Funciones de transferencia

EJERCICIOS
PLANTEAR LA SOLUCIÓN EN EL DOMINIO DE LA FRECUENCIA

F
v
1.

* FUNCIÓN DE TRANSFERENCIA
Gps
F(s)
v(s)

Hs=Gps=vsFs=1m∙s+b

* v(s)
Gps
F(s)
Gcs
r(s)
SISTEMA DE CONTROL DE LAZO ABIERTO

Gcs=Fsrs

Gps=v(s)F(s)

Hs=v(s)rs

vs=Gp(s)∙Gc(s)∙r(s)

* Entrada Tipo Escalón ( Gcs= 1s)

vs=1s∙1m∙s+b∙rs

vs=1m∙s2+b∙s∙rs

* Entrada Tipo Rampa ( Gcs=1s2)
vs=1s2∙1m∙s+b∙rs
vs=1m∙s3+b∙s2∙rs

* SISTEMA DE CONTROL CON RETROALIMENTACIÓN
F(s)
v(s)
Gps
Gcs
r(s)

Hs=v(s)rs
vs=Gps∙Fs
Fs=Gc(s)∙rs-v(s)
vs=Gps∙Gcs∙rs-vs

vs=Gp(s)∙Gc(s)∙r(s)1+Gp(s)∙Gc(s)

* Entrada Tipo Escalón ( Gcs= 1s)

vs=1m∙s+b∙1s1+1m∙s+b∙1s∙rs

vs=1m∙s2+b∙s+1∙rs

* Entrada Tipo Rampa ( Gcs= 1s2)

vs=1m∙s+b∙1s21+1m∙s+b∙1s2∙rs
vs=1m∙s3+b∙s2+1∙rs* SISTEMA DE CONTROL CON PERTURBACIONES
v(s)
F(s)
Z(s)
Gps
Gcs
r(s)
g(s)

vs=Gps∙gs+Zs
gs=Gcs∙rs-vs
vs=Gps∙Gcs∙rs-vs+Zs

vs=Gp(s)∙Gc(s)∙r(s)1+Gp(s)∙Gc(s)+Gp(s)1+Gp(s)∙Gc(s)∙Z(s)


* Entrada Tipo Escalón ( Gcs= 1s)

vs=1m∙s+b∙1s1+1m∙s+b∙1s∙rs+1m∙s+b1+1m∙s+b∙1s∙Zs

vs=1m∙s2+b∙s+1∙rs+sm∙s2+b∙s+1∙Zs

* Entrada Tipo Rampa ( Gcs= 1s2)vs=1m∙s+b∙1s21+1m∙s+b∙1s2∙rs+1m∙s+b1+1m∙s+b∙1s2∙Zs

vs=1m∙s3+b∙s2+1∙rs+s2m∙s3+b∙s2+1∙Zs

F
v1
v2
X2
X1
k
b
2.

* FUNCIÓN DE TRANSFERENCIA
Gps
F(s)
X1(s)- X2(s)

Hs=Gps=X1s-X2sFs=1m∙s2+2b+c∙s+2k

* SISTEMA DE CONTROL DE LAZO ABIERTO
X1s-X2s
Gps
F(s)
Gcs
r(s)

Gcs=Fsrs

Gps=X1s-X2sF(s)

Hs=X1s-X2srs

X1s-X2s=Gp(s)∙Gc(s)∙r(s)

* Entrada Tipo Escalón ( Gcs= 1s)

X1s-X2s=1s∙1m∙s2+2b+c∙s+2k∙rsX1s-X2s=1m∙s3+2b+c∙s2+2k∙s∙rs

* Entrada Tipo Rampa ( Gcs= 1s2)
X1s-X2s=1s2∙1m∙s2+2b+c∙s+2k∙rs
X1s-X2s=1m∙s4+2b+c∙s3+2k∙s2∙rs

* SISTEMA DE CONTROL CON RETROALIMENTACIÓN
F(s)
X1s-X2s
Gps
Gcs
r(s)

Hs=v(s)rs
X1s-X2s=Gps∙Fs
Fs=Gc(s)∙rs-X1s-X2s
X1s-X2s=Gps∙Gcs∙rs-(X1s-X2s)

X1s-X2s=Gp(s)∙Gc(s)∙r(s)1+Gp(s)∙Gc(s)

* Entrada Tipo Escalón ( Gcs= 1s)X1s-X2s=1m∙s2+2b+c∙s+2k∙1s1+1m∙s2+2b+c∙s+2k∙1s∙rs

X1s-X2s=1m∙s3+2b+c∙s2+2k∙s+1∙rs

* Entrada Tipo Rampa ( Gcs= 1s2)

X1s-X2s=1m∙s2+2b+c∙s+2k∙1s21+1m∙s2+2b+c∙s+2k∙1s2∙rs

X1s-X2s=1m∙s4+2b+c∙s3+2k∙s2+1∙rs

* SISTEMA DE CONTROL CON PERTURBACIONES
X1s-X2s
F(s)
Z(s)
Gps
Gcs
r(s)
g(s)

X1s-X2s=Gps∙gs+Zs
gs=Gcs∙rs-(X1s-X2s)
X1s-X2s=Gps∙Gcs∙rs-X1s-X2s+ZsX1s-X2s=Gp(s)∙Gc(s)∙r(s)1+Gp(s)∙Gc(s)+Gp(s)1+Gp(s)∙Gc(s)∙Z(s)


* Entrada Tipo Escalón ( Gcs= 1s)

X1s-X2s=1m∙s2+2b+c∙s+2k∙1s1+1m∙s2+2b+c∙s+2k∙1s∙rs+1m∙s2+2b+c∙s+2k1+1m∙s2+2b+c∙s+2k∙1s∙Zs

X1s-X2s=1m∙s3+2b+c∙s2+2k∙s+1∙rs+sm∙s3+2b+c∙s2+2k∙s+1∙Zs

* Entrada Tipo Rampa ( Gcs= 1s2)

X1s-X2s=1m∙s2+2b+c∙s+2k∙1s21+1m∙s2+2b+c∙s+2k∙1s2∙rs+1m∙s2+2b+c∙s+2k1+1m∙s2+2b+c∙s+2k∙1s2∙Zs

X1s-X2s=1m∙s4+2b+c∙s3+2k∙s2+1∙rs+s2m∙s4+2b+c∙s3+2k∙s2∙Zs

k
bθ(t)
T(t)
3.

* FUNCIÓN DE TRANSFERENCIA
Gps
T(s)
θ(s)

Hs=Gps=θsTs=1I∙s2+b∙s+k

* θ (s)
Gps
T(s)
Gcs
r(s)
SISTEMA DE CONTROL DE LAZO ABIERTO

Gcs=Tsrs

Gps=θ(s)T(s)

Hs=θ(s)rs

θs=Gp(s)∙Gc(s)∙r(s)

* Entrada Tipo Escalón ( Gcs= 1s)

θs=1s∙1I∙s2+b∙s+k∙rs

θs=1I∙s3+b∙s2+k∙s∙rs

* Entrada Tipo Rampa ( Gcs= 1s2)
θs=1s2∙1I∙s2+b∙s+k∙rs
θs=1I∙s4+b∙s3+k∙s2∙rs* SISTEMA DE CONTROL CON RETROALIMENTACIÓN
T(s)
θ (s)
Gps
Gcs
r(s)

Hs=θ(s)rs
θs=Gps∙Ts
Ts=Gc(s)∙rs-θ(s)
θs=Gps∙Gcs∙rs-θs

θs=Gp(s)∙Gc(s)∙r(s)1+Gp(s)∙Gc(s)

* Entrada Tipo Escalón ( Gcs= 1s)

θs=1I∙s2+b∙s+k∙1s1+1I∙s2+b∙s+k∙1s∙rs

θs=1I∙s3+b∙s2+k∙s+1∙rs

* Entrada Tipo Rampa ( Gcs= 1s2)

θs=1I∙s2+b∙s+k∙1s21+1I∙s2+b∙s+k∙1s2∙rs
θs=1I∙s4+b∙s3+k∙s2+1∙rs

*SISTEMA DE CONTROL CON PERTURBACIONES

θ (s)
T(s)
Z(s)
Gps
Gcs
r(s)
g(s)

θs=Gps∙gs+Zs
gs=Gcs∙rs-θs
θs=Gps∙Gcs∙rs-θs+Zs

θs=Gp(s)∙Gc(s)∙r(s)1+Gp(s)∙Gc(s)+Gp(s)1+Gp(s)∙Gc(s)∙Z(s)


* Entrada Tipo Escalón ( Gcs= 1s)

θs=1I∙s2+b∙s+k∙1s1+1I∙s2+b∙s+k∙1s∙rs+1I∙s2+b∙s+k1+1I∙s2+b∙s+k∙1s∙Zs

θs=1I∙s3+b∙s2+k∙s+1∙rs+sI∙s3+b∙s2+k∙s+1∙Zs

* Entrada Tipo...