Funcion de Transferencia y Frecuencia Lerby Arteaga

Diapositiva 1

Repblica Bolivariana de Venezuela

Ministerio del Poder Popular para la Educacin Superior

Instituto Universitario de Tecnologa Antonio Jos de Sucre

Extensin - Maracaibo

Sistemas de Controles Industriales

SAIA

Realizado por:

Lerby Arteaga

CI. 19750470

Maracaibo, Julio de 2015

Energa Elica


Respuesta en frecuencia Ejemplo


Respuesta en frecuencia Ejemplo


Ejemplo: Determinar mediante un diagrama de bode la respuesta en frecuencia de:




Observe que este sistema de 2 orden presenta una frecuencia en el que se alcanza una

amplitud de oscilacin es mxima. Este suele ocurrir con determinados sistemas.

Otra manera de estudiar grficamente la respuesta en frecuencia es el diagrama polar.

En este tipo de grficos, se representa la evolucin el nmero complejo F( j ) para cada

uno de los valores que puede tomar . Se obtiene representando en el eje de ordenadas la

parte real de F( j ) y en el eje de accisas la parte imaginaria de F( j ). Matlab permite

obtener fcilmente este tipo de diagramas.


Funcin de Respuesta en Frecuencia (Un ejemplo)

Respuesta en Frecuencia de un Sistema por Transformada de Laplace

+

-

vi(t)

R

+

-

C

vc(t)


Funcin de Respuesta en Frecuencia (Un ejemplo)


w

|H(jw)|

a = 1

w

H(jw)

p/2

-p/2

a = 1


Funcin de Respuesta en Frecuencia (otro ejemplo)



Funcin de Respuesta en Frecuencia (otro ejemplo)


w

|H(jw)|

w

H(jw)



Ejemplo. Hacer el diagrama de Bode y analizar la estabilidad de:

Fin


=

+

=

=

+

=

=

=

+

=

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w

w

a

w

a

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w

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arctg

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donde

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evaluando

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2

j

H

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H

j

H

j

H

j

j

H

j

s

s

H

RC

s

s

H

-2

-1

0

1

2

-10-50510

0

0,5

1

1,5

-10-8-6-4-20246810

Grfico3-10-9-8-7-6-5-4-3-2-1012345678910
0.099503719

0.1104315261

0.1240347346

0.1414213562

0.1643989873

0.1961161351

0.242535625

0.316227766

0.4472135955

0.7071067812

1

0.7071067812

0.4472135955

0.316227766

0.242535625

0.1961161351

0.1643989873

0.1414213562

0.1240347346

0.1104315261

0.099503719

Hoja1valor de R=valor de wmagnitud de Hfase de H1-100.0995037191.4711276743valor de C=-90.11043152611.46013910561-80.12403473461.4464413322-70.14142135621.42889927221-60.16439898731.4056476494-50.19611613511.3734007669-40.2425356251.3258176637-30.3162277661.2490457724-20.44721359551.1071487178-10.70710678120.785398163401010.7071067812-0.785398163420.4472135955-1.107148717830.316227766-1.249045772440.242535625-1.325817663750.1961161351-1.373400766960.1643989873-1.405647649470.1414213562-1.428899272280.1240347346-1.446441332290.1104315261-1.4601391056100.099503719-1.4711276743

Hoja1

Hoja2

Hoja3

Grfico2-10-9-8-7-6-5-4-3-2-1012345678910
fase de H

1.4711276743

1.4601391056

1.4464413322

1.4288992722

1.4056476494

1.3734007669

1.3258176637

1.2490457724

1.1071487178

0.7853981634

0

-0.7853981634

-1.1071487178

-1.2490457724

-1.3258176637

-1.3734007669

-1.4056476494

-1.4288992722

-1.4464413322

-1.4601391056

-1.4711276743

Hoja1valor de R=valor de wmagnitud de Hfase de H1-100.0995037191.4711276743valor de C=-90.11043152611.46013910561-80.12403473461.4464413322-70.14142135621.42889927221-60.16439898731.4056476494-50.19611613511.3734007669-40.2425356251.3258176637-30.3162277661.2490457724-20.44721359551.1071487178-10.70710678120.785398163401010.7071067812-0.785398163420.4472135955-1.107148717830.316227766-1.249045772440.242535625-1.325817663750.1961161351-1.373400766960.1643989873-1.405647649470.1414213562-1.428899272280.1240347346-1.446441332290.1104315261-1.4601391056100.099503719-1.4711276743

Hoja1

Hoja2
fase de H

Hoja3

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2

4

2

2

2

2

2

4

2

2

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4

w

w

w

w

w

w

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H

jw

s

s

s

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s

H

-350

-300

-250

-200

-150

-100

-50

0

00,511,522,533,544,55

0

0,2

0,4

0,6

0,8

1

00,511,522,53

Grfico100.1250.250.3750.50.6250.750.87511.1251.251.3751.51.6251.751.87522.1252.252.3752.5
1

1.0000017927

0.9999998949

0.9998224817

0.9980874927

0.9886185987

0.95350726

0.8628242844

0.7072135785

0.5296422661

0.3790796417

0.2694421613

0.1938005008

0.1419682973

0.1060264718

0.0806484184

0.0623804683

0.0489841717

0.0389898053

0.0314153044

0.0255921467

Hoja1valor de a=valor de ww cuadradomagnitud de Hfase de H2.6130010valor de b=0.1250.0156251.0000017927-18.75495380913.4140.250.06250.9999998949-37.76473408560.3750.1406250.9998224817-57.34441646030.50.250.9980874927-77.95947966170.6250.3906250.9886185987-100.30854563310.750.56250.95350726-125.16201256370.8750.7656250.8628242844-152.460506594110.7072135785-1801.1251.2656250.5296422661-204.42890728911.251.56250.3790796417-224.14436962471.3751.8906250.2694421613-239.5631347251.52.250.1938005008-251.713678271.6252.6406250.1419682973-261.49117713621.753.06250.1060264718-269.53524787251.8753.5156250.0806484184-276.2845054726240.0623804683-282.04052033832.1254.5156250.0489841717-287.01727516962.255.06250.0389898053-291.3696196262.3755.6406250.0314153044-295.2127095042.56.250.0255921467-298.63415449532.6256.8906250.0210569055-301.70195404482.757.56250.0174827655-304.46981474292.8758.2656250.0146355381-306.980803599390.0123449095-309.26991759133.1259.7656250.0104853167-311.36593014483.2510.56250.0089630161-313.29274394243.37511.3906250.0077072007-315.07039944443.512.250.0066638085-316.71583856343.62513.1406250.0057911484-318.24349110883.7514.06250.005056769-319.66573085983.87515.0156250.0044351917-320.99323432774160.0039062496-322.23526591444.12517.0156250.0034538595-323.3999067224.2518.06250.0030651033-324.49423974314.37519.1406250.0027295362-325.52450094354.520.250.0024386598-326.49620342594.62521.3906250.0021855182-327.41424016474.7522.56250.0019643868-328.28296954544.87523.7656250.0017705289-329.10628700725250.0016000055-329.8876853731

Hoja1

Hoja2
fase de H

Hoja3

Grfico200.1250.250.3750.50.6250.750.87511.1251.251.3751.51.6251.751.87522.1252.252.3752.52.6252.752.87533.1253.253.3753.53.6253.753.87544.1254.254.3754.54.6254.754.8755
fase de H

0

-18.7549538091

-37.7647340856

-57.3444164603

-77.9594796617

-100.3085456331

-125.1620125637

-152.460506594

-180

-204.4289072891

-224.1443696247

-239.563134725

-251.71367827

-261.4911771362

-269.5352478725

-276.2845054726

-282.0405203383

-287.0172751696

-291.369619626

-295.212709504

-298.6341544953

-301.7019540448

-304.4698147429

-306.980803599

-309.2699175913

-311.3659301448

-313.2927439424

-315.0703994444

-316.7158385634

-318.2434911088

-319.6657308598

-320.9932343277

-322.2352659144

-323.399906722

-324.4942397431

-325.5245009435

-326.4962034259

-327.4142401647

-328.2829695454

-329.1062870072

-329.8876853731

Hoja1valor de a=valor de ww cuadradomagnitud de Hfase de H2.6130010valor de b=0.1250.0156251.0000017927-18.75495380913.4140.250.06250.9999998949-37.76473408560.3750.1406250.9998224817-57.34441646030.50.250.9980874927-77.95947966170.6250.3906250.9886185987-100.30854563310.750.56250.95350726-125.16201256370.8750.7656250.8628242844-152.460506594110.7072135785-1801.1251.2656250.5296422661-204.42890728911.251.56250.3790796417-224.14436962471.3751.8906250.2694421613-239.5631347251.52.250.1938005008-251.713678271.6252.6406250.1419682973-261.49117713621.753.06250.1060264718-269.53524787251.8753.5156250.0806484184-276.2845054726240.0623804683-282.04052033832.1254.5156250.0489841717-287.01727516962.255.06250.0389898053-291.3696196262.3755.6406250.0314153044-295.2127095042.56.250.0255921467-298.63415449532.6256.8906250.0210569055-301.70195404482.757.56250.0174827655-304.46981474292.8758.2656250.0146355381-306.980803599390.0123449095-309.26991759133.1259.7656250.0104853167-311.36593014483.2510.56250.0089630161-313.29274394243.37511.3906250.0077072007-315.07039944443.512.250.0066638085-316.71583856343.62513.1406250.0057911484-318.24349110883.7514.06250.005056769-319.66573085983.87515.0156250.0044351917-320.99323432774160.0039062496-322.23526591444.12517.0156250.0034538595-323.3999067224.2518.06250.0030651033-324.49423974314.37519.1406250.0027295362-325.52450094354.520.250.0024386598-326.49620342594.62521.3906250.0021855182-327.41424016474.7522.56250.0019643868-328.28296954544.87523.7656250.0017705289-329.10628700725250.0016000055-329.8876853731

Hoja1

Hoja2
fase de H

Hoja3

Funcion de Transferencia y Frecuencia Lerby Arteaga

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