Modelación de sistemas en matlab

PRIMER PROYECTO DE TEORIA DE CONTROL I
MODELACIÓN

Sistema 1:
R1= 2(, R2=3(, C1=470(F y L= 0.25H

[pic]
a) Función de Transferencia por Diagrama de Bloques
Entrada: vt
Salida: iLEcuaciones:
1. vt = vr1 + vr2
2. v1 = r1i1 = 2i1
3. v2 = r2i2 = 3i2
4. v2 = vC + vL
5. i3 = i2 + i1
6. i3 = iC = iL
7. [pic]
8. [pic]
9. [pic]
10. [pic]Ecuaciones en Laplace

v1 = 3iS
v2 = 2is
[pic]
[pic]
VLS = 0,25S i3S

Diagrama de Bloques

[pic]
g1 = 0.5000
g2 = 3
[pic]

g4= 0,25S
[pic]
[pic]
g6=(1/g5)= 0,2505sg7=g5g2 =[pic]
[pic]
[pic]
[pic]
g9= g8g1 =[pic]
[pic]
[pic]
[pic]
b) Verificación en MatLab

>> g1=(1/2)

g1 =

0.5000

>> g2=(3)

g2 =

3

>> g3=tf([01],[0.000470 0])

Transfer function:
1
---------
0.00047 s

>> g4=tf([0.25 0],1)

Transfer function:
0.25 s

>> g5=feedback(g3,g4)

Transfer function:
1
--------
0.2505 s

>>g6=(1/g5)

Transfer function:
0.2505 s

>> g7=series(g5,g2)

Transfer function:
3
--------
0.2505 s

>> g8=feedback(g7,1)

Transfer function:
3
------------
0.2505 s + 3

>>g9=series(g8,g1)

Transfer function:
1.5
------------
0.2505 s + 3

>> g10=feedback(g9,g6)

Transfer function:
1.5
------------
0.6262 s + 3

Sistema 2:
K1= 3 N/m2, K1= 4 N/m2, ( = 3Kgrf/m, m1=10kg
[pic]

c) Función de Transferencia por Diagrama de Bloques
Entrada: FX
Salida: X

Ecuaciones:
1. ∑F = ma = m[pic]
2. Fe = KX
3. Fe1 = 3X
4. Fe2 = 4X
5. Fr= βv → Fr = 3 v = [pic]
6. FX – Fe1 – Fe2 – Fr = ma = m[pic]

Ecuaciones en L:

Fe1S = 3XS
Fe2S = 4XS
FrS = 3SXS
∑F = ma → FXS – 3XS – 4XS – 3SXS = m S2XS
FXS – 3XS = m S2XS + 3XS + 4XSm S2XS + 3XS + 4XS = Xs(mS2 + 3 + 4) = Xs(mS2 +7)

[pic]

Diagrama de Bloques
[pic]
[pic]
g2= 3s

[pic]

b) Verificación en MatLab

>> g1=tf(1,[10 0 7])

Transfer function:...