ufrd
Uncertain frequency response data model
Description
An uncertain frequency response data (ufrd
) model consists of a
set of fixed frequency-response data points and one or more dependent uncertain elements. You
can use ufrd
for robust stability and worst-case performance analysis.
Creation
There are several ways to construct a ufrd
model, including:
Combine a numeric
frd
model with uncertain state-space (uss
) models or uncertain elements such asureal
,ultidyn
, orumargin
using model arithmetic. For example:fsys = frd(rand(100,1),logspace(-2,2,100)); k = ureal('k',1); D = ultidyn('Delta',[1 1]); ufrd_sys = k*fsys*(1+0.1*D)
Uncertain continuous-time FRD model with 1 outputs, 1 inputs, 100 frequency points. Delta: Uncertain 1x1 LTI, peak gain = 1, 1 occurrences k: Uncertain real, nominal = 1, variability = [-1,1], 1 occurrences Model Properties
ufrd_sys
is aufrd
model with uncertain elementsk
andD
.Convert a
uss
model toufrd
by computing the response at a set of frequencies. For example:a = ureal('a',1,'range',[0.5 1.8]); usys = tf(a,[1 a]); freqs = logspace(-2,2,100); ufrd_sys = ufrd(usys,freqs)
Uncertain continuous-time FRD model with 1 outputs, 1 inputs, 100 frequency points. a: Uncertain real, nominal = 1, range = [0.5,1.8], 1 occurrences Model Properties Type "ufrd_sys.NominalValue" to see the nominal value and "usys.Uncertainty" to interact with the uncertain elements.
The resulting
ufrd
model has the same uncertain elements as the originaluss
model.To specify the frequency units of the frequencies in
freqs
, useufrd_sys = ufrd(M,freqs,frequnits)
The argument
frequnits
can take the same values as theFrequencyUnit
property.More generally, convert any dynamic system model or static model
M
toufrd
as follows:ufrd_sys = ufrd(M,freqs)
If
M
contains blocks that do not represent uncertainty (such as tunable parameters), those blocks are replaced by their current value. (To obtain a frequency-response model that preserves both tunable and uncertain blocks, usegenfrd
instead.)To specify the frequency units of the frequencies in
freqs
, useufrd_sys = ufrd(M,freqs,frequnits)
. To further specify the time units whenM
is a static model, useufrd_sys = ufrd(M,freqs,frequnits,timeunits)
. The argumentsfrequnits
andtimeunits
can take the same values as theFrequencyUnit
andTimeUnit
properties, respectively.Use
frd
to construct aufrd
model from an uncertain matrix (umat
) representing uncertain frequency response data. For example:a = ureal('delta',1,'percent',50); freq = logspace(-2,2,100); RespData = rand(1,1,100) * a; ufrd_sys = frd(RespData,freq,0.1)
Properties
Object Functions
Most functions that work on numeric frd
models also work on
ufrd
models. These include model interconnection functions such as
connect
and feedback
, and frequency-domain linear
analysis functions such as bode
. Some functions that generate plots, such
as bodeplot
, plot random samples of the uncertain model to give you a
sense of the distribution of uncertain dynamics. Analysis functions that return data, however,
typically operate on the nominal value of the system only. ufrd
models do not
work with any time-domain analysis functions.
In addition, you can use functions such as robstab
and
wcgain
to perform robustness and worst-case analysis of uncertain
systems represented by ufrd
models. You can also use tuning functions such as
systune
for robust controller tuning.
The following lists contain a representative subset of the functions you can use with
ufrd
models.
Examples
Version History
Introduced before R2006a