Reference Book
Modern Control Engineering
Katsuhiko Ogata, Prentice-Hall
Ogata_Modern_Control_Engineering_5th
http://lpsa.swarthmore.edu/LaplaceXform/FwdLaplace/LaplaceProps.html
Introduction
Any system can be described using a mathematical model.
One way to classify mathematical models is to place them into static modelling and dynamic modelling.
Static model
General equation for static model : y = f(u)
Dynamic model :
A dynamic model input/output is usually expressed by a differential equation.
Um modelo dinâmico expressa a capacidade de um sistema de “recordar” a sua “história”. Esta propriedade dos sistemas radica na sua capacidade de armazenar energia, massa ou informação.
Estado
Variáveis de estado
The Laplace Transform
The Laplace transform method is an operational method that can be used advantageously for solving linear differential equations.
By use of Laplace transform we can transform many common functions into algebraic functions of a complex variable s.
Review of complex variables and complex functions
Complex variable : a complex number has a real part and an imaginary part, both of which are constant. If the real part and/or imaginary part are variables, a complex number is called a complex variable.
Euler Formula
i² = -1
Geometric interpretation of Euler Formule
In the Laplace transformation we use the notation s as a complex variable, that is :
s = σ + jw
.
.
Linearity
para simplificar foi criada uma tabela….
This list is not a complete listing of Laplace transforms
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