User`s guide

Using Frequency-Response Plots to Validate Models
is scaled by the sampling interval T to make the frequency function periodic
with the sampling frequency
2π
T
.
How Frequency Response Helps to Validate Models
You can plot the frequency response of a model to gain insight into the
characteristics of linear m odel dynamics, including the frequency of the peak
response and stability margins. Frequency-response plots a re available for all
linear parametric models and spectral analysis (nonparametric) models.
Note Frequency-response plots are not available for nonlinear models. In
addition, Nyquist plots do not support time-series models that have no input.
The frequency respo n se of a linear dynamic model describes how the model
reacts to sinusoidal inputs. If the input u(t) is a sinusoid of a certain frequency,
then the output y(t) is also a sinusoid of the same frequency. However, the
magnitude of the response is different from the magnitude of the input signal,
and the phase of the response is shifted relative to the input signal.
Frequen c y resp on s e plots provide insight into linea r systems dynamics, such
as frequency-dependent gains, resonances, and phase shifts. Frequency
response plots a lso contain information about controller requirements and
achievable bandwidths. Finally, frequency response plots can also help you
validate how well a linear param etric mo del, su ch as a l in ear ARX mod el or a
state-space model, captures the dy namics.
One ex ample of how frequency-response plots help validate other models
is that you can estimate a frequency response from the data using spectral
analysis (nonparametric model), and then plot the spectral analysis result
on top of the frequency response of the parametric models. Because
nonparametric and parametric models are deriv ed using differe nt algorithms,
agreement between these models incre as es con fidence in the parametric
model results.
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