| Laplace Transfer Function |
The previous proofs were presented to establish the theoretical basis for this method, however tables of values will be presented in a later section for the most popular transforms.
17.2 APPLYING LAPLACE TRANSFORMS
The process of applying laplace transform to analyze linear system involves the basic steps listed below.
- convert the system transfer function, or differential equation, to the s-domain by replacing �D� with �s� (note: if any of the initial conditions are non-zero these must be also be added.)
- convert the input function (s) to the s-domain using the transform tables.
- algebraically combine the input and transfer function to the an output function .
- use partial fractions to reduce the output function to simpler components.
- convert the out put equation back to the time �domain using the tables.
17.2.1 A Few Transform Tables
Laplace transform tables are shown in figure 17.5, figure 17.7 and figure 17.8. these are commonly used when analyzing systems with laplace transforms. The transforms shown in figure 17.5 are general properties normally used for manipulating equations, and for converting them to/ from the s-domain.
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