Specifications

Creating LTI Models
2-17
Frequency Response Data (FRD) Models
Insomeinstances, you may only have sampled frequency responsedata, rather
than a transfer function or state-space model for the system you want to
analyze or control. For information on frequency response analysis of linear
systems, see Chapter 8 of [1].
Forexample,suppose the frequencyresponse functionfortheSISOsystem you
want to model is G(w). Suppose, in addition, that you perform an experiment
to evaluateG(w)at a fixed set of frequencies, . You can do this by
drivingthesystem with a sequenceof sinusoids at each of these frequencies,as
depicted below.
Here is the input frequency of each sinusoid, i =1...n,andG(w) =
. The steady state output response of this system satisfies
A frequency response data (FRD) object is a model form you can use to store
frequency response data (complex frequency response, along with a
corresponding vector of frequency points) that you obtain either through
simulations or experimentally. In this example, the frequency response data is
obtained from the set of response pairs: .
Once you store your data in an FRD model, you can treat it as an LTI model,
andmanipulateanFRDmodelinmostofthesamewaysyoumanipulateTF,
SS, and ZPK models.
The basic syntax for creating a SISO FRD model is
sys = frd(response,frequencies,units)
where
•
frequencies is a real vector of length Nf.
w
1
w
2
…
w
n
,,,
w
i
tsin
G(w) =
y
i
t
()
w
i
Gw
()
jGw
()∠()
exp
y
i
t
()
Gw
i
()
w
i
tGw
i
()∠
+
()
i;sin 1
…
n==
Gw
i
()
w
i
(,){}
i
,
1
…
n=