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Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
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Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
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Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
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Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
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Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
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Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
Notice: Trying to access array offset on value of type int en element_children() (línea 6422 de /home1/montes/public_html/drupal/includes/common.inc).
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Deprecated function: The each() function is deprecated. This message will be suppressed on further calls en book_prev() (línea 775 de /home1/montes/public_html/drupal/modules/book/book.module).
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Deprecated function: implode(): Passing glue string after array is deprecated. Swap the parameters en drupal_get_feeds() (línea 394 de /home1/montes/public_html/drupal/includes/common.inc).

Cuestion 3 (Sistema Discreto, estabilidad, criterio de Jury)

Solapas principales

Enviado por pichu en Lun, 07/09/2012 - 13:06

Enunciado de la cuestion 3 del examen de la 2 semana de Septiembre del 2007 de Regulacion Automatica II

Solucion:

Vamos a utilizar el criterio de estabilidad de Jury para verificar la estabilidad. La Ecuacion caracteristica sera:

El criterio tiene que verificar:

$\vert a_{n}\vert< a_{0}$
$P(z)\vert _{z=1}>0$
$P(z)\vert _{z=-1}>0$ si n par y

$P(z)\vert _{z=-1}<0$ si n impar
$\vert b_{n-1}\vert> \vert b_{0}\vert$
....

La primera condicion no se verifica

con lo que no es estable

Calculos y comprobacion con scilab

z=%z;
g=2*(z-2)/(z^4+0.5*z^2+0.5)
gz=syslin('d',g)

//Ecuacion caracteristica
ec=numer(gz)+denom(gz)


//Comprobacion mediante transformacion bilineal y Routh
s=%s
z1=(s+1)/(s-1)
g1=2*(z1-2)/(z1^4+0.5*z1^2+0.5)
gs1=syslin('c',g1)
axec2=numer(gs1)+denom(gs1);
ec2=numer(axec2)
routh_t(ec2)

-->routh_t(ec2)
 ans  =
 
    1.8888889    3.3333333  - 0.3333333  
  - 0.2222222    4.2222222    0.         
    39.222222  - 0.3333333    0.         
    4.2203336    0.           0.         
  - 0.3333333    0.           0.

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Cuestion 3 (Sistema Discreto, estabilidad, criterio de Jury)