Preliminaries - Real-Time Rendering: Computer Graphics with Control Engineering - page 12

measured at sufficiently good resolution. In general, the following principles should
be observed:

1. Select inputs that can excite the system dynamics adequately.

2. Minimise the effects of noise and disturbance to obtain a good signal-to-noise
ratio.

3. Choose appropriate sampling intervals for measuring data.

4. Set a sufficient long duration of data collection to ensure capture of impor-
tant time constants.

2.2.2 m odel s election

In system identification, we begin by determining the model structure best expressed
by a mathematical relationship between input and output variables. This model
structure typically provides the flexibility to describe a system based on certain
parameters. Some examples of model structures include parameterised functions
and state space equations. To illustrate, a linear parametric model is provided in the
equation below.

() = ( ) + ()

yk ay k − 1 buk (2.1)

where u is the input, y , the output, k , the discrete time step and a and b are model
structure variables.
Essentially, system identification is a systematic approach that begins with the
selection of a model structure and then using approximation techniques to estimate
the numerical values of the model parameters. While it may seem arbitrary to start
with the selection of a model structure, it is not an entirely ad hoc process. The fol-
lowing approaches may be adopted in deciding on an appropriate model structure.

1. Start with the simplest system model structures to avoid unnecessary com-
plexity in cases where the data can be modelled by a simple structure.
Alternatively, a user can try various mathematical structures in a technique
known as black-box modelling.

2. Designate a specific model structure for the data to be modelled by establish-
ing certain predetermined principles; this technique is known as grey-box
modelling.

Some well known system model structures from established research include the:

Auto-regressive exogenous (ARX) model
Auto-regressive moving average (ARMA) model
Box-Jenkins model
Output error model
State space model