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Taller #1 Evolución e
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Escuela Profesional De Ingeniería Eléctrica
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UNIVERSIDAD NACIONAL DE SAN AGUSTÍN -AREQUIP -AREQUIPA A ESCUELA PROFESIONAL DE INGENIERIA ELECTRICA
U N S
TEMA: ESTABILIDAD POR LGR Y RESPUESTA EN FRECUENCIA
DOCENTE:
ING. LIZ PAREDES Master your semester with Scribd Read Free Foron 30this Days Sign up to vote title & The New York Times CURSO: Useful Not useful Special offer for students: Only $4.99/month. LABORATORIO DE CONTROL 2 Cancel anytime.
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Ejercicio 1: resolver el LRG y explicar paso a paso para su análisis, ¿cómo verifico la estabilidad?
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Tememos que saber La función de transferencia es: G=tf(num,den)
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El Programa MATLAB dibujará el lugar de las raíces para este sistema. % --------- Lugar de las raíces --------num=[1 0 1]; den=[1 4 3 0]; rlocus(num,den) b=roots(den) v=[-2 2 -2 2]; axis(v); axis('square') title ('Lugar de las raíces de G(s)=k(s^2+1)/(s^3+4s^2+3s)]')
Grafica lugar de raíces
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You're Reading a Preview Unlock full access with a free trial.
Vemos la estabilidad del sistema num=[1]; den=[1 4 3 0]; T=tf(num,den) Sisotool
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K=6
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Withes Free Trial por el Lugar Ejercicio 2:Definir cuándoDownload el sistema estable Geométrico de Raíces.
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Para este problema, el denominador se obtiene como un producto de términos de prime y segundo orden. Por tanto, se deben multiplicar estos términos para obtener u polinomio en s. La multiplicación de estos términos se realiza de una manera sencil mediante la orden de convolución, tal y como se muestra a continuación.
a=[1 1 0]; b=[1 6 8]; c= conv(a,b)
Observe que conv(a, b) proporciona el producto de dos polinomios, a y b. Observe la siguiente salida del ordenador
c =
1
7
14
8
0
Para encontrar los polos complejos conjugados en lazo abierto, se utiliza la orden roots de la siguiente manera: You're a Preview r Reading =roots(b) r =
Unlock full access with a free trial.
-4 -2 Download With Free Trial
El Programa MATLAB dibujará el lugar de las raíces para este sistema.
% --------- Lugar de las raíces --------num=[1 3]; Read Free Foron 30this Days Sign up to vote title den=[1 7 14 8 0]; Useful Not useful rlocus(num,den) Cancel anytime. Special offer for students: Only6$4.99/month. v=[-6 -6 6]; axis(v); axis('square')
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Grafica lugar de raíces
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Ejercicio 3:Analizar el Diagrama de Bode de manera teórica comprobarlo en simulación para el siguiente sistema:
num = [1 10000 0]; den = [1 100 1000000]; G=tf (num,den) Sisotool G = s^2 + 10000 s -----------------s^2 + 100 s + 1e06 Continuous-time transfer function. Grafica del diagrama de bode
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V. PROCEDIMIENTO
1. Hacer el análisis de Lugar Geométrico de Raices. Teorica y experimentalmen con el simulador.
Por
El Programa MATLAB dibujará el lugar dealas raíces para este sistema. You're Reading Preview num=[1 0];
Unlock full access with a free trial.
den=[1 2 0]; rlocus(num,den) Download With Free Trial title ('Lugar de las raíces de G(s)=k(s)/[s^2+2s]' )
La función de transferencia es: G=tf(num,den) G =
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Representación gráfica de lugar de raíces
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2. Construir los Diagramas de Bode de Lazo Cerrado y obtengan información d respuesta a la frecuencia para las funciones de transferencia de transferencia d lazo abierto de la Ec. (3) analizada parta diferentes valores de la ganancia K K1=2.4, K2=24 y K3=240.
La función transferencia num=[1]; den=[1 8 12 0]; G=tf(num,den) G= 1 -----------------s^3 + 8 s^2 + 12 s Continuous-time transfer function. Sisotool K=1
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Utilize la herramienta rltool en cada uno de los casos obtener los Diagramas d Bode de Lazo Cerrado, el Ancho de Banda ω1 a ω2, la Frecuencia d Resonancia ωR, la Magnitud Máxima, Mmax. y la respuesta en el tiempo a u escalón unitario para realizando comparaciones concluir como afecta comportamiento del sistema en el dominio del tiempo al variar los valores de Read Free Foron 30this Days Sign up to vote title Ganancia K.
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a=[1 6 8]; b=[1 12 48]; c= conv(a,b) c = 1 18 num=[1]; den=[1 18 G=tf(num,den) G =
Contro
128
384
384
128
384
384];
1 -----------------------------------s^4 + 18 s^3 + 128 s^2 + 384 s + 384 Continuous-time transfer function. Sisotool
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K=10
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K=1000
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K=3000
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a) Cuáles serían los pasos para encontrar el LGR
1. Puntos de origen (k=0) S= -2 S=-4
S=-6 S=-8
2. Puntos terminales: ceros infinitos (no hay ceros) 3. Numero de ramas separadas (N) Sabemos N =Polos – Zeros N= 4-0 N= 4 4. Asíntotas de lugar de raíces (+) You're = Reading a Preview
j=0, 1, 2,3
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= = =
180 (2 ∗ 0 1) Download Free Trial = 45With 4 180 (2 ∗ 1 1) = 135 4 180 (2 ∗ 2 1) = 225 4 ( 180 2 ∗ 3 1) = 315 Read Free Foron 30this Days Sign up to vote title 4
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Completado .Estabilidad Por LGR y Respuesta en Frecuencia
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Escuela Profesional De Ingeniería Eléctrica
Contro
6. Lugar de raíces sobre el eje real
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Master your semester with Scribd Read Free Foron 30this Days Sign up to vote title & The New b) York Times Useful Not useful ¿Según su criterio puedo encontrar el valor de K, con el método de lugar Special offer for students: Only $4.99/month. geométrico de Raíces?
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Escuela Profesional De Ingeniería Eléctrica
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Con la ayuda de una calculadora científica hacemos una tabla , y realizamos el trazo en una hoja semilogaritmica, con la yuda de un trasportador y escalimetro…
d) Como explica Ud. Que la respuesta en frecuencia ayuda a verificar estabilidad. Si es la función de transferencia de un sistema, entonces el sistema es estable si el polinomio d(s), conocido como el polinomio característico del sistema, es Hurwitz. Sistemas de control Estabilidad Criterio de Routh-Hurwitz Sirve para determinar si un polinomio a(s) es Hurwitz o no. e) ¿Qué significa Margen de Fase, Margen de Amplitud?
Margen de fase (MF): es el ángulo en grados que la traza de Nyquist L(jw) se debe rotar alrededor del origen, para que el cruce d ganancia pase por el punto crítico (-1,j0) y el sistema se vuelve inestable. El margen de fase puede medirse en la traza de bode de la fase de G(jw)en lazp abierto. Margen de ganancia (MG): Es la cantidad de ganancia en decibeles (dB) que se puede añadir al lazo antes You're se Reading Preview que el sistema en lazo cerrado vuelvaainestable. Unlock full access with a free trial.
Download With Free Trial OBSERVACIONES Y CONCLUSIONES:
La característica básica de la respuesta transitoria de un sistema en lazo cerrad se relaciona estrechamente con la localización de los polos en laz cerrado.(MATLAB proporciona una solución sencilla para este problema).
Master your semester withdel Scribd Mediante el método lugar de las raíces, el estudiante puede predecir l Read Free Foron 30this Days Sign up to vote title efectos que tiene en la localización de los polos en lazo cerrado, variar el val & The New York Times Useful Not useful de la ganancia o añadir polos y/o ceros en lazo abierto. Por tanto, es convenient
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que el estudiante comprenda bien el método para generar los lugares de la
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La ventaja principal de utilizar el diagrama de Bode es que la multiplicación d magnitudesse convierte en suma. Además, cuenta con un método simple par dibujar una curva aproximadade magnitud logarítmica.
Los diagramas de Bode son de amplia aplicación en la Ingeniería de Contro pues permiten representar la magnitud y la fase de la función de transferencia d un sistema, sea éste eléctrico, mecánico. Su uso se justifica en la simplicidad co que permiten, atendiendo a la forma del diagrama, sintonizar diferent controladores (mediante el empleo de redes de adelanto o retraso, y lo conceptos de margen de fase y margen de ganancia, estrechamente ligados ésto últimos a los llamados diagramas de Nyquist), y porque permiten, en u reducido espacio, representar un amplio espectro de frecuencias.
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