Laplace transformation is a method for solving linear differential equations with constant coefficients based on given initial conditions. It can also be used for fault functions which give the value zero in the event of a negative argument. The operations and the differentiation and integration of time functions are converted, based on the form of transformation used, into algebraic operations with associated frequency functions. Laplace transformation is mainly used to solve differential equations in control technology.
With Laplace transformation, a function f(t) within the time range (original range) is assigned a function F(s) in the image or frequency range as part of a reversible but unique arrangement. This creates a unique but reversible relationship between the original function and the image function. It can be described using the following equation:
The variable s = σ + jω describes a complex frequency.