Comanda vectoriala a MAS

8/13/2019 Comanda vectoriala a MAS

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2/19

34

rd r rq= ; = 0 ;

0=r i +1 d

dt

0 =r i +f

=x i +x i

0 =x i +x i

m = { i } = - i

r rd

n

r

r rq r r

r r rd m sd

r rq m sq

e r r*

r rq

r m sd r r

em

rr sq

r

r

rm

rsq

e r

r2 s

=x i - Td

dt

m =x

x i

f =r

xx

1i =

m r= sf

rd

r n

r

rq

m

r

sq

i = -1

r

1 d

dt

i = -x

x

i


3/19

35

s s s s s sm

rru = (r+ jf x )i + jf

x

x

j f xx

sm

rr

0 =rs

x

xi + jf

x

x

r m

rr s

m

rr

s s s s

m

r

m sd s s s

r m

2

r2

sq sm

r

m sd

u =r i + j fx

xx i + j f x i

0 = - rs

xx

i + j f xx

x i


4/19

36


5/19

37

=f -f =f -m r

s r s

e r

r2

sc

u =r i -f x i =rx

-f x i

u =r i +f x i =r i +f xx

sd s sd s s sq sr

m

s s sq

sq s sq s s sd s sq s sr

m

s s

r

ms s sq

2s sq s s

r

m

2u= (r

x-f x i ) +(r i +f x

x)


6/19

38

sr

m

s2

s

2s2u =

xr +f x

sc

r= f( ) ekm sc rn

rn

sn

sn

sn

sn

u

f= 1

sn sk = = 1

rn rk =

s2

s sd2

s sq2

= (x i ) +(x i )

e mr

r sqm

2

r

sd sq m

2

r

sd s

2s sd

2

s

m =x

xi =

x

xi i =

x

xi

- (x i )

x

dm

di= 0

e

sd

sdn

sn

s s

sdk

sqk

sn

s s

i =2x

=1

2x= i

i

=2x

=1

2x


7/19

39

rn rk m sdn m

sn

s

m

s

ek

m sn2

s s r

m2

s s r

rk

rn2

r

rk

r

r n r

= =x i =x 2x =

x

2x

m =(x )

2x x x=

x

2x x x= f

r

f =r

x=

1

T

rn

scsf sc

su sku = 1 r rn sqi

sqk ek r m rni = m x / (x )

sk2 srn

ms s sqk

2s sqk s s

rn

m

2u = 1 = [ r

x-f x i ] +[ r i +f x

x]

sc sc

scs

f

f =

-r x

xi + ( r x

xi ) -x [(

x) +( i ) ]{r [ i +(

x) ] - u }

x [(x

) +( i ) ]

cu i =m x

x si u =1 cu i =

m x

x si u = 1

scs

s rn

m

r

sqk s rn

m

r

sqk2

s2 rn

m

2sqk

2s2

sqk2 rn

m

2sk2

s2 rn

m

2sqk

2

sqk

ek r

m rn

sk sqk

ek r

m rn

sk

scs

f

sc s rk= f -fsc

r= f( )


8/19

40

s d - q

sd s sq= ; = 0

d - q

m = { i } = i

=x i + =x [(1+x

x)i +i ] =x i

e s*

s s sq

s s s m m

s

m

s r m ms

i =(1+x

x)i +i =

x

xi +i ms

s

m

s r

s

m

s m


9/19

41

q

d

msi

r

r n r

m

ss=

1

1+ j f T

x

x

s s s s s

m

s

ms

r s

m

2

sr

s

m

2r

m

s ss ms

m

s

u = r i + j f xx

xi

0 = [r

s(x

x) + j f x (

x

x) ]i

x

x+ j f x i

x

x


10/19

42

r rr

n r

T = T = x

r

sqi

ss

r n r

r n r

si =1

x

1+ j f T

1+ j f T

s

s

s

r n r2

r n r2

i =x

1+ ( f T )

1+ ( f T )

e s sq s*

s

r

r n r

r n r2

m

s

s2

m = i = { i } =1

x

f T

1+(f T )(x

x)

r2

s r2

e r m s2

r e s r 2

f ( x x ) m -f (x ) r +m (x r ) = 0

dm

df

e

r


11/19

43

rk

r

r

ek

m s2

s s r

f =r

x

m =(x )

2x x x

sq k

m2

s

s s r

i =x

2x x x


12/19

44

s sn< = 1 sc

s

m

mdm m mqm= ; = 0


13/19

45

e m*

s m sqm

m m m m sdm rdm

m sqm rqm

m= { i } = i

=x i =x ( i +i )

0 =x ( i +i )


14/19

46

u =r i + j f (x i + ) = (r + j f x )i + j f x i

0 = (r

s+ j f x )i + j f x i

s s s s s s m s s s s s m m

r

s r r s m m

rr n r

r n r

m

s r

si =-jf T

1+ j f T

x

x x

m m s rm

s r

r r n r r

r n r

s=x ( i +i ) =x

x x

x+ j f T x

1+ jf T

sr n r

r r n r r

r

m

mi =1+ jf T

x+ j f T x

x

x


15/19

47

e m*

sr r

r2

r s2 m

2 m2

r

r2

s

s r2

m = { i } =f r

r +(f x )=

r

r

sf+ sf x

r2

r2

e r r m2

e r2f x m-f r + m r = 0

dm

d f= 0

e

r

rk

r

r

ekm2

r

f =r

x

m =2x

sqmki

sqmk

m

r

i =2x


16/19

48

s= 1

r rkf =f e ekm =m

0 =r i +f x i

0 =r i +fx

x-f x i

r rdm r r sqm

r rqm r

r

m

m r r sdm

r rkf =f

i = -i = -2x

i =(2x +x )

2x x

sqmk rdmk m

r

sdmkm r m

r m


17/19

49

sn s sdmk mn2

s sqmk2

= (x i + ) +(x i )

m,n snr m

s r m s r 2

m s2

=2x x

[2x x +x (x +2x )] +(x x )

scs

f

sc

u =r i -f x i

u =r i +f (x i + )

sdm s sdm s s sqm

sqm s sqm s s sdm m

sdmi sqmi skf skf

f [(x x ) +(x x +2x x ) ] +

+2f x x r (x - 2x )+ [ r (x +x ) -

(2x x u )

] = 0

sk

2s m

2r s r m

2

sk m r s s m s2

r r2 r m sk

2

mn2

sc


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Comanda vectoriala a MAS

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