Digitalni Sistemi Upravljanja Skripta Rev1207

7/30/2019 Digitalni Sistemi Upravljanja Skripta Rev1207

1/16

..


2/16

1

1.

1.

.

.

,

. /D, .

, .

, ,

,

.

, d

,

.

D/ - .

.

e

r(t)

T-

TsdTe

* u*

m

c

.

e

r(t)

T-

TsdTe

* u*

m

c

1.

2. 2.

,

f(t) :

==

=0k

*)kTt()kT(f)t(i)t(f)t(f . (1)

t

f(t)

t

i(t)

0 T 2T 3T -T-2T

t

f*(t)

0 T 2T 3T -T-2T

=

==

=0k

*

)kTt()kT(f

)t(i)t(f)t(f

0t

0)t(f

/2

:

f(t) 0 rad/s,

)/2(2

1T 0 .

.

F(s):

=

C)ps(T

*dp

e1

1)p(F

j2

1)s(F

. (6)

(6) F(s).

4.

NF .

.

. D/

- .

5, 6 gh0(t):

)Tt(h)t(h)t(g 0h = (7)

h(t) . (7)

Gh0(s):

[ ] se1

)t(gL)s(G

Ts

0h0h

==

. (8)


5/16

4

(8) 7

, 5 , NF

.

t

mk(t)m(kT)

mk(t)=m(kT)

kT


6/16

5

:

T2T52sT22s

sT25s

sT2sTsT22

0s

sT22s

sT25s

sT0s

2

ez

z

12

1

ez

z

75

1

)1z(

z

10

T

1z

z

100

7

ez

z

)5s(s

1lim

ezz

)2s(s1lime

)ez(z

)2s)(5s(T

ezz

)2s()5s(7s2lim

ez

z

)5s(s

1lim

ez

z

)2s(s

1lim

ez

z

)2s)(5s(

1

ds

dlim

)2s)(5s(s

1Z

+

+

=

++

+

++

++

+++=

=

++

++

++=

=

++

, z

. z

. , ,

,

.

6. z z , :

- :

{ } )z(Fz)nTt(fZ n = (15) (11):

{ }

)z(Fzz)mT(fz

z)nTkT(fzz)nTkT(f)nTt(fZ

n

0t,0)t(fnm

mn

0k

)nk(nk

0k

== =

= = =


7/16

6

)z(R)s(G)s(GZ)z(C p0h = . (19)

)s(G)s(GZ p0h .

.

r(t)

T

r(t)*

Gh0(s) Gp(s)

c(t)*

c(t)Tr(t)

T

r(t)*

Gh0(s) Gp(s)

c(t)*

c(t)T

8.

(8)s

e1)s(G

sT

0h

=

{ }

=

=

s

)s(GZ)z1()s(G

s

e1Z)s(G)s(GZ

p1p

sT

p0h (20)

(9).

.

1:

e(t)

T

e(t)*

H(s)

G(s)c(t)r(t)

-

e(t)

T

e(t)*

H(s)

G(s)c(t)r(t)

-

9.

)s(E)s(G)s(H)s(R)s(E *=

{ } )s(E)s(G)s(H)s(R)s(E **** =

{ })s(R

)s(G)s(H1

1)s(E

*

*

* +

=

)s(E)s(G)s(C)s(E)s(G)s(C**** ==

)z(R)z(HG1

)z(G)z(C)s(R

)s(HG1

)s(G)s(C

*

*

**

+=

+=

2:

u

T

H1(s)

Gs(s)c

-

T

D2(z)

H2(s)T

r

-

D1(z)e

T

u

T

H1(s)

Gs(s)c

-

T

D2(z)

H2(s)T

r

-

D1(z)e

T

10.

{ } )z(U)s(H)s(GZ)z(D)z(D)z(E)z(U 1s21 = { } )z(U)s(G)s(HZ)z(R)z(E s2 = { }[ ] { } )z(U)s(H)s(GZ)z(D)z(D)z(U)s(G)s(HZ)z(R)z(U 1s21s2 =


8/16

7

{ } { })z(R

)z(D)s(H)s(GZ)z(D)s(G)s(HZ1

)z(D)z(U

21s1s2

1 ++

=

{ } )z(U)s(GZ)z(C s =

)z(D)z(GH)z(D)z(GH1

)z(G)z(D

)z(R

)z(C

2s11s2

s1

++

=

8.

, , D(z),

.

z:

+

==

=

=

n

1k

kk

m

0k

kk

zb1

za

)z(R

)z(U)z(D (21)

ak bk j .

D(z), .

(21) :

)z(U)zb...zbzb()z(R)za...zazaa()z(Un

n2

21

1m

m2

a1

10 +++++++= .

t=jT z (15) :

[ ] [ ] [ ]

[ ] [ ] [ ]T)nj(ub...T)2j(ubT)1j(ub

T)mj(ra...T)2j(raT)1j(ra)jT(ra)jT(u

n21

m210

++++=(22)

(22) D(z),

11 .

z-1

, u .

t=jT r(jT)

a0, r[(j-

1)T], r[(j-2)T],..., r[(j-m)T] u[(j-1)T], u[(j-2)T],..., u[(j-n)T] a1, a2,..., am, -b1, -

b2,..., -bn. u(jT).

r(jT) z-1

,

.

r*(t)

T

z-1

a0

a1

z-1

a2

z-1

am

.

.

.

.

.

.

z-1

-b1

z-1

-b2

z-1

-bn

.

.

..

.

.

u*(t)r*(t)

T

z-1

a0

a1

z-1

a2

z-1

am

.

.

.

.

.

.

z-1

-b1

z-1

-b2

z-1

-bn

.

.

..

.

.

u*(t)

11.


9/16

8

a0r(jT), u .

(21) G1(z) G2(z)

, :

)za...zaa(zb...zbzb1

1)z(G)z(G

)z(R

)z(U)z(D

mm

110n

n2

21

1

21

+++

++++===

u1(t):

nn

11

11zb...zb1

)z(R)z(R)z(G)z(U

+++==

)z(U)za...zaa()z(U)z(G)z(U 1m

m1

1012 +++==

t=jT :

[ ] [ ] [ ]T)nj(ub...T)2j(ubT)1j(ub)jT(r)jT(u 1n12111 =

[ ] [ ]T)mj(ua...T)1j(ua)jT(ua)jT(u 1m1110 +++= . 12

.

u . ,

r*(t)

T

z-1

a0

a1

z-1

a2

z-1

am

.

.

.

..

.

-b1

-b2

-bm

.

.

.

u*(t)

u1

*(t)

z-1

-bn

.

.

.

.

.

.

r*(t)

T

z-1

a0

a1

z-1

a2

z-1

am

.

.

.

..

.

-b1

-b2

-bm

.

.

.

u*(t)

u1

*(t)

z-1

-bn

.

.

.

.

.

.

12.

u1,

u1, u. ,

.

.

9. z z z=

.

,

. z.

1-2, 2-3, 3-4, 4-5 5-1

13 . 1-2 s=j,


10/16

9

z=ej

. z , . 0

/2=/, 0 . 2-3s=-+j 0


11/16

10

Re(z)

jIm(z)

x xxxx x

x

x

x

x

xx

x

x

4123

5

5

6

6

7

7

8

8

9 10

1

4

6

523

9

10

8 7

Re(z)

jIm(z)

x xxxx x

x

x

x

x

xx

x

x

4123

5

5

6

6

7

7

8

8

9 10

1

4

6

523

9

10

8 7

15. z

10. ,

. :

:

2

T < . (23)

,

. , 1/10 95%

.

. ,

.

3 4

,

. f

(23) :

o

f)43(

1

2

1T

= (24)


12/16

11

1


13/16

12

)s(E

)s(U

as

a)s(Gr =

+= (26)

(26) :

)t(ea)t(ua)t(u += (27)

)t(u u(t).u(t) :

[ ] +=

t

d)(ea)(ua)t(u . (28)

t=kT,u(kT) :

[ ] [ ]

[ ] [ ] ++=

= ++ +=

kT

T)1k(

kT

T)1k(

T)1k(

d)(ea)(uaT)1k(u

d)(ea)(uad)(ea)(ua)kT(u

(29)

u(kT) u[(k-1)T]

(k-1)T


14/16

13

13. PIPI PI

. PI :

+=t

0I

P dt)t(eT

1)t(eK)t(u . (36)

e(iT)

(i=0, 1, 2, ...) PI:

+==

k

0mI

P )m(eT

T)k(eK)k(u . (37)

2. , z ,

(34), PI :

1I

Pz1

1

T

TK

)z(E

)z(U

+= (38)

, 18.

, .

u

TGs(s)

c

-

TKP

r

-

e

T Gh0(s)1I z1

1

T

T

u

TGs(s)

c

-

TKP

r

-

e

T Gh0(s)1I z1

1

T

T

18. PI

14.

.

19.

u

TGs(s)

cr

-

D(z)e

T Gh0(s)u

TGs(s)

cr

-

D(z)e

T Gh0(s)

19.

Wf

Gh0, (8), ,

, G:

)s(Gs

e1)s(W s

sT

f

=

. (39)

z :

[ ])z(C)z(R)z(D)z(W)z(C f = (40) Wf(z) . (40)

D(z):


15/16

14

)z(R

C1

)z(R

C

)z(W

1)z(D

f = (41)

)z(R

C .

.

1/ d=NT

. 20,

(42).

sTNe)s(s

)s(C

+=

(42)

1/

.

tNT

c(t)

1

0,63

1/ tNT

c(t)

1

0,63

1/

20.

z (z):

+=

+

= )s(s

Zze)s(s

Z)z(CNsTN

(43)

:

)ez)(1z(

)e1(z

ez

z

s

1lim

ez

z

s

1lim

s0ssz

z

)s(s

1sRe

)s(s

1Z

T

T

sTs

sT0s

sT

=

+

+=

===

+

=

+(44)

(z):

)ez)(1z(

)e1(z)z(C

T

T)1N(

+

= . (45)

)z(RC

(45) z , . { }1z

z

s

1Z)s(RZ

=

= :

)ez(

)e1(z

1z

z

1)z(C)z(

R

CT

TN

=

= . (46)

(46) Wf(z), z (39), (41)

D(z).

1.

Gs

1. 1 d=NT:


16/16

15

sTN

1

s e1sT

K)s(G

+= . (47)

z (39) :

1T/T

1T/TN

1

N1sTN

1

sT

fez

)e1(zK

)1sT(s

1Zz)z1(Ke

1sT

K

s

e1Z)z(W

=

+=

+

=

(48)

(48) (46) (41) 1T/Te1C = D(z):

)]e1(zze1[CK

)ze1)(e1(

ez

)e1(z1

ez

e1z

ez

CzK

1)z(D

T1N1T

11T/TT

T

TN

T

TN

1T/T

N

=

= (49)

.N=2. :

0z)e1(ze13T1T = (50)

:

0)]e1(z)e1(z1)[z1(T2T11

=++

. (51)

4

ee23

2

e1z

T2TT12,1

++

= ,

.

. D(z)

.

, z=1

. (51), (49),

:

+

==

1

1T/T1T/T

T

T

1T

11T/TT

z1

e1e

)e23(CK

)e1(

)z1)(e23(CK

)ze1)(e1()z(D

(52)

PI

:

)e23)(1e(K

e1K

T1T/T

T

P

= , )1e(K

T

TK 1

T/TP

I

I == . (53)

,

.

. 21 .,

, 18.

c

t

=0,2=0,5=0,8

=0,1

c

t

=0,2=0,5=0,8

=0,1

21.

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Digitalni Sistemi Upravljanja Skripta Rev1207