Formulario Laplace PDF

INSTITUTO PROFESIONAL VIRGINIO GÓMEZ CARRERA : Ingeniería Ejecución Electrónica ASIGNATURA : Control Automático. Semestre 2 - 2007 PROFESOR : Renán Cisternas Lillo FORMULARIO: TRANSFORMADA DE LAPLACE σo + j∞ 1 f (t ) = F ( s )e st ds s = σ + jw ∫ 2πj σo − j∞

∞

F ( s ) = ∫ f (t )e − st dt 0

1 s 1 s2 n! s n +1

1 t

tn 1

π

t

s 1 s+a 1 (s + a )2 n! (s + a )n+1 w 2 s + w2 s 2 s + w2 s ⋅ sen(θ ) + w ⋅ cos(θ ) s 2 + w2 s ⋅ cos(θ ) − w ⋅ sen(θ ) s 2 + w2 w (s + a ) 2 + w 2 s+a (s + a ) 2 + w 2 2 ws

e

− at

t ⋅ e − at t n ⋅ e − at

sen(wt ) cos(wt ) sen(wt + θ ) cos(wt + θ )

e − at ⋅ sen(wt ) e − at ⋅ cos(wt ) t ⋅ sen(wt ) t ⋅ cos(wt ) senh(wt )

cosh (wt )

(s

2

+ w2

)

2

s 2 − w2

(s

)

+ w2 w 2 s − w2 s 2 s − w2 2

2

INSTITUTO PROFESIONAL VIRGINIO GÓMEZ CARRERA : Ingeniería Ejecución Electrónica ASIGNATURA : Control Automático. Semestre 2 - 2007 PROFESOR : Renán Cisternas Lillo

FORMULARIO: TRANSFORMADA DE LAPLACE e − at ⋅ f (t ) t n ⋅ f (t )

f (t − a )U (t − a ), a > 0

δ (t − to) df (t )

dt d f (t ) dt 2 f n (t ) 2

t

∫ f (τ )dτ 0

f (t − t1 )

c1 f1 (t ) + c 2 f 2 (t ) t

∫ f (τ ) ⋅ f (t − τ )dτ 1

0

2

sF (s + a )

(− 1)n ⋅

dn

F (s ) ds n e − as ⋅ F (s )

e − sto sF (s ) − f (0 + )

s 2 F (s ) − s ⋅ f (0 + ) − f (1) (0 + ) s n F (s ) − s n −1 ⋅ f (0 + ) − ... − f (n −1) (0 + ) F (s ) s e −t1s F (s ) c1 F1 (s ) + c 2 F2 (s ) F1 (s ) ⋅ F2 (s )