Sistema Sub-Amortiguado 9 Pasos

Sistemas de Control Automático

Tarea 3
Sistema sub-amortiguado (9 pasos)

T=TS=1.45seg
m=y2-y1/x2-x1= m=4400-0/10-0 m=440B=1/m B=1/440 B=0.0022

J=BT/5= (0.0022) (1.45s) / 5 J=0.00319/5 J=0.000638Paso 1.
Desarrollar la Planta
1/(Js+B)= 1/(0.000638+0.0022)= (/J)/(/J)= 1567.39/(s+3.448)

Paso 2.
(w(s))/(v(s)) = (1567.39/s+3.448)(KP+KDS+KI/s)1+(1567.39/s+3.448)(KP+KDS+KI/s)
Paso 3.

(w(s))/(v(s))= 1567.39(KP+KDS+KI/s)/s+3.448
1+ 1567.39(KP+KDS+KI/s)/s+3.448

Paso 3b. Desarrollando el denominador(w(s))/(v(s))= 1/1+ (1567.39(KP+KDS^2+KI/s)/s+3.448
= (s+3.448) + [1567.39(KP+KDS+KI/s)/s+3.448]

Paso 4.
(w(s))/(v(s))= 1567.39(KP+KDS^2+KI/s)/s+3.448(s+3.448)+ [1567.39(KP+KDS^2+KI/s)/s+3.448]

Paso 5.
(w(s))/(v(s))= 1567.39(KP+KDS^2+KI/s)
s+3.448+ [1567.39(KP+KDS^2+KI/s)]

Desarrollando parte de KP, KDS y KI
KD/1 +KDS/1+KIs = KDS^2+KPS+KI/s
Paso 6.
(w(s))/(v(s))= 1567.39(KDS^2+KPS+KI/s)/s
(s+3.448)+ [1567.39(KDS^2+KPS+KI/s)/s]

Se desarrolla el denominador.((s+3.448)/1)+( 1567.39(KDS^2+KPS+KI)/s)
=S^2+3.448s+1567.39(KDS^2+KPS+KI)/s

Paso 7. Aplicando la ley de la tortilla se eliminan las S
W(s)/V(s)= 1567.39(KDS^2+KPS+KI)/s/S^2+3.448+1567.39(KDS^2+KPS+KI)/sPaso 8.
W(s)/V(s)= 1567.39(KDS^2+KPS+KI)/ S^2+3.448s+1567.39(KDS^2+KPS+KI)

Paso 8b. Ecuación antes de ser factorizada
W(s)/V(s)= 1567.39(KDS^2+KPS+KI)/S^2+1567.39KDS^2+1567.39KPS+3.448s+1567.39KI

Paso 9.
Ecuacion Final
(w(s))/(v(s))= (1567.39(KDS2+KPS+KI))/( s^2 (1+1567.39KD) +S (3.448+1567.39KP) + (1567.39KI))

Función de transferencia de Segundo orden.
(C(s))/(R(s))=...