Sistemas dinamicos

[pic]

R = Resistencia de Armadura L = Inductancia Armadura [pic] = Fuerza Electromotriz [pic] = Torque delEje [pic]= Velocidad Angular del EjeJ = Momento de Inercia b = Fricción Viscosa

1. Una ecuaciónlineal e invariante en el tiempo

[pic] + R i (t) + [pic]

[pic]) = [pic]

[pic]i (t)

[pic] = [pic] bw[pic]

2. La Función de transferencia [pic] Y Diagrama en BloquesAplicando la transformada de la Place con condiciones iníciales a Cero

[pic](s) = RI(s) + Eb(s) + [ LSI(s) - L[pic]

[pic](s) = I(s) [R + LS] + Eb(s)

[pic])

[pic]i(t)

d. J [SW(s) - [pic] ] = [pic] BW[pic]

J [SW(s) + BW[pic] = [pic]

W(s) [ JS + B ] = [pic]

CAUSA – EFECTO

a. [pic](s) - Eb(s) = I(s) [R + LS][pic] = [pic]

b. Eb(s) = W(S)

c. [pic] = I (S)

d. [pic] = [pic]

[pic] I(s) [pic] W(s)_

La Función de Transferencia Seria

[pic] [pic]

[pic] [pic]

[pic] [pic]

[pic] [pic]

3. Representación matricial enespacio de estados

VE En L : I = [pic]

En J : W = [pic]

Entrada [pic]; Salida W(t)

1. [pic] = L [pic] + R [pic] + [pic]

[pic] = L [pic] + R[pic] + [pic]

2. [pic] = [pic] - B[pic]

Reorganizando

[pic] = [pic] + [pic]

[pic] = [pic] - [pic] [pic] [pic]

Luego se escribe matricialmente...