CHAPTER 4
 MODELING

 A model of a system can be described by comparing the relationship between the

signals which are observed [19]. A model can be developed with the use of data which

is collected in experiments. System identification considers the development of the

model of a system with the use of observed data. For this purpose the signals typically

considered are the output signals, which are measured, as well as the input signals,

which consider the effect the observer has on the response of a system. Other signals

which can be considered are outside disturbances, which are signals that are produced

from outside sources such as noise, wind gusts and sensor drift.

 A model is therefore a mathematical description of a system considering several

aspects but is not an exact description of the physical system [19]. System identifica-

tion is performed by first collecting data which emphasizes the parameters that are to

be considered in the model estimation. Therefore, the input and output signals as well

as specific maneuvers are selected prior to the data collection.

 For some systems it is useful to describe the models using graphical interpre-

tations. More specifically, they can be described using impulse, step and frequency

responses. Certain systems can also be described using mathematical models. These

can include continuous-time and discrete-time systems as well as linear and nonlinear

systems.

 A set of models can then be selected according to the specific application or

dynamic system. A model which uses a black box approach is used for this project.

This approach considers the input and output signals of the system in order to perform

a fit to the data without providing physical meaning to the values. This model is then