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(Not recommended) Options for slow-fast decomposition

freqsepOptions is not recommended. Specify the SepTol option directly as a name-value argument to freqsep (since R2023b). For more information on updating your code, see Version History.


opt = freqsepOptions returns the default options for freqsep.


opt = freqsepOptions(SepTol,st) sets the SepTol option equal to st.


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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.

options = freqsepOptions('SepTol',5e10);
[Gs,Gf] = freqsep(G,2,options);

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

Input Arguments

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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

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Options for freqsep, returned as a freqsepOptions options set. Use opt as the last argument to freqsep when computing slow-fast decomposition.

Version History

Introduced in R2014a

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R2023b: Not recommended

freqsepOptions is not recommended. Specify the SepTol option directly as a name-value argument to freqsep. This table describes the change in the workflow.

Before R2023bR2023b
opt = freqsepOptions("SepTol",5e10);
[Gs,Gf] = freqsep(G,2,opt);
[Gs,Gf] = freqsep(G,2,SepTol=5e10);

See Also