[Gs,Gf]
= freqsep(G,fcut) decomposes
a linear dynamic system into slow and fast components around the specified
cutoff frequency. The decomposition is such that G = Gs + Gf.

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.

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 cotains 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, increase the absolute or relative tolerances ("AbsTol" and
"RelTol" options). Type "help freqsepOptions" for more information.

These poles are too close together for freqsep to separate. Increase the relative tolerance to allow the separation.

Cutoff frequency for fast-slow decomposition, specified as a
positive scalar. The output Gs contains all poles
with natural frequency less than fcut. The output Gf contains
all poles with natural frequency greater than or equal to fcut.

Options for the decomposition, specified as an options set you
create with freqsepOptions. Available options include
absolute and relative tolerance for accuracy of the decomposed systems.

Slow dynamics of the decomposed system, returned as a numeric
LTI model of the same type as G. Gs contains
all poles of G with natural frequency less than fcut,
and is such that G = Gs + Gf.

Fast dynamics of the decomposed system, returned as a numeric
LTI model of the same type as G. Gf contains
all poles of G with natural frequency greater
than or equal to fcut, and is such that G = Gs + Gf.