askiseis sae

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... 1 1999 , , . Comprehensive Control . ) 2 ( ) 1 (2) (2+ +

s s ss G : ( ) . genter . ( ) . Laplace . ( ) . . . ( ) . ( routh stability ) . . ( ) . Bode Bode . . ( ) . . ( ) . G(s) G(z) . ( ) . G(z) . ( Sampled inverse Laplace transform ) . ( ) . Bode .. . ( ) . ... . . . ( ) . G(z) . . poles . Fadeeva . ... 2 1999 : . : : : G(s) . ) 2 ( ) 1 ( ) 1 ( ) 2 ( ) 1 (2) (2212 112+++++

+ +

sksksks s ss G : [ ][ ][ ] 4) 2 (2lim ) 2 )( ( lim4) 2 (2 ) 2 ( 2lim) 1 )( (lim222lim ) 1 )( ( lim222 22122121121112111 ]]],,+ + ]]],,+ +

+

]]],,+ + ks ss s G kks s sdss s G dkks ss s G ks ss ss s : t t t t te t e t g e e te t g s G Ls s ss G2 2 124 ) 4 2 ( ) ( 4 4 2 ) ( )] ( [) 2 (4) 1 (4) 1 (2) ( + + ++++ ... 3 1999 . : : : . ) 2 ( ) 1 (2 1) ( ) ( ) ( ) (2+ + s s ss G s U s G s Y Laplace : ) 2 ( ) 1 ( ) 1 () (2 12211+++++

sksksks Y : ... 4 1999 [ ][ ][ ] 2) 1 (2lim ) 2 )( ( lim2) 2 (2lim) 1 )( (lim2) 2 (2lim ) 1 )( ( lim222 22122121121112111 ]]],,+ + ]]],,+

+

]]],,+ + kss s Y kks dss s Y dkkss s Y ks ss ss s : ) 2 (2) 1 (2) 1 (2) (2++++

s s ss Y Laplace : [ ]< +

+ 0 t 00 t 2 2 2 ) () (2 2 2 ) ( ) (1t t tt t te e te t yt ye e te t y s Y L t Y(t) 0 0 0.5 0.13 1 0.27 1.5 0.32 2 0.31 2.5 0.26 3 0.20 3,5 0.15 4 0.11 4.5 0.08 5 0.05 : ... 5 1999 < +

0 t 00 t 4 ) 4 2 () () ( ) ( 1 ) ( ) (2t te e tt yt g t y s G s Y t Y(t) 0 0 0.5 0.35 1 0.20 1.5 0.02 2 -0.07 2.5 0.11 3 -0.11 3,5 -0.09 4 -0.07 4.5 -0.06 5 -0.04 . : : : ... 6 1999 =1 ( stability ) p(s) Routh 0 2 7 4 0 ) ( . .2 3 + + + s s s s p E X Routh 3s 1 7 2s 4 2 1s 6.5 0 0s 2 =1 . ( Routh ) p(s) Routh 0 2 ) 2 5 ( 4 0 ) ( . .2 3 + + + + s K s s s p E X Routh 3s 1 5+2 2s 4 2 1s 2+4.5 0 0s 2 Routh Kcr . (2+4,5)=0 Kcr=-2.25 2.5 . : ( -2.5 , +00 ) . . ... 7 1999 : : s=j* G(s)H(s) (,\,(j+(,\,(j+(,\,(j

+ +

1211 1) 2 ( ) 1 () ( 2) ( ) (2 2j jjj j jj H j G : 2= 3=1 rad/sec 4= 2 rad/sec ... 8 1999 ( ) 40db - j1 G(s)H(s) 20db - 1 G(s)H(s) 0db) ,secrad 1 ( 20db (jj G(s)H(s) 244 3 22 < < < + < . (,\,(j 2tan ) ( tan 2 90 1 1 . . rad/sec () 0.1 75.7 0.5 22.8 1.0 -26.6 5.0 -135.6 10.0 -157.3 50,0 -175.4 100.0 -177.8 500.0 -179.5 ... 9 1999 . : : : ) 2 ( ) 1 (2) (2+ +

s s ss G ( ) 0 z2 p , 113 2 1

p p . 1z 1p 2p 3p : + + 0201 0p0270 1 90 0 0 9 1) 2 (n 180 1) 2 (zn 0 0270 , 90 . . ... 10 1999 2 1 30 ) 2 1 1 (

z p n n z p . break way point ( ) ( )

+ + 618 . 0 62 . 1 0 2 2 211 1 1 4 212 11 2bbb2bb b bb bb b b 62 . 1 b . ... 11 1999 . : : Forward rectangle : Backward rectangle : Bilinear : ... 12 1999 Pole Zero mapping : Sampled inverse Laplace transform Zero order hold : ... 13 1999 : Forward rectangle : G(s) 1 T , 1

Tzs . ) 1 () 1 () (21+

z z z zz F Backward rectangle : G(s) 1 T , 1

T zzs . ) 33 . 0 ( ) 5 . 0 () 1 ( 166 . 0) () 2 1 ( ) 1 1 () 1 ( 2) (2221 2 112 + +

z z z zz Fz z zz F Bilinear : G(s) 1 T , ) 1 () 1 ( 2) 1 () 1 ( 211

+

+

z T zz T zs . 22323) 333 . 0 () 1 ( ) 1 ( 111 . 0)2112 1112114) + ]]],,++ ]]],,+++

z z z zz Fzzzz zzz F Pole Zero mapping : ( CONVERT ) ) ( ) ( ) () 1 ( ) 1 () (224 T T Tdce z e z e z z z Kz F + T=1 dcK 0 14) ( ) ( s z s G z F 086 . 0 dcK . . ... 14 1999 ) 135 . 0 ( ) 368 . 0 () 1 ( ) 1 ( 086 . 0) (224 +

z z z zz F Sampled inverse Laplace transform : t te t es s sL s G L221 14 ) 2 4 () 2 ( ) 1 (2)] ( [ ]]],,+ + t=kT : kT kT kT kT kTe kTe e T k g e T k e T k g2 24 2 4 ) ( 4 ) 2 4 ( ) ( . ( ) ( ) ( )) 135 . 0 ( ) 368 . 0 () 24 . 1 ( 194 . 0) ( 4 2 4 ) (2512 25

z z z zz Fe z ze z e z Te z zz F TTTTT Zero order hold : ( )) 135 . 0 ( ) 368 . 0 () 071 . 0 270 . 0 )( 1 ( 270 . 0) (2 2 2 1) () 2 (2) 1 (2) 1 (2) 1 () () 1 ( ) (262 1 2116121 16 + ((,\,,(j+

]]],,++++ ]]],, z z z zz Fe z ze z ze z e zzzz Fs s sZ zss GZ z z F T : (n) (n) . ... 15 1999 . : : : WINDOWS . : . 14 . 0 62 . 0 ) 49 . 0 15 . 1 ( ) ( ) 1 (14 . 0) 135 . 0 (62 . 0) 368 . 0 (64 . 1) 368 . 0 ( 159 . 1) (1 ) 135 . 0 ( ) 368 . 0 () 24 . 1 ( 194 . 0) ( ) ( Y(z)21 T , ] [22251 + +

n nZe n e n yz zz zz zz zz Yz zz z z zz U z F IZT Y(z). ... 16 1999 y(n) ( 3 ) . n Y(n) 0 -0.010 1 0.180 2 0.110 3 0.009 4 -0.060 5 -0.100 6 -0.120 7 -0.133 8 -0.137 9 -0.138 10 -0.139 . : n nZe n e n yz F z Y21 T , ] [597 . 3 ) 98 . 3 991 . 1 ( ) (1 ) ( ) ( 1

+ y(n) ( 3 ) . n Y(n) 0 0.0100 1 -0.1900 2 -0.0700 3 -0.1100 4 -0.0700 5 -0.0400 6 -0.0200 7 -0.0100 8 -0.0040 9 -0.0010 10 -0.0007 ... 17 1999 . : : ... 18 1999 . : : : ... F5(z) >0 . F5(z) K > =1 . ... 21 1999 . : ( * ) . CC . : : ( ) F5(z) T=1 . F5(z) ) 135 . 0 (537 . 0) 368 . 0 (733 . 0) 368 . 0 (272 . 0) 135 . 0 ( ) 368 . 0 () 248 . 1 ( 194 . 0) (2 25++

z z z z z z zz F block . z-1 z^-1z^-1 -0.5370.1350.368 0.368-0.2720.733R(z)Y(z)++++++ r(k)y(k)x2(k+1) x2(k) x1(k+1) x1(k)x3(k+1) x3(k)+++ block . ) ( 537 . 0 ) ( 733 . 0 ) ( 272 . 0 ) () ( 135 . 0 ) ( ) 1 () ( 368 . 0 ) ( ) 1 () ( 368 . 0 ) ( ) 1 (3 2 13 32 21 2 1k x k x k x k y k x k r k x k x k r k x k x k x k x + + + + + + + . ... 22 1999 [ ] ) ( 0) () () (537 . 0 733 . 0 272 . 0 ) () (110) () () (135 . 0 0 00 368 . 0 00 1 368 . 0) 1 () 1 () 1 (321321321k rk x k x k xk yk rk x k x k xk x k x k x +]]]]],,,, ]]]]],,,,+]]]]],,,,]]]]],,,,

]]]]],,,,+++ : F5(z) - . . . A , B , C , D . P = [ A ,B ; C , D ] . : z . 1 368 . 0 1 135 . 0 0.135) - ( 0.368) - (00.135 - 0 00 0.368 - 00 1 - 0.368 - 0 - 0 p(z) : . .3 31,2 1,22 < < E X : : ]]]]],,,, ]]]]],,,, 018 . 0 135 . 0736 . 0A , 135 . 0368 . 0 12B B A . ...