Control-programacion

TALLER TIPOS DE PROGRAMACIÓN

G(z)=(z^2+3-2)/(z^4+z^3+〖5z〗^2+6)

Programación serie-estándar

Y(z)/H(z) *H(z)/X(z) =(z^2+3-2)/(z-2.91237)(z+3.01673)(z^2-0.104356z+0.796736)

Y(z)/H(z) =1/(z-2.91237)(z+3.01673) ^ H(z)/X(z) =(z^2+3-2)/((z^2-0.104356z+0.796736) )

Implementación para Y(z)/H(z)

Y(z)/P(z) *P(z)/H(z) =1/((z-2.91237) )*1/((z+3.01673) )

Y(z)/P(z) =1/((z-2.91237) )*z^(-1)/z^(-1) =z^(-1)/(1-2.91237z^(-1) )

P(z)/H(z) =1/((z+3.01673) )*z^(-1)/z^(-1) =z^(-1)/(1+3.01673z^(-1) )

Implementación para H(z)/X(z)

H(z)/Q(z) =(z^2+3-2)/(z^2-0.104356z+0.796736)*z^(-2)/z^(-2) = (1+3z^(-1)-2z^(-2))/(1-0.104356z^(-1)+0.796736z^(-2) )

Y(z)/M(z) *M(z)/P(z) Programación estándar

Y(z)/M(z) =z^(-1 ) ^ M(z)/P(z) =1/(1-2.91237z^(-1) )

{█(Y(z)=z^(-1) M(z)@^@M(z)=P(z)+2.91237z^(-1) M(z))}→Z^(-1) {┤}→{█(y(k)=m(k-1)@^@m(k)=p(k)+2.91237m(k-1))}

P(z)/N(z) *N(z)/H(z) Programación estándar

P(z)/N(z) =z^(-1 ) ^ N(z)/H(z) =1/(1+3.01673z^(-1) )

{█(P(z)=z^(-1) N(z)@^@N(z)=H(z)-3.01673z^(-1) N(z))}→Z^(-1) {┤}→{█(p(k)=n(k-1)@^@n(k)=h(k)-3.01673n(k-1))}

H(z)/Q(z) *Q(z)/X(z) Programación estándar

H(z)/Q(z) =1+3z^(-1)-2z^(-2) ^ Q(z)/X(z) =1/(1-0.104356z^(-1)+0.796736z^(-2) )

{█(H(z)=Q(z)+3z^(-1) Q(z)-2z^(-2) Q(z)@∧@Q(z)=X(z)+0.104356z^(-1) Q(z)-0.796736z^(-2) Q(z) )}

→Z^(-1) { }→

{█(h(k)=q(k)+3q(k-1)-2q(k-2)@^@q(k)=x(k)+0.104356q(k-1)-0.796736q(k-2))}

A continuación el diagrama de flujo…

IMPLEMENTACIÓN

G(z)=(6z^3+z^2+3z+5)/(z^4+z^3+〖5z〗^2+6)

Paralela-Directa

(6z^3+z^2+3z+5)/(z^2-0.476449z+1.39147)(z^2+1.47645z+4.31198)

=(Az+B)/(z^2-0.476449z+1.39147)+(Cz+D)/(z^2+1.47645z+4.31198)

6z^3+z^2+3z+5=(Az+B)(z^2-0.476z+1.391)+(Cz+D)(z^2+1.48z+4.31)

6z^3+z^2+3z+5=Az^3-0.476Az^2+1.391Az+Bz^2-0.476Bz+1.391B+Cz^3+1.48〖Cz〗^2+4.31Cz+Dz^2+1.48Dz+4.31D

6=A+C

1=-0.476A+B+1.48C+D

3=1.391A-0.476B+4.31C+1.48D

5=1.391B+4.31D

A=6.576; B=5.644; C=-0.576; D=0.661.

G(z)=(6.576z+5.644)/(z^2-0.476z+1.391)+(-0.576z+0.661)/(z^2+1.476z+4.31)

(Y_1 (z))/X(z) =(6.576z+5.644)/(z^2-0.476z+1.391)*z^(-2)/z^(-2) =(6.576z^(-1)+5.644z^(-2))/(1-0.476z^(-1)+1.391z^(-2) )

(Y_1 (z))/X(z) =(6.576z^(-1)+5.644z^(-2))/(1-0.476z^(-1)+1.391z^(-2) )

y_1 (z)(1-0.476z^(-1)+1.391z^(-2) )=x(z)(6.576z^(-1)+5.644z^(-2) )

Y_1 (z)=6.576z^(-1) X(z)+5.644z^(-2) X(z)+0.476z^(-1) Y_1 (z)-1.391z^(-2) Y_1 (z)

y_1 (k)=6.576x(k-1)+5.644x(k-2)+0.476y_1 (k-1)-1.391y_1 (k-2)

(Y_2 (z))/X(z) =(-0.576z+0.661)/(z^2+1.476z+4.31)*z^(-2)/z^(-2) =(-0.576z^(-1)+0.661z^(-2))/(1+1.476z^(-1)+4.31z^(-2) )

Y_2 (z)(1+1.476z^(-1)+4.31z^(-2) )=X(z)(-0.576z^(-1)+0.661z^(-2) )

Y_2 (z)+1.476z^(-1) Y_2 (z)+4.31z^(-2) Y_2 (z)=-0.576z^(-1) X(z)+0.661z^(-2) X(z)

Y_2 (z)=0.661z^(-2) X(z)-0.576z^(-1) X(z)-1.476z^(-1) Y_2 (z)-4.31z^(-2) Y_2 (z)

y_2 (k)=0.661x(k-2)-0.576x(k-1)-1.476y_2 (k-1)-4.31y_2 (k-2)

IMPLEMENTACIÓN

CASCADA

G(z)=(6z^3+z^2+3z+5)/(z^4+z^3+〖5z〗^2+6)=1/((z^4+z^3+〖5z〗^2+6)/(6z^3+z^2+3z+5))

z^4+z^3+〖5z〗^2+6 6z^3+z^2+3z+5

〖-z〗^4 〖-1/6 z〗^3-1/3 z^2-5/6 z -1/6 z

0+〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6

G(z)=1/((z^4+z^3+〖5z〗^2+6)/(6z^3+z^2+3z+5))=1/(-1/6 z+(〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6)/(6z^3+z^2+3z+5))

G_1 (z)=(〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6)/(6z^3+z^2+3z+5)=1/((6z^3+z^2+3z+5)/(〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6))

6z^3+z^2+3z+5 〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6

〖-6z〗^3-168/5 z^2+6z-216/5 -36/5

0-〖163/5 z〗^2+9z-191/5

G_1 (z)=1/((6z^3+z^2+3z+5)/(〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6))=1/(-36/5+(-〖163/5 z〗^2+9z-191/5)/(〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6))

G_2 (z)=(-〖163/5 z〗^2+9z-191/5)/(〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6)=1/((〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6)/(-〖163/5 z〗^2+9z-191/5))

〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6 -〖163/5 z〗^2+9z-191/5

〖-5/6 z〗^3+75/326 z^2-955/978 z 25/978 z

0+〖4789/978 z〗^2-295/163 z+6

G_2 (z)=1/((〖5/6 z〗^3+〖14/3 z〗^2-5/6 z+6)/(-〖163/5 z〗^2+9z-191/5))=1/(25/978 z+(〖4789/978 z〗^2-295/163 z+6)/(-〖163/5 z〗^2+9z-191/5))

G_3 (z)=(〖4789/978 z〗^2-295/163 z+6)/(-〖163/5 z〗^2+9z-191/5)=1/((-〖163/5 z〗^2+9z-191/5)/(〖4789/978 z〗^2-295/163 z+6))

-〖163/5 z〗^2 +9z -191/5 〖4789/978 z〗^2-295/163

...