確定根軌跡與虛軸交點，判斷系統穩定時增益k的取值範圍
**如下
num=[1 2 4];
den1=conv([1 0],[1 4]);den2=conv([1 6],[1 1.4 1]);
den=conv(den1,den2);
w=tf(num,den);
%求根軌跡與虛軸的交點資訊
a=allmargin(w)
%交點增益值
k=a.gainmargin
%交點頻率
wg=a.gmfrequency
rlocus(w)
axis([-8 2 -5 5]);
allmargin產生乙個結構。gainmargin表示增益，gmfrequency表示對應的頻率
a =
gainmargin: [15.6153 67.5209 163.5431]
gmfrequency: [1.2132 2.1510 3.7551]
phasemargin: 77.3823
pmfrequency: 0.1659
delaymargin: 8.1404
dmfrequency: 0.1659
stable: 1
k =15.6153 67.5209 163.5431
wg =
1.2132 2.1510 3.7551
matlab對函式allmargin的解釋
>>help allmargin
allmargin all stability margins and crossover
frequencies.
s = allmargin(sys) provides detailed information
about the gain, phase,
and delay margins and the corresponding c
ross over frequencies of the
siso open-loop model sys.
the output s is a structure with the following
fields:
* gmfrequency: all -180 deg crossover
frequencies in rad/timeunit
(relative to the time units specified in
sys.timeunit, the default
being seconds)
* gainmargin: corresponding gain margins (g.m.
= 1/g where g is the
gain at crossover)
* pmfrequency: all 0 db crossover frequencies (in rad/timeunit)
* phasemargin: corresponding phase margins (in
degrees)
* delaymargin, dmfrequency: delay margins (in
the units specified
in sys.timeunit for continuous-time systems,
and in multiples of
the sample time for discrete-time systems) and
corresponding
critical frequencies
* stable: 1 if nominal closed loop is stable, 0 if
unstable, and nan
if stability cannot be assessed (as in the case of
most frd
systems)
s = allmargin(mag,phase,w,ts) computes the
stability margins from the
frequency response data w, mag, phase and the
sampling time ts. allmargin
expects the magnitude values mag in linear scale
and the phase values phase
in degrees. interpolation is used between
the true stability margins.
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