User`s guide

Using Impulse- and Step-Response Plots to Validate Models
correlation analy sis result on top of the transient responses of the parametric
models.
Because nonparametric and parametric models are de riv ed using different
algorithms, agreement between these models increases confidence in t h e
parametric model results.
What Does a Transient Response Plot Show?
Transient response plots show the val ue o f the im pulse or step response on
the v ertical axis. The horizontal axis is in units of time you specified for the
data used to estimate the m odel.
The impulse response of a dynamic model is the output signal that results
when the input is an impulse. That is, u(t) is zero for a ll val u es of t except at
t=0, w here u(0)=1. In the following difference equation, you can compute the
impulse response by setting y(-T) =y(-2T)=0, u(0)=1, and u(t>0)=0.
yt yt T yt T
ut ut T
() . ( ) . ( )
.() .( )
−−+−=
+−
15 07 2
09 05
Thestepresponseistheoutputsignalthat results from a step input, where
u(t<0)=0 and u(t>0)=1.
If your model includes a noise model, you can display the transient response
of the noise model associated with each output channel. For more information
about how to display the transient response of the noise model, see “How to
Plot Impulse and Step R esponse Using the GU I” on page 8-26.
The following figu re shows a sample Transient Response plot, created in
the System Identification Tool GUI.
8-25