User`s guide

Using Pole-Zero Plots to Validate Models

Reducing Model O

rder Using Pole -Zero Plots

You can use p ole-

zeroplotstoevaluatewhetheritmightbeusefultoreduce

model order. Whe

nconﬁdence int erv als for a pole-zero pair overlap, th i s

overlap indicat

es a possible p ole-zero cancelation.

For example, yo

u can use the foll owing syntax to plo t a 1-standard-deviation

conﬁdence inte

rval around mode l p oles and zeros.

pzmap(model,'sd',1)

If poles and zero

s overlap, try estimating a lower order model.

Always validat

e model output and residuals to see if the quality of the

ﬁt changes afte

r reducing model order. If the p lot indicates pole-zero

cancellations

, but reducing model order degrades the ﬁt, then the extra

poles p robabl

y describe noise. In this case, you can choose a different model

structure tha

t decouples system dynamics and noise. For example, try

ARMAX, Output

-Error, or Box-Jenkins polynomial model structures with

an A or F polyn

omial of an order equal to tha t of the number of uncanceled

poles. For mo

re information about estimati ng linear polyn omial models, see

“Identifyin

g Input-Output Polynomial Models” on page 3-41.

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