1. Control de procesos. JP/RS/2010
Tabla 1. Transformada de Laplace de las funciones más usuales
f(t) F(s)=ℒሼ݂(‫)ݐ‬ሽ
1 ‫݋ݏ݈ݑ݌݉ܫ‬ ‫݋݅ݎܽݐ݅݊ݑ‬ ߜ(‫)ݐ‬ 1
2 ‫݈ܽܿݏܧ‬ó݊ ‫݋݅ݎܽݐ݅݊ݑ‬ ‫)ݐ(ݑ‬
1
‫ݏ‬
3 t
1
‫ݏ‬ଶ
4
‫ݐ‬௡ିଵ
(݊ − 1)!
(݊ = 1,2,3, … )
1
‫ݏ‬௡
5 ݁ି௔௧ 1
‫ݏ‬ + ܽ
6 ‫݁ݐ‬ି௔௧
1
(‫ݏ‬ + ܽ)ଶ
7 ‫ݐ‬௡
݁ି௔௧
݊!
(‫ݏ‬ + ܽ)௡ାଵ
8 ‫ݐ߱݊݁ݏ‬
߱
‫ݏ‬ଶ + ߱ଶ
9 ܿ‫ݐ߱ݏ݋‬
‫ݏ‬
‫ݏ‬ଶ + ߱ଶ
10 ݁ି௔௧
‫ݐ߱݊݁ݏ‬
߱
(‫ݏ‬ + ܽ)ଶ + ߱ଶ
11 ݁ି௔௧
ܿ‫ݐ߱ݏ݋‬
(‫ݏ‬ + ܽ)
(‫ݏ‬ + ܽ)ଶ + ߱ଶ
12
݂݀(‫)ݐ‬
݀‫ݐ‬
‫ݏ‬ ∗ ‫)ݏ(ܨ‬ − ݂(0)
13
݀ଶ
݂(‫)ݐ‬
݀‫ݐ‬ଶ
‫ݏ‬ଶ
∗ ‫)ݏ(ܨ‬ − ‫ݏ‬ ∗ ݂(0) −
݂݀
݀‫ݐ‬
(0)
14
݀௡
݂(‫)ݐ‬
݀‫ݐ‬௡
‫ݏ‬௡
∗ ‫)ݏ(ܨ‬ − ‫ݏ‬௡ିଵ
∗ ݂(0) − ‫ݏ‬௡ିଶ
∗
݂݀
݀‫ݐ‬
(0) − ⋯ − ‫ݏ‬ ∗
݀௡ିଶ
݂
݀‫ݐ‬௡ିଶ
(0) − ‫ݏ‬ ∗
݀௡ିଵ
݂
݀‫ݐ‬௡ିଵ
(0)