User`s guide

Using Pole-Zero Plots to Validate Models

In this section...

“Supported Models” on page 8-47

“What Does a Po le -Zero Plot Show?” on page 8-47

“How to Plot Model Poles and Zeros Using the GU I” on page 8-48

“How to Plot Poles and Zeros at the Command Line” on page 8-50

“Reducing Model Order Using Pole-Zero Plots” o n page 8-51

Supported Models

You can create pole-zero plots of linear input-output polynomial, state-space,

and grey-box models.

What Does a P ole-Zero Plot Show?

The general equation of a linear dynamic system is given b y:

yt G zut vt() ( ) () ()=+

In this equation, G is an operator that takes the input to the output and

captures the system dynam ics, and v is the additive noise term.

The poles of a linear system are the roots of the denominator of the transfer

function G. T he poles have a direct inﬂuence on the dynamic properties of

the system. The zeros are the roots of the numerator of G. If you estimated

anoisemodelH in addition to the dynamic model G, you can also view the

poles and zeros of the noise model.

Zeros and the poles are equivalent w ays of describing the coefﬁcients of a

linear difference equation, such as the ARX model. Poles are associated with

the output side of the difference equation, and zeros are associated with the

input side of the equation. The number of poles is equal to the number of

sampling intervals between the most-delayed and least-d e la yed output. The

number of zeros) is equal to the number of sampling intervals between the

8-47