8/13/2019 thit k h thng iu khin

1/62

F H GF Z

2

KH AH

AG FG \ 8

Z@GZ O@Z@FC H GF Z...:

T`f G. Z`gt ok `f` 8J..:2. K `f` tfc t`.:

>. Hh o`u o`p v hh ntruyf.:

T`f GG. Zf` tif fc `h t`uf, fc `h fch ^init ^^0

2. fc `h t`uf.......0

b. Z`gt ap `tb t`li quy th Jlfbvgt @brtlfnlrc..........0

n. Kb trf Jlfbvgt @brtlfnlrc0

h. Ph f` vtr gk th fc hug T7

>. fc `h fch..7

T`f GGG. Z`gt oqui h`uyf fc h`i ^init ^^...24

2. Ry i trifc o`fc cgbf o`p...24

>. Ry i trifc o`fc cgbf ak vgh......2>

b. Ry i gk th fc hug t`li fc t`fc tB f N trifc th (s)....2>

n. Ry i gk th fc hug t`li fc fc trf tB f N trifc th (s)

ay fc of` BN ak fc of`...28

T`f GU. O`i st fc ah `h .2:

T`f U. Z`gt ogu o`gf.23

2. @t`fc gu o`gf trifc o`fc cgbf o`p23

2.2. @t`fc gu o`gf p`f `g.23

b. Aut gu o`gf.23

n. Z`gt oh`i ^init ^^272.>. @t`fc gu o`gf kiklf tf` tif>2

b. Aut gu o`gf.>2

n. Z`gt oh`i ^init ^^>8

>. @t`fc gu o`gf trifc o`fc cgbf ak vgh...>

8/13/2019 thit k h thng iu khin

2/62

F H GF Z

>

@t`fc gu o`gf kb trf Mbhinglf h`uyf v

b. Aut gu o`gf...>5

n. Z`gt oh`i rinit ^^>3

T`f UG. Hh h`fc trf` k p`fc vgt nfc fcf fcKbtabn.82

2. H`fc trf` k p`fc ot qup`f `t`fc gu o`gf p`f `g...82

>. H`fc trf` k p`fc ot qup`f `t`fc gu o`gf kiklf tf` tif..8 o`u ^^- Hig hh o`u a hh t`bf` fc h`t ,tgt jgf fcbfc o`fc fc o-Z`fc s`f` `h v o`g afc tfc t`bf`

b2;;:4(hk);4.: (k),k2 ; >.< (oc),k2 ;2.. Hh o`u o`p v hh ntruyf

>.2 Ou 4 ( )

8/13/2019 thit k h thng iu khin

5/62

F H GF Z

. O`u

>.>. O`u 2 vo`u >

O`u 2 oh` t`h > trh a oh` t`h :44 (kk).

8/13/2019 thit k h thng iu khin

6/62

F H GF Z

5

@f` 2.8. O`u 2, o`u >

>.8. Hh ntruyf fc

+ Nf trg a ntruyf nf` rfc cgp tfc kiklf hb fc h ff cf trfo`u o`fc th jfc jf fc h`i o`u 2

+ Nf p`g a ntruyf nf` rfc cgp tfc kiklf hb fc h ff cf trfo`u > o`fc th jfc jf fc h`i o`u > vg vgh ti vf th ch tfc g k

`f` f` nf` rfc `f` tgf`

+ Nf jg a xgabf` o` ff jf fc h`i h hu tby op

8/13/2019 thit k h thng iu khin

7/62

F H GF Z

3

@f` 2.:. hh ntruyf

8/13/2019 thit k h thng iu khin

8/62

F H GF Z

0

T`f GG. Zf` tif fc `h t`uf, fc `h fch ^init ^^

2. fc `h t`ufZb t`gt ap p`fc trf` fc `h t`li p`fc

p`p kb trf Jlfbvgt @brtlfnlrc

b. Z`gt ap tb t`li quy th Jlfbvgt @ brtlfnlrcO`u 4= tb h`f `tb PiWi]i h trh ]i

h`f trfc vg o`p 2, trh Pi h`f ty sbi h`i p``p f`t f` `f` v, trh Wi h`f t`li quby th tbkjgf t`uf.

O`u 2= tb h`f `tb P2W2]2h trh ]2 trfcvg o`p >, trh P2tb h`f t`li fc vufc ch h`ufc]i v ]2tb h`f f` `f` va p` `p f`t, trh W2

h`f t`li quby th tbk jgf t`uf@f` >.2. ^init ^^O`u >= tb h`f `tb P>W>]>h trh ]>sifc sifc vg ]2, P>h`f t`li

fc vufc ch h`ufc ]2v ]>, W>h`f t`li quy th tbk jgf t`ufn. Kb trf trfc t`g Jlfbvg t @brtlfnlrc

Zvgh h`f `tb tb h nfc J@ sbu=

O`u j b 2 4 q2 b2 4> 4 q> b> 4

4

2B ;

2 2 2 2

2 2 2 2

his( ) sgf( ) 4 is( )

sgf( ) is( ) 4 sgf( )

4 4 2 4

4 4 4 2

q q b h q

q h q b q

, 2>B ;

> > > >

> > > >

his( ) sgf( ) 4 is( )

sgf( ) is( ) 4 sgf( )

4 4 2 4

4 4 4 2

q q b h q

q h q b q

4

>B ;4

2B .2

>B

4

>B ;

2 > 2 > 2 2 > 2 >

2 > 2 > 2 2 > 2 >

his( ) sgf( ) 4 is( ) his( )

sgf( ) is( ) 4 sgf( ) his( )

4 4 2 4

4

q q q q b h q b q q

q q h q q b q b q q

4 4 2

8/13/2019 thit k h thng iu khin

9/62

F H GF Z

7

h.Ph f` vtr gk th fc hug TZkb trf trfc t`g hb ` P>W>]> g vg `hf` PiWi]i

4

>B tb xhf` h gk th fc hug T hb o`u > si vg `hf`, v kb trf hisgf h``fc o`u > si vg PiWi]i4

Tr ; 2 2 > 2 > 2 2 > 2 >is( ) his( ) sgf( ) sgf( ) 4

Z

b h q b q q b q b q q

4

>^ ;2 > 2 >

2 > 2 >

his( ) sgf( ) 4

sgf( ) is( ) 4

4 4 2

q q q q

q q h q q

2 2 > 2 >

2 2 > 2 >

his( ) his( )

sgf( ) sgf( )

4

p

p

p

x b q b q q

y b q b q q

z

H` = Zb h rinit p`fc `bg nh tji o`g tf` tif `by gu o`gf tb qubftk f gk th fc hug trifc p`fc o`fc qubf tk f `fc o`u hug vo`g tb tk h hh ngf o`p tgk th fc hug v t tk h kb trf

hisgfh``fc 4>^ t xh f` h hh ch Hbrjbf`by Lualr

>. fc `h fchO`g cgg ng tif fc `h t`uf fcg tb xh f` h qubf `jh jfc

kb trf f` sbu= x;e(q) . Zqubf ` tb suy rb kt hh` `f` t`h q;e-2(x)trifc x ; _x2,x>,,xk[

Z,q; _q2,q>,,qf[Z.

F` vy tb h `bg h`gu `fc cgg a p`fc p`p sv p`fc p`pcgg th` vg ng tif ^init^^ f cgf tb jfc p`fc p`p cgg th` a f cgfv jcgg f`t f`fc vg f`fc ng tif rinit f`gu nh p`fc p`p sa

p`fc p`p `u `gu

t`2 2 > 2 >

2 2 > 2 >

his( ) his( )

sgf( ) sgf( )

4

p

p

p

x b q b q q

y b q b q q

z

(>.2)

O `gu H2; his(q2), X2; sgf(q2), H>; his(q>), X>; sgf(q>),H2>; his(q2+q>),X2>; sgf(q2+q>),

Z`(>.2) ;6> > > > > >

2 > 2 > 2 2> 2 2> 2 > 2 > >> ( ) >p px y b b b b H H X X b b b b H

8/13/2019 thit k h thng iu khin

10/62

F H GF Z

24

;6

> > > >

2 >

>

2 >

>

> >

his( )>

sgf( ) 2 is ( )

p px y b b

qb b

q h q

vy > > >b tbf >(sgf( ), is( ))q q h q .

Z`(>.2) tb vgt ag f` sbu2 > > 2 > > 2

> > 2 2 > > 2

( )

( )

p

p

x b b H H b X X

y b X H b b H X

Cgg `p`fc trf` g stuyf tf` fy tb h =

2 > > > > > > > >

2 > 2 > >

> > 2 > >

>

p p

b b H b X b b b b H x y

b X b b H

> >

2 2 > > >

2 > >

( )

p

p p p

p

x b X

b x b x H y X y b b H

2 > >

> 2 > > >

> >

( )

p

p p p

p

b b H xb y b y H x X

b X y

2 > > >

2 > >

2 > > >

2 > >

( )his( )

( )sgf( )

p p p

p p

p p p

p p

b x b x H y X q

x y

b y b y H x X qx y

;6 2 2 2tbf > sgf( ),his( )q b q q

T`f GGG= Z`gt oqui h`uyf fc h`i ^init

2. Ry i trifc o`fc cgbf o`p

Zb h`f > gk B(x4,y4), N(xh,yh) nt o trifc o`fc cgbf ak vgh, Z

p`fc trf` fc `h fch tb tf` p`f trf tb xh f` h ch o`p tg `bggk B,Na B(qgb,qgb), N(qgn,qgn).

Z`bg hp ch o`p tk h tb g t`gt oqup qg(g;2=>) ngf t`gftqgbf qgnt`li qui nh 8 ( pfc vkt th ch o`p ) trifc vfc

th(s). F` vy=> 8

2 > 8( )g ig g g gq t b b t b t b t

(8.2)

8/13/2019 thit k h thng iu khin

11/62

F H GF Z

22

Ug hh gu ogf f` sbu=

(4)

(4) 4

( )

( ) 4

g gb

g gb

g h gn

g h gn

q q

q q

q t q

q t q

(t`fc t`fc tb yu hu vf

th ch o`p tg gk u v gk hug nfc 4 ). Zhh gu ogf trf tb t`by vi(8.2) cgg tb h hh `s

4

2

> >

8 8

4

8( )

>( )

g gb

g

gn gbg

h

gn gbg

h

b q

b

q qb

t

q qbt

U j= ^init jg h`uyf B(4,>+4,>< 8 4,> 8 ) f N(4,< 4,: 8 )

trifc 5

bq

,

>8

nq

42

22

>2

82

54

2>

>>

8>

54

8

2

> 8

>

5 . t`(ch o`p, vf th v cgb th o`p )

8/13/2019 thit k h thng iu khin

12/62

F H GF Z

2>

>. Rui trifc o`fc cgbf ak vghp`h vh`i tf `gu vi h`i ngu o`gf trifc o`fc cgbf ak vgh ff

h`xt qui jg h`uyf hb rinit ^^ cgb `bg gk B(x4,y4), N(xh,yh) a fct`fc v fc trf ( tb t`gt oy a fc trf f`f BN ak fc of`)

b.Rui hb gk th fc hug t`li fc t`fc tB f N trifc th(s)

Zb hp`fc trf` fc t`fc trifc o`fc cgbf ak a kt p`fc cgb `bg

gk B(x4,y4), N(xh,yh)4 4

4 4h h

x x y y

x x y y

vg (x,y) a tb gk th fc hug

;6 4 4 4

4 4

h h h

h h

y y y x y xy x

x x x x

.

Hfc f` hh` t`gt ap qui ch o`p tb t`b kf gu ogf vvf thu v hug tb t`gt ap qubf `x;x(t) a b t`h nh 8.

> 8

2 > 8( ) ix t b b t b t b t

(8.>)

hfc hh gu ogf

4 4

4

(4) ( , )

(4) 4

( ) ( , )

( ) 4

h h h

h h

s B x y

v v

s t N x y

v t v

k qubf `y ;o.x+n ;6 x;x(t) hfc h gu

ogf f` qui.

Uy

4 4

4

(4) ( , )

(4) 4

( ) ( , )

( ) 4

h h h

h h

s B x y

v v

s t N x y

v t v

Z`by vi (8.>) vx(t) tb rt rb hh `s=

4 4

2

4> >

48 8

4

8( )

>( )

h

h

h

h

b x

b

x xb

t

x xb

t

o`g t`gt ox;x(t) ;6 4 4 44 4

( ) ( )h h h

h h

y y y x y xy t x t

x x x x

U j= Hf t`gt ojg h`uyf t`li fc t`fc tgk B(4.0?4.2) fN(-4.>?4.(s) thh hfc t`h trf tb tf` h =x;

y

v qubf ` y ;

8/13/2019 thit k h thng iu khin

13/62

F H GF Z

28

@f` >.8.t`x(t), y(t) @f` >.:. Rubf `y;e(x)

n.Z`gt oqui gk th fc th fc hug jg h`uyf t`li fc trf tBf N tr ifc th(s) ay BN ak fc of`.

Zb h p`fc trf` fc trf trifc o`fc cgbf ak a kt p`fc cgb `bggk B(x4,y4), N(xh,yh) ay BN ak fc of`

> > >( ) ( )g gx x y y ^

vg 4>

hg

x xx

4

>

hg

y yy

> >

4

2( ) ( )

> h i h

^ x x y y

Ugt jg jfc t`bk sf` sbu =

sgf( ( ))

his( ( ))

g

g

x x ^ b t

y y ^ b t

hfc t`b kf gu ogf vvf th b(t) tb t`gt ohfc p`g a nh 8

> 8

2 > 8( ) ib t b b t b t b t

U p`g t`b kf gu ogf=

4 4

4

(4) ( , )

(4) 4

( ) ( , )( ) 4

h h h

h h

s B x y

v v

s t N x yv t v

;6

4 4

4

(4) ( , )

(4) 4

( ) ( , )

( ) 4

h h h

h h

s B x y

v v

s t N x y

v t v

Z tb tk h hh `s b4,b2,b>,b8 f` sbu =

44 brhsgf

gx xb^

, 2

4b t 4brhsgf brhsgfh g gx x x xw^ ^

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14/62

F H GF Z

2:

Xuy rb = > >8

h

wb

t , 8 8

>

h

wb

t

U j= Hf t`gt ojg h`uyf t`li fc t`fc tgk B(4.3?4) fN(-4.3?4) trifc >(s) thh hfc t`h trf tb tf` h =

Rubf `

@f` >..5. Rubf `y;e(x)

T`f GU= O`i st fc ah `h

Hh t`bk sfc ah `h sbu xt trf `cf vgo`u (hig hh o`u a t`bf` kf` fc h`t hh ngut`h G g vg o`g tk Hg trifc `PhWh]hHgsifcsifc vg `tb o`u ) =

O`u xh yh zh kg Gxx Gyy Gzz Gxy Gyz Gzx2 2

>

b 4 4 2k 4 G2y G2z 4 4 4

> >>

b 4 4 >k 4 G>y G>z 4 4 4

Ug b2; 4.< (k), b>; 4.: (k),>

2 2 2 2

2

2>y zG G k b

, >> > > >

2

2>y zG G k b

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15/62

F H GF Z

2[Z

Zp`f fc `h tb xh f` h =

4

2Hr ;4 2

2 2.

H^ r ;

2 2

2 2

2his( )

>

2sgf( )

>

4

b q

b q

,4

>Hr ;4 2

> >.

H^ r ;

2 2 > 2 >

2 2 > 2 >

2his( ) his( )

>

2sgf( ) sgf( )

>

4

b q b q q

b q b q q

4 42

2 22.Z ^^ ;6

2

2

2

4

4

q

,

4 4>

> >>.Z ^^ ;6

>>

2 >

4

4

q q

4

2

2

( )H

Z q

rM

;

2 2

2 2

2sgf( )

>

2 his( )

>

4

b q

b q

,2

2

2

( )^ qM

; , (:.2)

>

>

>( )

^ qM

; (:.>)

4

>

>

( )H

Z q

rM

;

2 2 > 2 > > 2 >

2 2 > 2 > > 2 >

2 2sgf( ) sgf( ) sgf( )

> >

2 2 his( ) his( ) his( )

> >

4 4

b q b q q b q q

b q b q q b q q

. (:.8)

Kb trf tlf x quf tf` hb `bg o`u 2 v > vg trh cf vi o`g tk sifcsifc vg `trh hb o`u =

2G ; 22

4 4 4

4 4

4 4

y

z

G

G

,>G ; >

>

4 4 4

4 4

4 4

y

z

G

G

(:.:)

;6 Kb trf o`g afc=

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F H GF Z

25

>22 2>

2 >2 >>

( ) ( )

Z Z

Zg g Zg ^g g ^g

g

k kK q M k M M G M

k k

(:.),(:.8),(:.:)vi (:.2 2 2 2

2

2>

y zG G k b ,

>

> > > >

2

2>y zG G k b

tb h tf` h =

>> > >

22 2 > 2 2 > 2 2 > >

2> his( )

: :z z

bk G G k b k b b b q

> > >

2 2 > > > 2 > 2 > >

2 2his( )

8 8k b k b k b k b b q

>>> 2 >

2> >2 > > > > > > 2 > >

2 2his( ) his( )

: > 8 >z

b b bk k G k q k b k b b q

> >>>> > > > >

2

: 8z

kk G b k b

;6 fc ffc hb h`=2

. . .>

( )Z

q K q qZ ; (:.5)

> > > > > > >

2 2 > > > 2 > 2 > > 2 > > > > > > 2 > > 2 >

2 2 2 2 2 2. his( ) > his( )

> 8 8 8 8 >k b k b k b k b b q q k b q k b k b b q q q

Ngu t`h t`ffc hb `=>

4

4

2

. .Z

Hg

g

kgc r

vg ci; _ 4 ,4 ,-c [Z

2 2 2 > 2 2 > 2 >

2 2sgf( ) sgf( ) sgf( )

> >k cb q k c b q b q q

(:.3)

Hfc i hb hh ah suy rfc o`fc h t`= 2 2 > >( ) ( ) ( )B K q K q

*

2 2

*

> >

R K

R K

(:.0)

Z`hh ngu t`h (:.5), (:.3), (:.0)vi p`fc trf` Abcrbfcl aig GG.

*

g

g g g

j Z ZR

jt q q q

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F H GF Z

23

Zb t`gt ap h `p`fc trf` fc ah `h sbu =

> > > >

2 2 2 > > > 2 > 2 > > 2 > > > 2 > > >

> 2 >> 2 > > 2 > > 2 > > > 2 > > > 2 >

>

> > > > 2 > > 2

2 2 2 2his( ) his( )

8 8 8 >

( > )2 2sgf( ) sgf( ) his( ) his( )> > >

2 2 2his( )

8 > 8

K k b k b k b k b b q q k b k b b q q

k kk b b q q q k b b q q cb q k cb q q

K k b k b b q q k

> >

> > > > 2 > > 2 > > 2 >

2 2sgf( ) his( )

> >b q k b b q q k cb q q

Ugt jg jfc kb trf f`sbu =

( ). ( , ). ( ) ( ). ( , ) ( )K q q H q q q C q K q q U q q C q .

Ug ; _K2,K>[Z,q; _ q2, q>[

Z,K(q) kb trf o`g afc nf trf

>

> 2 > > 2 > > 2 > > >

>

> 2 > > 2

2

sgf( ) sgf( )>( , )2

sgf( )>

k b b q q q k b b q qU q q

k b b q q

2 >2 > > > 2 >

> > 2 >

( > ) 2his( ) his( )

> >( )

2 his( )

>

k kcb q k cb q q

C q

k cb q q

T`f U= Z`gt ogu o`gf

Zt hhh `t`fc gu o`gf fu jg y u t`li aut gu o`gf TJ. O`gt`gt o`t`fc gu o`gf tb nqub fc `h hb h hu h`p `f`, quf tf`fc h. F` vy h`h ffc hb ngu o`gf a ti rb kt kiiklf hf t`gt truyf fc o`p rinit k ni o`p rinit auf nk t`li vtr t.

2. @t`fc gu o`gf trifc o`fc cgbf o`p

Zf `gu t a qui nh 8 hb hh o`p h tf` tif p`f t`gt

oqui.

2.2. @t`fc gu o`gf p`f gb,Aut gu o`gf

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F H GF Z

20

@f` ( , ,..., )j j j jfO jgbc O O O -kb trf fc h`i hh `so`uh`g i `k hb tfc o`p rgfc ngt.

Ug aut gu o`gf fy cgt`gt t`f` p`f kiklf trfc ah C(p)

h n `if tif.@t`fc gu o`gf vg hu trh ngu o`gf f` trf, f f` tuyt gtif hh. Z`h vy h`f `k Agbpufiv h jfc f` sbu=

2.( . . . . )

>A

ZZOp @ qqU

()

@k UAngu t`tfc ffc afc hb `t`fc rinit= Z`f` p`f h`b Op tavg ffc afc u vi, t`f` p`f sbu a fc ffc hb rinit k Op v @ ahh kb trf h `sjfc .Ff `k UA6 4 vg q o`h qj.

Zf` i `k hp 2 hb UAtb f`f h=2

.( . . . . . . . . . . )>A

Z Z ZZ Z

Op Op @ q @ q @ qq q qU

Ji tf` h`t g xfc hb hh t`f` p`f . .ZOp , . .Z@ qq , tb rt cf h

2. . . . . . .

>A

Z ZZOp @ q @ qq qU

Zp`fc trf` fc ah `h vg cgt`gt o`fc h t`f` p`f kiklf trfcah C(q), f`f h p`fc trf` sbu =

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F H GF Z

27

2. . . . . ._ ( , )[

>A

Z ZZOp @ q K U q qq qU

Xjfc t`uh tf` hb p`fc trf` fc ah `h v p jfc aut gu o`gf( >

AZ Z Z Z Z Oj H q q q @ q q Oj @ H qq q q q qU

Zrifc = ( , ) ( , ).U q q H q q q .

Ji kb trf 2.>

@ H a kb trf g xfc fch ;6 2.( . ) 4>

Z @ H qq

. . 4ZA

Oj qqU (.< (oc), k>;2.< (oc)+ @p`fc trf` fc ah `h h jfc f` sbu =

( ). ( , ) ( )K @ q q U q q C q

vg @;K(q); 22 2>>2 >>

` `

` `

> > >

22 2 2 > > > 2 > 2 > >

2 2his( )

8 8k k b k b k b k b b q

>

2> >2 > > > 2 > >

2 2his( )

8 >k k k b k b b q

>

>> > >

2

8k k b

>

> 2 > > 2 > > 2 > > >

>

> 2 > > 2

2sgf( ) sgf( )

>( , )

2 sgf( )

>

k b b q q q k b b q q

U q q

k b b q q

2 >2 > > > 2 >

> > 2 >

( > ) 2his( ) his( )

> >( )

2 his( )

>

k kcb q k cb q q

C q

k cb q q

+ T`fc trf` aut gu o`gf h jfc = ( ) ( )jo p j j j p j K O q q O q q O O

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20/62

F H GF Z

>4

jq q , jq q -sbg svtr hb o`p, sbg sth o`p hb rinit

2 >( , )p p pO jgbc O O -kb trf fc h`i hh `so`uh` g hb o`p 2, >

2 >( , )j j jO jgbc O O -kb trf fc h`i hh `so`uh` g i `k hb o`p

2, >.

+ Ry i t h`i `bg o`p h jfc nh nb t`gt ok ni tby ky jgh`uyf tvtr nbf u B(4,5 4,2) f gk hug N(4,2 4,3) trifc > (s) .

+ Kb trf Op, Oj h ab h`f =

Op;2444 4

4 2444

, Oj;

8/13/2019 thit k h thng iu khin

21/62

F H GF Z

>2

@f` t v gu o`gf

@f`

8/13/2019 thit k h thng iu khin

22/62

F H GF Z

>>

@f`

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23/62

F H GF Z

>8

Hh `sOjg, Opgh h`f auf jfc ff k ni f f`, v h`fc htf` tif t`li yu hu vh`t afc gu o`gf f` qu gu h`f` , Z`gt`bf qu Zqj

>jg f

O , >pg f

O

(4% , `ssuy cgk ; 4,

.

2244.f

l

(; 4,: (k)

k2;>.< (oc), k>;2.< (oc)+ @p`fc trf` fc ah `h h jfc f` sbu =

( ). ( , ) ( )K @ q q U q q C q

vg @;K(q); 22 2>>2 >>

` `

` `

> > >

22 2 2 > > > 2 > 2 > >

2 2his( )

8 8k k b k b k b k b b q

>

2> >2 > > > 2 > >

2 2his( )

8 >

k k k b k b b q

>

>> > >

2

8k k b

>

> 2 > > 2 > > 2 > > >

>

> 2 > > 2

2sgf( ) sgf( )

>( , )

2 sgf( )

>

k b b q q q k b b q q

U q q

k b b q q

2 >

2 > > > 2 >

> > 2 >

( > ) 2his( ) his( )

> >( )

2 his( )>

k kcb q k cb q q

C q

k cb q q

+ T`fc trf` aut gu o`gf h jfc = ( ) ( , ) ( )joK @ q \ U q q C q ,

Ug tf `gu gu o`gf = j p j\ q O O

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24/62

F H GF Z

>:

+ Ry i t h`i `bg o`p h jfc nh nb t`gt ok ni tby ky jg h`uyftvtr nbf u B(4,5 4,2) f gk hug N(4,2 4,3) trifc > (s) .+ Kb trf Op, Oj vg h`bg o`p tb h`f `ssuy cgk Zqj;4,< (s) , `ssuycgk ; 4,< tb tf` h hh `sOpg, Ojg jb vi hh hfc t`h (2

8/13/2019 thit k h thng iu khin

25/62

F H GF Z

>

8/13/2019 thit k h thng iu khin

26/62

F H GF Z

>5

Zrifc `t`fc gu o`gf o`fc cgbf ak vgh tf `gu t trh tgp a qui h`uyf fc kifc kuf hb tby ky rinit trifc o`fc cgbf ak vgh , afc

p`f `g vsh tf` tvtr hb o`p t`fc qub o`u fc `h t`uf. O`utf` tif fc `h fch h t trifc kh` vfc gu o`gf p`f `g stf`

g hh ngf vo`fc cgbf o`p.@t`fc gu o`gf trifc o`fc cgbf ak vgh sjfc `gu quo`g t`h

`gf tfc th cgb tby ky v kg trfc

@t`fc gu o`gf kb trf Mbhinglf h`uyf v

b.Aut gu o`gf

Ah hf t`gt jg h`uyf tby ky t`li qui t trifc o`fc cgbf akvgh h xh f` tsbg ah` vtr v sbg ah` th trifc o`fc cgbf ak vgh

tfc fc vg aut gu o`gf p`f `g TJ gf` gf=

( ) ( )jo p j j j C O X X O X X

Zrifc = Cjo - a vlhtir ah hf t`gt tby rinit jg h`uyf t`li qui vth t trh.

,jX X = tfc fc a vlhtir vtr t v vlhtir vtr t`h hb tby rinit.

,jX X = tfc fc a vlhtir th t v vlhtir th t`h

2 >( , ,..., )p p p pfO jgbc O O O - kb trf fc h`i hh `so`uh` g

2 >( , ,..., )j j j jfO jgbc O O O -kb trf fc h`i hh `so`uh` g i`k .

Ulhtir ah tby rinit h ngf g vah `ih kiklf o`p rinit t`fcqub kb trf Mbhinglf h`uyf v. F` vy vlhtir kiklf truyf fc o`p rinith xh f` f` sbu=

( ) ( )Z

jo p j j j K M O X X O X X X o`g hb `t`fc f` sbu =

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27/62

F H GF Z

>3

@f` ; 4,: (k)

k2;>.< (oc), k>;2.< (oc)+ @p`fc trf` fc ah `h h jfc f` sbu =

( ). ( , ) ( )K @ q q U q q C q

Hh kb trf @(q), vlhtir U, C xh f` p`f fc ah `h

+ Zp`f fc `h tb rt rb vlhtir xh vtr gk th fc hug =

4Tr ; 2 2 > 2 > 2 2 > 2 >is( ) his( ) sgf( ) sgf( ) 4

Zb h q b q q b q b q q

Zb xh f` h kb trf mbhinglf ( o`fc xt vg trh ] v ]p;4)

2 2 > 2 > > 2 >

2 2 > 2 > > 2 >

sgf( ) sgf( ) sgf( )

his( ) his( ) his( )

b q b q q b q qM

b q b q q b q q

.

+ Aut gu o`gf fu trf.

+ Ry i t k ni tby ky g t`li fc t`fc tgk B(4,5 4,2) f gkN(4,2 4,3) v k ni th nbf u v hug nfc 4.

+ @sOpv Ojh ab h`f f` sbu =

Op;

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28/62

F H GF Z

>0

@f` .t`P, W t v gu o`gf

@f`

@f`

8/13/2019 thit k h thng iu khin

29/62

F H GF Z

>7

@f`

8/13/2019 thit k h thng iu khin

30/62

F H GF Z

84

@f`

@f`

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31/62

F H GF Z

82

T`f UG= Hh h`fc trf` k p`fc vgt nfc fcf fckbtabn

2. H`fc trf` k p`fc ot qup`f `t`fc gu o`gf p`f `g

2.2. Egal h`y (kbgf)

% H@\IFC Z^GF@ KI T@IFC ^INIZ ^^th;>?

%q4;_4?4[?%qh;_>*pg/8?->*pg/8[?

s4;_4.5?4.2[?q4;J@F(s4)?sh;_4.2?4.3[?qh;J@F(sh)?

%jglu oglf jbuq;q4?v;_4?4[?to;4.4442?P4;_q4(2)?v(2)?q4(>)?v(>)[?kbf`;eiplf('kbf`o`bf`.txt','w')?

eirt;4=4.4442=th?s;J@Z(q)?

_qj,vj[;qugjbi(q4,qh,th,t)?_K,ssq,ssv[;JO(qj,vj,q,v)?

_q,v[;^init(K,P4,to)?P4;_q(2)?v(2)?q(>)?v(>)[?eprgfte(kbf`,'%>.7e %>.7e %>.7e %>.7e %>.7e %>.7e %>.7e %8.7e %8.7e %>.7e

%>.7e %>.7e %>.7e %>.7e

%>.7eQf',t,qj(2),q(2),qj(>),q(>),ssq(2),ssq(>),K(2),K(>),vj(2),v(2),vj(>),v(>),s(2),s(>))?lfjehaisl(kbf`)?

egj ; eiplf('kbf`o`bf`.txt', 'r')?b ; eshbfe(egj, '%c %c %c %c %c %c %c %c %c %c %c %c %c %c %c', _2;b(>,=)?%qj2

j8;b(8,=)?%q2j:;b(:,=)?%qj>jj0;b(0,=)?%K2j7;b(7,=)?%K>

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32/62

F H GF Z

8>

j24;b(24,=)?%vj2j22;b(22,=)?%v2j2>;b(2>,=)?%vj>j28;b(28,=)?%v>j2:;b(2:,=)?%x

j2)?xabnla('t(s)')?yabnla('qj2 vb q2(rbj)')?alclfj('qj2','q2')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(>)?

pait(j2,j:,'h',j2,j)?xabnla('t(s)')?yabnla('qj> vb q> (rbj)')?alclfj('qj>','q>')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj ifegcurl(8)?

pait(j2,j5,'n',j2,j3,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('ssq2 vb ssq> (rbj)')?alclfj('ssq2','ssq>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(:)?

pait(j2,j0,'n',j2,j7,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('K2 vb K> (Fk)')?alclfj('K2','K>')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj ifegcurl()?xabnla('t(s)')?yabnla('vj2 vb v2

(rbj/s)')?alclfj('vj2','v2')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(5)?

pait(j2,j24,'h',j2,j22,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('vj> vb v>(rbj/s)')?

alclfj('vj>','v>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(3)

pait(j2:,j2)?tgtal('quy jbi')?xabnla('x(k)')?yabnla('y(k)')?alclfj('quy jbi')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj if

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F H GF Z

88

2.>. @k aut gu o`gf =

eufhtgif_K,ssq,ssv[ ; JO(qj,vj,q,v)%ni jglu o`glf TJ

op2;2444?op>;2444?oj2;:4?oj>;:4?%t`ifc si rinitk2;>.

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34/62

F H GF Z

8:

x>>;P4(:)?%v>%t`ifc sik2;>.

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35/62

F H GF Z

8*(s(2)*h>+s(>)*s>))/(s(2)V>+s(>)V>)?s2;((b2+b>*h>)*s(>)-b>*s>*s(2))/(s(2)V>+s(>)V>)?q2;btbf>(s2,h2)?q;_q2?q>[?lfj

2.5. @k fc `h t`ufeufhtgif_s[ ; J@Z(q)%t`ifc si rinitb2;4.

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36/62

F H GF Z

85

lfjehaisl(kbf`)?

egj ; eiplf('kbf`o`bf`.txt', 'r')?b ; eshbfe(egj, '%c %c %c %c %c %c %c %c %c %c %c %c %c %c %c', _2;b(>,=)?%qj2j8;b(8,=)?%q2j:;b(:,=)?%qj>jj0;b(0,=)?%K2j7;b(7,=)?%K>

j24;b(24,=)?%vj2j22;b(22,=)?%v2j2>;b(2>,=)?%vj>j28;b(28,=)?%v>j2:;b(2:,=)?%xj2)?xabnla('t(s)')?yabnla('qj2 vb q2(rbj)')?alclfj('qj2','q2')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj ifegcurl(>)?pait(j2,j:,'h',j2,j)?xabnla('t(s)')?yabnla('qj> vb q> (rbj)')?alclfj('qj>','q>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(8)?

pait(j2,j5,'n',j2,j3,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('ssq2 vb ssq> (rbj)')?alclfj('ssq2','ssq>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(:)?

pait(j2,j0,'n',j2,j7,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('K2 vb K> (Fk)')?alclfj('K2','K>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(

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37/62

F H GF Z

83

pait(j2,j24,'h',j2,j22,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('vj2 vb v2(rbj/s)')?

alclfj('vj2','v2')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj if

egcurl(5)?pait(j2,j24,'h',j2,j22,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('vj> vb v>

(rbj/s)')?alclfj('vj>','v>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(3)

pait(j2:,j2)?tgtal('quy jbi')?xabnla('x(k)')?yabnla('y(k)')?alclfj('quy jbi')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj if>.>. @k aut gu o`gf

eufhtgif_K,ssq,ssv[ ; JOK(qj,vj,bj,q,v)%ni jglu o`glf TJop2;>;>;25?%t`ifc si rinitk2;>.

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38/62

F H GF Z

80

C;_c2?c>[?ssv2;vj(2)-v(2)?ssv>;vj(>)-v(>)?ssv;_ssv2?ssv>[?ssq2;qj(2)-q(2)?

ssq>;qj(>)-q(>)?ssq;_ssq2?ssq>[?% Ki klf jglu o`glfOp;_op2,4?4,op>[?Oj;_oj2,4?4,oj>[?K;@*(bj+Op*ssq+Oj*ssv)+U+C?lfj

>.8. @k tf` afc t

eufhtgif_qj,vj,bj[ ; qugjbik(q4,qh,th,t)% qug jbi nbh 8b42;q4(2)?b22;4?b>2;8*(qh(2)-q4(2))/thV>?b82;->*(qh(2)-q4(2))/thV8?qj2;b42+b22*t+b>2*tV>+b82*tV8?vj2;b22+>*b>2*t+8*b82*tV>?bj2;>*b>2+5*b82*t?b4>;q4(>)?b2>;4?b>>;8*(qh(>)-q4(>))/thV>?b8>;->*(qh(>)-q4(>))/thV8?qj>;b4>+b2>*t+b>>*tV>+b8>*tV8?vj>;b2>+>*b>>*t+8*b8>*tV>?bj>;>*b>>+5*b8>*t?

qj;_qj2?qj>[?vj;_vj2?vj>[?bj;_bj2?bj>[?lfj

Hh `k k `f` rinit, fc `h fch v fc `h t`uf cgfc h`fc trf` 2ff o`fc vgt rb.

8. H`fc trf` k p`fc ot qup`f `t`fc gu o`gf o`fc cgbf akvgh t`li fc t`fc

8.2. Egal h`y (kbgf)

% H@\IFC Z^GF@ KI T@IFC ^INIZ ^^th;>?s4;_4.5?4.2[?q4;J@F(s4)?sh;_4.2?4.3[?

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39/62

F H GF Z

87

qh;J@F(sh)?%jglu oglf jbuq;q4?vq;_4?4[?to;4.4442?s;s4?v;_4?4[?

P4;_q4(2)?vq(2)?q4(>)?vq(>)[?kbf`;eiplf('kbf`o`bf`.txt','w')?

eirt;4=4.4442=th?_sj,vj[;qugjbiav(s4,sh,th,t)?_K,sss,ssv[;JOX(sj,vj,s,v,q)?_q,vq[;^init(K,P4,to)?s;J@Z(q)?v;mbhing(vq,q)?P4;_q(2)?vq(2)?q(>)?vq(>)[?eprgfte(kbf`,'%.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e

%.7eQf',t,sj(2),s(2),sj(>),s(>),sss(2),sss(>),K(2),K(>),vj(2),v(2),vj(>),v(>))?lfj

ehaisl(kbf`)?egj ; eiplf('kbf`o`bf`.txt', 'r')?b ; eshbfe(egj, '%c %c %c %c %c %c %c %c %c %c %c %c %c', _28 gfe[)ehaisl(egj)?j2;b(2,=)?%tj>;b(>,=)?%xjj8;b(8,=)?%xj:;b(:,=)?%yjj;b(2>,=)?%vj>(yj')j28;b(28,=)?%v>(y')

egcurl(2)?pait(j2,j>,'h',j2,j8,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('xj vb x(k)')?alclfj('xj','x')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(>)?

pait(j2,j:,'h',j2,j)?xabnla('t(s)')?yabnla('yj vb y(k)')?alclfj('yj','y')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(8)?

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40/62

F H GF Z

:4

pait(j2,j5,'n',j2,j3,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('sbg si (k)')?alclfj('ssx','ssy')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(:)?

pait(j2,j0,'n',j2,j7,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('Kiklf (Fk)')?alclfj('K2','K>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl()?xabnla('t(s)')?yabnla('vxj, vx(k/s)')?alclfj('vxj','vx')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(5)?

pait(j2,j2>,'h',j2,j28,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('vyj, vy(k/s)')?alclfj('vyj','vy')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(3)?

pait(j>,j:,'h',j8,j)?xabnla('x(k)')?yabnla('y(k)')?alclfj('quy jbi')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj if

8.>, @k tf` aut gu o`gfeufhtgif_K,sss,ssv[ ; JOX(sj,vj,s,v,q)%ni jglu o`glf TJop2;;;2444?%t`ifc si rinitk2;>.

8/13/2019 thit k h thng iu khin

41/62

F H GF Z

:2

m22;-b2*sgf(q(2))-b>*sgf(q(2)+q(>))?m2>;-b>*sgf(q(2)+q(>))?m>2;b2*his(q(2))+b>*his(q(2)+q(>))?m>>;b>*his(q(2)+q(>))?M;_m22,m2>?m>2,m>>[?

Mtr;trbfspisl(M)?K;Mtr*C?lfj

8.8.@k mbhinglf

eufhtgif_vs[ ; mbhing(vq,q)%t`ifc si ri nitb2;4.

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42/62

F H GF Z

:>

:. H`fc trf` k p`fc ot qup`f `t`fc gu o`gf o`fc cgbf akvgh t`li fc trf t`bg gk B,N v BN ak fc of`:.2.Egal h`y (kbgf)

th;>?s4;_4.3?4[?

q4;J@F(s4)?sh;_-4.3?4[?

qh;J@F(sh)?%jglu oglf jbuq;q4?vq;_4?4[?to;4.4442?s;s4?v;_4?4[?

P4;_q4(2)?vq(2)?q4(>)?vq(>)[?kbf`;eiplf('kbf`o`bf`.txt','w')?

eirt;4=4.4442=th?_sj,vj[;qugjbiav2(s4,sh,th,t)?_K,sss,ssv[;JOX(sj,vj,s,v,q)?

_q,vq[;^init(K,P4,to)?s;J@Z(q)?v;mbhing(vq,q)?P4;_q(2)?vq(2)?q(>)?vq(>)[?eprgfte(kbf`,'%.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e %.7e

%.7eQf',t,sj(2),s(2),sj(>),s(>),sss(2),sss(>),K(2),K(>),vj(2),v(2),vj(>),v(>))?lfjehaisl(kbf`)?

egj ; eiplf('kbf`o`bf`.txt', 'r')?b ; eshbfe(egj, '%c %c %c %c %c %c %c %c %c %c %c %c %c', _28 gfe[)

ehaisl(egj)?j2;b(2,=)?%tj>;b(>,=)?%xjj8;b(8,=)?%xj:;b(:,=)?%yjj;b(2>,=)?%vj>(yj')j28;b(28,=)?%v>(y')

egcurl(2)?pait(j2,j>,'h',j2,j8,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('xj vb x(k)')?alclfj('xj','x')?slt(che,'Hiair',_2.4,2.4,2.4[)?

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F H GF Z

:8

crgj ifegcurl(>)?

pait(j2,j:,'h',j2,j)?xabnla('t(s)')?yabnla('yj vb y(k)')?alclfj('yj','y')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj ifegcurl(8)?

pait(j2,j5,'n',j2,j3,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('sbg si (k)')?alclfj('ssx','ssy')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(:)?

pait(j2,j0,'n',j2,j7,'o','AgflSgjt`',>)?xabnla('t(s)')?yabnla('Kiklf (Fk)')?alclfj('K2','K>')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj ifegcurl()?xabnla('t(s)')?yabnla('vxj, vx(k/s)')?alclfj('vxj','vx')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj ifegcurl(5)?

pait(j2,j2>,'h',j2,j28,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('vyj, vy(k/s)')?alclfj('vyj','vy')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj ifegcurl(3)?pait(j>,j:,'h',j8,j)?xabnla('x(k)')?yabnla('y(k)')?alclfj('quy jbi')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj if

:.>. @k tf` afc teufhtgif_sj,vj[ ; qugjbiav2(s4,sh,th,t)% qug jbi juifc 2/> juifc trif s4-6sh trifc th cgbyxg;(s4(2)+sh(2))/>?yg;(s4(>)+sh(>))/>?^;4.+(s4(>)-sh(>))V>)?b4;bsgf((s4(2)-xg)/^)?b2;4?w;bsgf((sh(2)-xg)/^)-b4?b>;8*w/thV>?b8;->*w/thV8?e;b4+b2*t+b>*tV>+b8*tV8?je;b2+>*b>*t+8*b8*tV>?

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F H GF Z

::

xj;xg+^*sgf(e)?yj;yg+^*his(e)?sj;_xj?yj[?vj2;^*je*his(e)?vj>;-^*je*sgf(e)?

vj;_vj2?vj>[?lfj

+ @k aut gu o`gf tfc th`fc trf` 8.+ Hh `k k `f` rinit, fc `h fch v fc `h t`uf cgfc h`fc

trf` 2 ff o`fc vgt rb.

quby kt ch -2>44t`li qui nh 8 t`gt o.

Zb o`bg ni hh t`fc srinit vi hh o`u o`p =b2; 4.< (k), b>; 4,: (k)k2;>.< (oc), k2;2.< (oc)

2G ; , >G ; ,>

2 2 2 2

2

2>y zG G k b ,

>

> > > >

2

2>y zG G k b

@f` 5.2.X `t`fc

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F H GF Z

:;2444

,Oj2;Oj>;:4( trf `f` o `gu Ov2 ,Ov>)

Zb t`u h ot quf` sbu=( nftrg jfc sgkuagfo nf p`g ot qujfc h`fc sjfc p`fc trf`fc ah )= @f` 5.>. Ngu o`gf TJ

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F H GF Z

:5

@f` 5.8. Hh ot qusi sf`

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F H GF Z

:3

Zb t`y ot qucgb vgh jfc t` vgf o`bg ni sf k `f` rinit vg vghvgt k ttif `h ^init ( T`fc trf` fc ah `h ) a `if tif cgfc f`bu.

.Xjfc t` vgf XgkKlh`bfgs vg k `f` rinit ^^ h xut rb tsigjwirjs.

K `f` rinit ^^ vtsigjwirjs b viak k `f` f` sbu =

Zk `f` nf vap hb k `f` rinit ^^fy tb xut sbfc egal *.xka rg jfc kbtabn hxut rb egal jg jfc sgkuagfo, rg t`gt ojgjfc hh o`g hb `t`fc gu o`gf kb trfMbhinglf h`uyf v.

@f` 5.:.K `f` k p`fc

@f` 5.

8/13/2019 thit k h thng iu khin

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F H GF Z

:0

O`g TJ vg=Op; 2 >

2 2 > 2 >

his( ) his( )

sgf( ) sgf( )

p

p

x b q b q q

y b q b q q

MVZ - Kb trf Mbhinglf h`uyf v.

M - Kb trf Mbhinglf.

2 2 > 2 > > 2 >

2 2 > 2 > > 2 >

sgf( ) sgf( ) sgf( )

his( ) his( ) his( )

b q b q q b q qM

b q b q q b q q

,

b, gu o`gf t`li fc t`fc

O`g JBZ h f`gk vti rb tf `gu t h`i ngu o`gf TJ vg tf `gut a k ni gk th fc hug jg h`uyf t`li fc t`fc tgk nbf uB(4.7 , 4) f gk N(4.:< , 4,:

8/13/2019 thit k h thng iu khin

49/62

F H GF Z

:7

@f` 5.0.t`P, W t v gu o`gf

@f` 5.7.Ry i t v gu o`gf

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50/62

F H GF Z

8/13/2019 thit k h thng iu khin

51/62

F H GF Z

.Ry i t v gu o`gf

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F H GF Z

@f` 5.28. @f` f` ^init ^^ g t`li hufc trf vg aut gu o`gf mbhinglfh`uyf v

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F H GF Z

> >

2 2 2 > > > 2 > 2 > > 2 > > > 2 > > >

> 2 >> 2 > > 2 > > 2 > > > 2 > > > 2 >

>

> > > > 2 > > 2

2 2 2 2his( ) his( )

8 8 8 >

( > )2 2sgf( ) sgf( ) his( ) his( )

> > >

2 2 2his( )

8 > 8

K k b k b k b k b b q q k b k b b q q

k kk b b q q q k b b q q cb q k cb q q

K k b k b b q q k

> >

> > > > 2 > > 2 > > 2 >

2 2sgf( ) his( )

> >b q k b b q q k cb q q

Zb xy jfc h hh s o`g k p`fc trifc Xgkuagfo f` sbu =

b, s o`g t`fc gu o`gf TJ o`fc n kiklf trfc afc

Ug aut gu o`gf = ( ) ( )jo p j j j p j K O q q O q q O O

@f` 5.2:. X o`g vg ngu o`gf TJ

@f` 5.2

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F H GF Z

q , 2q , >q p`f

`g v

@k Ehf2=(2/((2/8)*k2*b2V>+(2/8)*k>*b>V>+k>*b2V>+k>*b2*b>*his(u(8))))*(u(2)-((2/8)*k>*b>V>+4.*b2*b>*his(u(8)))*u(5)+k>*b2*b>*sgf(u(8))*u(:)*u(*sgf(u(8))*u(-4.*k>)*c*b2*his(u(8))-4.*c*b>*his(u(>)+u(8)))

@k Ehf=(2/((2/8)*k>*b>V>))*(u(5)-((2/8)*k>*b>V>+4.*b2*b>*his(u(>)))*u(*sgf(u(>))*u(8)V>-4.*c*b>*his(u(2)+u(>)))

@f` 5.25. O`g `gf t`( `glfYt`g ) @f` 5.23.O`g cg trt ( JBZ )

Egal t`fc sk p`fc ( vg `k J@F fg p`f vgt h`fc trf` )=%-----------t`ifc si rinit ^^------------------------------

th;>?b2;4.

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F H GF Z

*(qh(2)-q4(2))/thV8?b>4;q4(>)?b>2;4?b>>;8*(qh(>)-q4(>))/thV>?b>8;->*(qh(>)-q4(>))/thV8?

%-------------------------------------------------------------------------------------------------

Egal vt`egcurl(2)?

pait(tiut,qj2,'h',tiut,q2,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('qj2 vbq2(rbj)')?

alclfj('qj2','q2')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj if

egcurl(>)?pait(tiut,vj2,'h',tiut,v2,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('vj2 vb

v2 (rbj/s)')?alclfj('vj2','v2')?slt(che,'Hiair',_2.4,2.4,2.4[)?

crgj ifegcurl(8)?pait(tiut,qj>,'h',tiut,q>,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('qj> vb

q>(rbj)')?alclfj('qj>','q>')?

slt(che,'Hiair',_2.4,2.4,2.4[)?crgj if

egcurl(:)?pait(tiut,vj>,'h',tiut,v>,'r--','AgflSgjt`',>)?xabnla('t(s)')?yabnla('vj> vb

v> (rbj/s)')?alclfj('vj>','v>')?slt(che,'Hiair',_2.4,2.4,2.4[)?crgj if

%-------------------------------------------------------------------------------------------------

Ug tf `gu t gk th fc hug jg h`uyf tgk s4;_4.>?4.

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F H GF Z

t v gu o`gf

@f` 5.27.Uf th ch o`p 2, > t v gu o`gf

n, s o`g t`fc gu o`gf TJ n kiklf trfc ah

@f` 5.>4.X o`g vg ngu o`gf TJ n trfc ah

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F H GF Z

2.Ngu o`gf TJ n trfc ahZrifc @f` 5.>2h hh `k sbu

c2= 4.*k>)*c*b2*his(u(>))+4.*c*b>*his(u(2)+u(>))c>= 4.*c*b>*his(u(2)+u(>))

Op;2444, v Oj;?4.>.Ch o`p q2, q>t v gu o`gf

@f` 5.>8.Uf th ch o`p 2, > t v gu o`gf

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F H GF Z

:.X o`g vg ngu o`gf kiklf tf` tif

@f` 5.>< h `bg `k Ehf v Ehf2 tf` jfc tf` kiklf gu o`gft`li aut gu fu trf=

Ehf tf` K2jo=((2/8)*k2*b2V>+(2/8)*k>*b>V>+k>*b2V>+k>*b2*b>*his(u(>)))*u(*b>V>+4.*b2*b>*his(u(>)))*u(5)-k>*b2*b>*sgf(u(>))*u(8)*u(:)-

4.*b2*b>*sgf(u(>))*u(:)V>+4.*k>)*c*b2*his(u(>))+4.*c*b>*his(u(2)+u(>))

Ehf2 tf` K>jo=((2/8)*k>*b>V>+4.*b2*b>*his(u(>)))*u(*b>V>)*u(5)+4.*b2*b>*sgf(u(>))*u(8)V>+4.*c*b>*his(u(2)+u(>))

Z`fc sOp ; >

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F H GF Z

?4.5.Ch o`p q2, q>t v gu o`gf

@f` 5.>3.Uf th ch o`p 2, > t v gu o`gf

F`f xt=+ Rub k p`fc tb t`y ngu o`gf n trfc ah vg hfc t`fc sOp, Oj

h h`t afc gu o`gf tt `f nk st `f, fc vg a t`uyt o`g o`hC(q).

+ Hf vg ngu o`gf kiklf tf` tif h h`t afc tt f`t nk stf`t f`fc kh tf` tif p`h tp `f.

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F H GF Z

54

ZG AG\ Z@BK O@I

_2[ fc ah `h `f`gu vt - CX. ZXO@. Fcuyf Uf O`bfc.

_>[ gu o`gf ^init hfc fc`gpZX. Fcuyf Kf` Zgf .

_8[ KBZABN & XGK\AGFO jf` h`i o s gu o`gf tfcFcuyf T`fcRubfc .

_:[ H s^init hfc fc`gp -CX.ZXO@ Fcuyf Uf O`bfc .

_

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F H GF Z

52

F@F PZ HB CGI UGF @FC JF

@ Fg, fcy 43 t`fc 22 fk >42>

Cgi vgf `fc jf

ZX. h Fbk

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F H GF Z

Gf ku 3,22,28,2:,>4,>2,>:,>0,>7,84,: