freqsep
Slow-fast decomposition
Syntax
Description
[
computes the decomposition where G1
,G2
]
= freqsep(G
,[fmin,fmax]
)G1
contains all modes with
natural frequency fmin ≤
ωn ≤
fmax and G2
contains the remaining modes. (since R2023b)
Examples
Decompose Model into Fast and Slow Dynamics
Load a dynamic system model.
load numdemo Pd bode(Pd)
Pd
has four complex poles and one real pole. The Bode plot shows a resonance around 210 rad/s and a higher-frequency resonance below 10,000 rad/s.
Decompose this model around 1000 rad/s to separate these two resonances.
[Gs,Gf] = freqsep(Pd,10^3); bode(Pd,Gs,Gf) legend('original','slow','fast','Location','Southwest')
ans = Legend (original, slow, fast) with properties: String: {'original' 'slow' 'fast'} Location: 'southwest' Orientation: 'vertical' FontSize: 8.1000 Position: [0.1673 0.6060 0.1807 0.1278] Units: 'normalized' Use GET to show all properties
The Bode plot shows that the slow component, Gs
, contains only the lower-frequency resonance. This component also matches the DC gain of the original model. The fast component, Gf
, contains the higher-frequency resonances and matches the response of the original model at high frequencies. The sum of the two components Gs+Gf
yields the original model.
Separate Nearby Modes by Adjusting Tolerance
Decompose a model into slow and fast components between poles that are closely spaced.
The following system includes a real pole and a complex pair of poles that are all close to s = -2.
G = zpk(-.5,[-1.9999 -2+1e-4i -2-1e-4i],10);
Try to decompose the model about 2 rad/s, so that the slow component contains the real pole and the fast component contains the complex pair.
[Gs,Gf] = freqsep(G,2);
Warning: One or more fast modes could not be separated from the slow modes. To force separation, relax the accuracy constraint by increasing the "SepTol" factor (see "freqsepOptions" for details).
These poles are too close together for freqsep
to separate. Increase the relative tolerance to allow the separation.
[Gs,Gf] = freqsep(G,2,SepTol=5e10);
Now freqsep
successfully separates the dynamics.
slowpole = pole(Gs)
slowpole = -1.9999
fastpole = pole(Gf)
fastpole = 2×1 complex
-2.0000 + 0.0001i
-2.0000 - 0.0001i
Decompose State-Space Model to Obtain Modes in Frequency Range
This example shows how to decompose a model and retain the modes in a specified frequency range using freqsep
.
Load the model Gms
and examine its frequency response.
load modeselect Gms bodeplot(Gms)
Use freqsep
to retain the dynamics in the frequency range 0.1 rad/s to 50 rad/s.
[G1,G2] = freqsep(Gms,[0.1,50]);
In this decomposition, the output G1
contains all poles with natural frequency in the range [0.1,50]
and G2
contains the remaining poles.
bodeplot(Gms,G1,G2) legend
ans = Legend (Gms, G1, G2) with properties: String: {'Gms' 'G1' 'G2'} Location: 'northeast' Orientation: 'vertical' FontSize: 8.1000 Position: [0.8059 0.8188 0.1486 0.1278] Units: 'normalized' Use GET to show all properties
Input Arguments
G
— Dynamic system to decompose
numeric LTI model
Dynamic system to decompose, specified as a numeric LTI model,
such as a ss
or tf
model.
st
— Accuracy loss factor
10 (default) | nonnegative scalar
Since R2023b
Accuracy loss factor for slow-fast decomposition, specified as a
nonnegative scalar value. freqresp
ensures that the
frequency responses of the original system, G
, and the
sum of the decomposed systems G1+G2
, differ by no more
than SepTol
times the absolute accuracy of the computed
value of G(s)
. Increasing SepTol
helps
separate modes straddling the slow/fast boundary at the expense of
accuracy.
Output Arguments
info
— Additional information
structure | []
Since R2023b
Additional information about the decomposition, returned as structure with these fields.
Field | Description |
---|---|
TL | Left-side matrix of the block-diagonalizing transformation, returned as a matrix with dimensions Nx-by-Nx, where Nx is the number of states in the model G. |
TR | Right-side matrix of the block-diagonalizing transformation, returned as a matrix with dimensions Nx-by-Nx, where Nx is the number of states in the model G. |
The algorithm transforms the state-space realization
(A, B, C,
D) of the model G
to
The function returns an empty value []
for this
argument when the input model G
is not a state-space
model.
Version History
Introduced in R2014aR2023b: New syntax
Use the new syntax [G1,G2] = freqsep(G,[fmin,fmax])
to obtain a
decomposition where G1
contains all poles with natural
frequency in the range [fmin,fmax]
and G2
contains the remaining poles.
R2023b: Use simplified syntax
Starting in R2023b, you can specify the SepTol
option
directly as a name-value argument. For example:
[G1,G2] = freqsep(G,2,SepTol=1e9);
As a result of this change, freqsepOptions
and the syntax
[Gs,Gf] = freqsep(G,fcut,options)
are not recommended.
MATLAB 명령
다음 MATLAB 명령에 해당하는 링크를 클릭했습니다.
명령을 실행하려면 MATLAB 명령 창에 입력하십시오. 웹 브라우저는 MATLAB 명령을 지원하지 않습니다.
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