Chapter Two
Introduction
Although the dynamic modeling of control problems are based on the mathematical models of
physical systems is intrinsically complex, the fundamental ideas in control theory are enough
simple very intuitive. The physical laws lead to mathematical models that describe the
relationship between the input and output of dynamic systems. In some cases when mathematical
modeling based on physical laws is complex and inconvenient, modeling of a dynamic system is
obtained based on experimental input output data of the system.
There are three ways of modeling dynamic systems: ordinary differential equation, transfer
function and slate-space representation.
In this course, we focus on transfer function modeling. Transfer function model is derived from
the linear, time-invariant differential equation using what we call the Laplace transform.
Although the transfer function can be used only for linear systems, it yields more intuitive
information than the differential equation.