcv vic nhng (embed) P vo mi trng thit b.

Hnh trn: Cu trc bn trong ca mt P


4.3.1 Phn loi vi x l (tip)


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104


Vi xl tn hiu =Digital Signal Processing(DSP).c thit k tng tc x l, tnh tng tch ly:

Bn cht DSP: l P c thm thanh ghi ACC (vib rng gp i b rng ca Bus) v b nhn cng.Nhiu thao tc trong 1 lnh: DSP cho php thc

hin cc thao tc (lm trn, dch tri/phi vv) ng thi vi nhn v tch ly ch trong mt nhplnh duy nht.Cu trc Bus: Bus trn phin (on-chip) c thchin theo cu trc Harward.

b) Khi nim vi xl tn hiuVi x l

N h c h - n g t r n h N h s l i u

B u s a c h

B u s s l i u

i u k h i n

Vi x l

N h c h - n g t r n ht r n c h i p

N h s l i ut r n c h i p

i u k h i nBu

ssliu

1

Bu

ssliu

2

Bu

sach1

Bu

sach2

a)

b)

Progra m

B us

D at a B us

( )i ia x

Hnh bn: Cu trc Bus a) kiuVon-Neumann; b) kiu Harward


4.3.1 Phn loi vi x l (tip) c) Khi nim vi iu khin


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105

3 o (t p) c) Khi nim vi iu khin

Vi iu khin = P (hoc DSP) + ngoi vi + ngt khng cn th tc

Ch : C c phn bitvi P l do cc c im:a) c thm cc phn t ngoivi cbn trn phin(peripheries on-chip) v b) c

cch ngt khng cn th tcngt. iu ny cho php nngcao tc tnh ton, tng tin cy, ng thi gim githnh ca h thng.

C 1 6 6 - C o r e C 1 6 6 - C o r e

16 7

PL L

OS C

2KB

XR AM

P o r t 6

P

o r t 0

P o r t 4

P o r t 1 P o r t 5 P o r t 3 P o r t 2 P o r t 8 P o r t 7

CP U D u a l P o r t

R AM

2 K B y t e

I n t e r r u p t C o n t r o l l e r W a t c h d o g

P e r i p h e r a l D a t a

E x t e r n a lI n s t r . / D a t a

I n s t r . / D a t a

U S A R T

ASC

BRG BRG

SS C

S y n c .C h a n n e l

( S P I )

G P T 1

T3

T4

G P T 2

T2

T5

T6

C AP C O M 1 , 2

32C h a n n e l s

Timer7

Timer1

Timer0

Timer8

P W M M o d u l e

P T 1

P T 2

P T 3

P T 4

1 6 1 6 1 6 1 6 8 8

1 6

8

8

1 6

1 6

1 6

1 632

PE C

I n t e r r u p t B u s

D a t a

D a t a

E P R O M

R OM /

F l a s h

u p t o1 2 8 K B yt e

X B U S

(16-bitNON

MUXData/Addresses

)

E x t e r n a l B u s ,X B U S C o n t r o l ,5 * CSLogic

M u l t i F u n k t i on a l

1 0 - B i t

ADC1 6 C h a n n e l s

3 6 e x t . I R

XTAL

Hnh bn: Cu trc chi tit ca C16 Bit loi SAB C167 (Siemens)




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106

( p)

d) Khi nim DSP Controller

A (1 5- 0)

D ( 1 5 - 0 )

5 4 4 W x 1 6

P r o g r a m R O M /

1 6 kW x 1 6

D a t a R A M

CPU

1 6 - B i tB a r r e l

Shifter

1 6 - B i t T - r e g i s t e r

1 6 x 1 6 M u l t i p l y

3 2 - B i t P - r e g i s t e r

S h i f t L ( 0 , 1 , 4 , - 6 )

3 2 - B i t A L U

3 2 - B i t A c c u m u l a t o r

S h i f t L ( 0 - 7 )

8 L e v e l H / W S t a c k2 S t a t u s R e g i s t e r s

R e p e a t C o u n t

8 A u x i l i a r y R e g i s t e r s

F l a s h

Three I/O Ports8 - B i t

1 0 - B i t A D C

1 0 - B i t A D C

W a t c h d o gT i m e r

SPI

SC I

E v e n t M a n a g e r

3 T i m e r s

1 2 P W M

O u t p u t s9 C o m p a r e

O u t p u t s

D e a d B a n dL o g i c

IGRInterface

Hnh bn: S khi ca DSP Controller khiu TMS 320C/F240 (Texas Instruments)

Cch nh ngha C nh ta

nu mc 4.3.1c cng c thc p dng i vi DSP.

Thay v vit cng thc:C = P + ngoi vi

+ ngt khng cn th tc

ta vit:C = DSP + ngoi vi

+ ngt khng cn th tc= DSP Controller


4.3.2 Khi qut v nhim v thit k


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107

q

Minh ha nhim v thit k thng qua v d c th: H thng K s cho truyn ng in xoay chiu 3 pha.

Cn phi lm r cc vn c th:Hardware: La chn vi x l (h 1 hay nhiu P, C)? Cn nhng ngoi vi g v vi tnh nng th no?Software: Cng c, quy trnh v qun l (management) pht trin? Chun b lp trnh (thut ton, chunha, th vin, test)?

4.3.3 Hardware: Yu cu i vi vi x l



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108

Chn h 1 vi xl (Single Processor System) khi Hardware chphi thc hin cc bi ton K. Nhim v truyn thng vi mi

trng xung quanh mc rt hn ch. Chn h 2 vi xl (Double Processor System) khi Hardware

khng chphi thc hin cc thut ton thi gian thc m cn

phi cho php tch hp vo mt mi trng cng ngh t ng(v d: nhField Bus, K qua giao din vv...) phc hp.

Vi x l/cc vi x l cn phi c kh nngm ng ccnhim v ca ngoi vi (v d: ADC, iu ch, o tc quayvv...) ti mc ti a. V vy, nu l h 2 vi x l th 1 sphic chn l C.

4.3.3 Hardware: Yu cu i vi vi x l (tip)



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109

V d v mt h 2 vi x

l, bao gm DSP loiTMS 320C25 (TexasInstruments) v C loiSAB C167 (Siemens).

Tn dng kh nng tnhton ca DSP thchin cc thut ton thigian thc phc hp.

Tn dng ngoi vi phongph ca C ghp vimi trng cng ngh.

4.3.4 Hardware: Yu cu i vi ngoi vi (trn c s v d mc 4.3.2)



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110

Phi c n v PWM(Puls Width Modulation) vi phn giithi gian b nht (v d: 50ns ca SAB C167, TMS 320C/F240)phc v iu ch vectorin p.

o dng statorvi phn gii 10...12bit. i vi truyn ngcht lng cao phi l 12bit-ADC vi tc bin i


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Software

Tp hp tt c cc cng thc cn tnh (cc thut ton) cng vicc tham s ca i tng cng ngh (v d: s liu ng c).

Chun ha cc cng thc cn tnh, xc nh kch cca dliu(b rng word) cng nh chnh xc ca dliu (sbits saudu phy).

M t chu trnh tnh bng lu thut ton (flow chart). Xc nh chng trnh chnh, chng trnh con v chng trnh

ngt(chng trnh con theo mnh thi gian hay theo mc u

tin khc nhau). Xc nh cc module thvin.

4.3.5 Software: Cng c pht trin v cng tc qun l


b) Chun b cng c pht trin( i t ht t i )


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112

(mi trng pht trin)

Editor: Trnh son tho m ngun

C Compiler: Trnh bin dch m ngun C

Assembler: Trnh thng dch hp ng Linker, Locater: Hai trnh ghp, nh v

cc modules. i khi l 1 trnh vi 2options khc nhau.

Librarian: Trnh qun l th vin

Format Converter: Trnh o nh dng Object/Hex Converter: Trnh o m

chy/m hexa

Debugger: Trnh gri

Emulator: Thit b m phng chip

Target System: Hardware

EPROM Burner: My np EPROM


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d) Cc nguyn tc thc hin


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114

1) Cc bc pht trin

Xy dng danh mc yu cu i vi Software (theo nhu cuca th trng)

Khng nh kh nngp ng danh mc yu cu Phn tch phng n,phn tch h thng trn csHardware

thit k Xc nh cc modulesphn mm cn son tho Son tho cc modules c th Thnghim ring rtng module (Test Programs, Debugger,

Emulator, Hardware-in-the-Loop-Test) Thnghim tng thtrn thit b



d) Cc nguyn tc thc hin (tip)


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2) Qun l Files v k hiu

Cu trc th mc trn PC: Source Files, .obj Files, vv

Tn Files: mang ngha d hiu

Tn k hiu, tn bin: mang ngha d hiu, khai bo tp trung d qun l (trnh lng ph b nh, tng tc )

3) Qun l v to phin bn4) Cu trc ca tng module

Chc nng ca module Mt module Giao din vi bn trong module Lch s ca module Giao din vi bn ngoi module Tn module


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