User`s guide

Troubleshooting Models
Substantial Noi
se in the System
There are a coupl
e of indications that you m ight have substantial noise in
your system and m
ight need to use linear model structures that are better
equipped to mode
lnoise.
One indication
of noise is when a state-space model is better than an ARX
model at reprod
ucing the measured output; whereas the state-space structure
has sufficient fl
exibility to model noise, the ARX model structure is less able
to model noise b
ecause the A polynomial must account for both the system
dynamics and t
he noise. The following equation represents the ARX model
and shows that
A couples the dynamics and the noise by appearing in the
denominator
of both the dynamics term and the noise terms:
y
B
A
u
A
e=+
1
Another indi
cation that a noise model is needed appears in residual analysis
plots when y
ou see significant autocorrelation of residuals a t nonzero lags.
For more inf
ormation about residual analysis, see “Using Residual A nalysis
Plots to Val
idate Models” on page 8-16.
To model noi
se more carefully, use the ARMAX or the Box-Jenkins model
structure
, where the dynamics term and the noise term are m odeled by
different
polynomi als.
Unstable M
odels
One of the m
ost conclusive approaches to determining whether a linear model
is unstabl
e is by examining the pole-zero plo t of the model, w hich is described
in “Using
Pole-Zero Plots to Validate Models”onpage8-47. Thestability
threshol
d for pole values differs for discre te-time and continuous-time models,
as follow
s:
• For stabl
e continuous-time models, the real part of the pole is less than 0.
• For stabl
ediscrete-timemodels,themagnitudeofthepoleislessthan1.
In some c
ases, an unstable model is still a useful model. For example, your
system m
ight be unstable w ithout a controller, and you plan to use your
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