ingen.cajael.com

Problemas, examenes, practicas y simulaciones de: Regulacion(Scilab), Electronica(Micro-Cap; Spice) y Estadistica (R-Projec..

Mensaje de error

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).
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).
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).
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).
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 4 (Sistema Discreto, lugar de las raices)

Solapas principales

Enviado por pichu en Sáb, 07/14/2012 - 21:11

SOLUCION:

Polos y ceros

Cero en 2

Polos:

$\begin{displaymath}z^{4}+0.5\cdot z^{2}+0.5=0\end{displaymath}$

$\begin{displaymath}z^{4}+0.5\cdot z^{2}+0.5=(z^{2}-0.25+0.661j)\cdot(z^{2}-0.25-0.661j)\end{displaymath}$

$\begin{displaymath}z=a+jb\; ; z^{2}=a^{2}-b^{2}+(2\cdot a\cdot bj)=0.25-j0.661\end{displaymath}$

$\begin{displaymath}a^{2}-b^{2}=0.25\end{displaymath}$

$\begin{displaymath}2\cdot a\cdot b=-0.661\end{displaymath}$

$\begin{displaymath}(2ab)^{2}-4\cdot b^{4}=0.25 \cdot 4 \cdot b^{2} \; ;4\cdot b^{4}+ b^{2}-(2ab)^{2}=4\cdot b^{4}+ b^{2}-(-0.661)^{2}=0\end{displaymath}$

$\begin{displaymath}b=\pm\sqrt{0.228}=\pm 0.477\end{displaymath}$

$\begin{displaymath}a=\pm \frac{0.661}{2\cdot 0.477}=\pm 0.69\end{displaymath}$

$\begin{displaymath}z1=0.477-j0.69\end{displaymath}$

$\begin{displaymath}z2=-0.477+j0.69\end{displaymath}$

$\begin{displaymath}(z^{2}-0.25+0.661j)=(z-z1)\cdot (z-z2)\end{displaymath}$

$\begin{displaymath}z=a+jb\; ; z^{2}=a^{2}-b^{2}+(2a\cdot bj)=0.25+j0.661\end{displaymath}$

$\begin{displaymath}a^{2}-b^{2}=0.25\end{displaymath}$

$\begin{displaymath}2a\cdot b=0.661\end{displaymath}$

$\begin{displaymath}(2ab)^{2}-4\cdot b^{4}=0.25 \cdot 4 \cdot b^{2}\; ;4\cdot b^{4}+ b^{2}-(2ab)^{2}=4\cdot b^{4}+ b^{2}-(0.661)^{2}=0\end{displaymath}$

$\begin{displaymath}b=\pm\sqrt{0.228}=\pm 0.477\end{displaymath}$

$\begin{displaymath}a=\pm \frac{0.661}{2\cdot 0.477}=\pm 0.69\end{displaymath}$

$\begin{displaymath}z3=0.477+j0.69\end{displaymath}$

$\begin{displaymath}z4=-0.477-j0.69\end{displaymath}$

Ya tenemos todos los polos. El numero de ramas en el infinito

2. El lugar de las raices en el eje real

A la izquierda del cero en 2

3. Asintotas

$\begin{displaymath}\theta=\frac{180\cdot(2\cdot k+1)}{3}=[60,-180,-60]\end{displaymath}$

$\begin{displaymath}s=-\frac{-(-2)}{3}=\frac{2}{3}=-0.67\end{displaymath}$
4. Puntos de ruptura y ingreso

$\begin{displaymath}\frac{dK}{ds}=-\frac{d}{ds}\left(\frac{z^{4}+0.5\cdot z^{2}+0.5}{(z-2)} \right)=\end{displaymath}$

$\begin{displaymath}=-\frac{(4\cdot z^{3}+1\cdot z+0.5)\cdot (z-2)-(z^{4}+0.5\cdot z^{2}+0.5)}{(z-2)} =0\end{displaymath}$

$\begin{displaymath}(4\cdot z^{3}+1\cdot z+0.5)\cdot (z-2)-(z^{4}+0.5\cdot z^{2}+0.5)=0\end{displaymath}$

$\begin{displaymath}(4\cdot z^{4}+1\cdot z^{2}+0.5\cdot z)-(8\cdot z^{3}+2\cdot z+1)-(z^{4}+0.5\cdot z^{2}+0.5)=\end{displaymath}$

$\begin{displaymath}=- 0.5 - 2\cdot z + 0.5\cdot z^{2} - 8\cdot z^{3} + 3\cdot z^{4} =0 \end{displaymath}$

$\begin{displaymath}z=-0.2\end{displaymath}$
5. Angulos de salida

$\begin{displaymath}z3=0.477+j0.69\end{displaymath}$

$\begin{displaymath}\theta_{1}=180-\lfloor{z3-z1}-\lfloor{z3-z2}-\lfloor{z3-z4}+\lfloor{z1-c1}=190\end{displaymath}$

z1 es simetrico con respecto a z3 respecto al eje real.

$\begin{displaymath}z2=-0.477+j0.69\end{displaymath}$

$\begin{displaymath}\theta_{2}=180-\lfloor{z2-z1}-\lfloor{z2-z3}-\lfloor{z2-z4}+\lfloor{z2-c1}=310\end{displaymath}$
z4 es simetrico con respecto a z2 respecto al eje real

Representacion y calculos hechos con el Scilab

z=%z;
g=(z-2)/(z^4+0.5*z^2+0.5);
gz=syslin('d',g);
clf;
evans(gz,2)
zgrid;
p=roots(denom(g))
tet=%pi-atan(imag(p(1)-p(2)),real(p(1)-p(2)))-atan(imag(p(1)-p(3))
,real(p(1)-p(3)))-atan(imag(p(1)-p(4)),real(p(1)-p(4)))
+atan(imag(p(1)-2),real(p(1)-2))

angz1=360*tet/(2*%pi)
tet2=%pi-atan(imag(p(3)-p(1)),real(p(3)-p(1)))-atan(imag(p(3)-p(2))
,real(p(3)-p(2)))-atan(imag(p(3)-p(4)),real(p(3)-p(4)))
+atan(imag(p(3)-2),real(p(3)-2))

angz1=360*tet2/(2*%pi)
dg=derivat(1/gz)
rdg=roots(numer(dg))

Idioma Español

Añadir nuevo comentario

Menú principal

Menú secundario

Mensaje de error

Cuestion 4 (Sistema Discreto, lugar de las raices)

Solapas principales

Representacion y calculos hechos con el Scilab

Tags:

Añadir nuevo comentario

Plain text

Idiomas

Comentarios recientes

Seguidores en Google

Busquedas populares

Alexa widget

Contenido popular

Páginas

Today's popular content

Páginas

REGULACION AUTOMATICA

Menú principal

Menú secundario

Mensaje de error

Se encuentra usted aquí

Cuestion 4 (Sistema Discreto, lugar de las raices)

Solapas principales

Representacion y calculos hechos con el Scilab

Tags:

Añadir nuevo comentario

Plain text

Idiomas

Comentarios recientes

Seguidores en Google

Busquedas populares

Inicio de sesión

Alexa widget

Contenido popular

Páginas

Today's popular content

Páginas

REGULACION AUTOMATICA