sigma
Singular value plot of dynamic system
Syntax
Description
sigma(
plots the singular values of the
frequency response of a dynamic system model
sys
)sys
. sigma
automatically determines frequencies
to plot based on system dynamics.
If sys
is a single-input, single-output (SISO) model, then the
singular value plot is similar to its Bode magnitude response.
If sys
is a multi-input, multi-output (MIMO) model with
Nu
inputs and Ny
outputs, then the singular value
plot shows min(Nu,Ny)
lines on the plot corresponding to each singular
value of the frequency response matrix. For MIMO systems, the singular value plot extends
the Bode magnitude response and is useful in robustness analysis.
If sys
is a model with complex coefficients, then in:
Log frequency scale, the plot shows two branches, one for positive frequencies and one for negative frequencies. The plot also shows arrows to indicate the direction of increasing frequency values for each branch. See Singular Value Plot of Model with Complex Coefficients.
Linear frequency scale, the plot shows a single branch with a symmetric frequency range centered at a frequency value of zero.
sigma(___,
plots singular
values of the system response for frequencies specified by w
)w
.
If
w
is a cell array of the form{wmin,wmax}
, thensigma
plots the response at frequencies ranging betweenwmin
andwmax
.If
w
is a vector of frequencies, thensigma
plots the response at each specified frequency. The vectorw
can contain both negative and positive frequencies.
You can use w
with any of the input-argument combinations in
previous syntaxes.
sigma(___,
plots the
modified singular value responses based on the type
)type
argument. Specify
type
as:
1
to plot the singular values of the frequency response H-1, where H is the frequency response ofsys
.2
to plot the singular values of the frequency response I+H.3
to plot the singular values of the frequency response I+H-1.
You can only use the type
argument for square
systems, that is, systems that have the same number of inputs and
outputs.
[
returns the singular values of the response at each frequency in the vector
sv
,wout
]
= sigma(sys
)wout
. The output sv
is a matrix, and the value
sv(:,k)
gives the singular values in descending order at the
frequency wout(k)
. The function automatically determines frequencies in
wout
based on system dynamics. This syntax does not draw a
plot.
Examples
Input Arguments
Output Arguments
Tips
When you need additional plot customization options, use
sigmaplot
instead.
Algorithms
sigma
uses the MATLAB® function svd
to compute the singular values of the complex
frequency response.
For an
frd
model,sigma
computes the singular values ofsys.ResponseData
at the frequencies,sys.Frequency
.For continuous-time
tf
,ss
, orzpk
models with transfer function H(s),sigma
computes the singular values of H(jω) as a function of the frequency ω.For discrete-time
tf
,ss
, orzpk
models with transfer function H(z) and sample time Ts,sigma
computes the singular values offor frequencies ω between 0 and the Nyquist frequency ωN = π/Ts.
Version History
Introduced before R2006a