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phase margin and associated crossover frequency
[phm,fr] = p_margin(h) phm = p_margin(h)
a SISO linear system (see :syslin).
a number, the phase margin in degree if it exists or an empty matrix.
a number, the corresponding frequency (in Hz) or an empty matrix.
Given a SISO linear system in continuous or discrete time,
phase margin in degree of
fr, the achieved corresponding frequency in
The phase margin is the values of the phase at frequency
points where the nyquist plot of
h crosses the
unit circle. In other words the phase margin is the difference
between the phase of the frequency response of
h and -180° when the gain of
h is 1.
The algorithm uses polynomial root finder to solve the equations:
for the continuous time case.
for the discrete time case.
//continuous case h=syslin('c',-1+%s,3+2*%s+%s^2) [p,fr]=p_margin(h) [p,fr]=p_margin(h+0.7) show_margins(h+0.7,'nyquist') //discrete case h = syslin(0.1,0.04798*%z+0.0464,%z^2-1.81*%z+0.9048);//ok [p ,f]=p_margin(h) show_margins(h,'nyquist')
- g_margin — gain margin and associated crossover frequency
- show_margins — display gain and phase margin and associated crossover frequencies
- repfreq — frequency response
- black — Black-Nichols diagram of a linear dynamical system
- bode — Bode plot
- nicholschart — Nichols chart
- nyquist — nyquist plot
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