Control Digital

EJERCICIO NUMERO 1

t=0,001

20/s(s/2+1) ×3/2 = 40/(S^2 (S+2))

G(z)=(1-Z^(-1) )3 6csi/3 G(z)=(1-Z^(-1) )3 40/(s^2 (s+2) )

40/(s^2 (s+2) )=A/s^2 + B/S+ C/(S+2)

A Lim/(s→0)⁡〖〖 (C)〗^ 〗=20

B lim┬(S→-2 )⁡〖 ((S+2) 40)/(S^2 (S+2) ) =5 〗

C Lim/(s→0) 1/1! d/ds (s^2 40)/(s^2 s+2) 40/〖(s+2)〗^2 = -5

G〖Z=(1-Z〗^(-1))z ( 20/s^2 -5/s+5/(s+2))

Gz=(1-z^(-1) ) z/z (20 (TZ^(-1))/〖1-Z〗^(-1) Z^2/Z^2 (-5*1)/〖-1Z〗^(-1) Z/Z+5/(1-E^(-2T) Z^(-1) ) Z/Z)

Gz=((Z-1)/Z)(0,02Z/((〖Z-1)〗^2 )-5Z/(Z-1)+5Z/(Z-0,99))

Gz=0,02Z/(Z-1 )-5Z/1+5/(Z-0,99)

Gz=(0.02Z-0.99-5(Z-1)(Z-0.99)+E〖(Z-1)〗^2)/((Z-1)(Z-0,99))

Gz=(-0,03Z-1,04)/((Z-1)(Z-0,99))

ts=4/(3w_n ) 0,5=e^(-π3/√(1-3^2*100%)) 〖 w〗_n=4/ts= 4/((0,5)(0,01))=800rad/seg

s_1.2=-3w_n±j√(1-3^2 ) 〖 w〗_n=s_1.2=-0,01±692,8j

T=0,001

W_s=2π/0,001=6,28rad/seg wd=692rad/seg

ws/wd=(6,28rad/seg)/(692rad/seg)=0.0090

z=e^st=z=e^(-0,01+j692,8)0,001

z=e^(-0,00001) e^j0,69

z=e^(-0,00001) (cos0,69+jsen0,69

z=0,76+j0,63

θ_1=〖180〗^0-t9^(-1) (0,63/(1-0,76))=〖114,74〗^0

θ_2=〖180〗^0-t9^(-1) (0,63/(0,99-0,76))=〖110,11〗^0

θ=t9^(-1) (0,63/(0,76-1,04))=〖246,03〗^0

EJERCICIO NUMERO 1

t=0,001

20/s(s/2+1) ×3/2 = 40/(S^2 (S+2))

G(z)=(1-Z^(-1) )3 6csi/3 G(z)=(1-Z^(-1) )3 40/(s^2 (s+2) )

40/(s^2 (s+2) )=A/s^2 + B/S+ C/(S+2)

A Lim/(s→0)⁡〖〖 (C)〗^ 〗=20

B lim┬(S→-2 )⁡〖 ((S+2) 40)/(S^2 (S+2) ) =5 〗

C Lim/(s→0) 1/1! d/ds (s^2 40)/(s^2 s+2) 40/〖(s+2)〗^2 = -5

G〖Z=(1-Z〗^(-1))z

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