User`s guide

3 Linear Model Identification
information about the time-shift operator, see “Understanding the Time-Shift
Operator q” on page 3-43.
The following table summarizes common linear polynomial model structures
supported by the System Identification Toolbox product. If you have a specific
structure in mind for your application, you can decide whether the dynamics
and the noise have common or different poles. A(q) corresponds to poles that
are common for the dynam ic model a nd the n ois e model. Using com mon poles
for dynamics and noise is useful when the disturbances enter the system at
the input. F
i
determines the poles unique to the system dynamics, and D
determines the poles unique to the disturbances.
Model
Structure
Discrete-Time Form
Noise Model
ARX
Aqyt B qu t nk et
ii i
i
nu
()() () ()=−
()
+
=
∑
1
The noise model is
1
A
and the
noise is coupled to the dynamics
model. ARX does not let you
model noise and dynamics
independently. Estimate an
ARX model to obtain a simple
model a t good signal-to-nois e
ratios.
ARMAX
Aqyt B qu t nk Cqet
ii i
i
nu
()() () ()()=−
()
+
=
∑
1
Extends the ARX structure by
providin g more flexibility for
modeli ng noise u sing the C
parameters (a m oving average of
white noise). Use ARM AX when
the domina t in g disturbances
enter at the input. Such
disturbances are called load
disturbances.
3-44