gain margin and associated crossover frequency
[gm, fr] = g_margin(h)
a SISO linear system (see :syslin).
a number, the gain margin (in dB) if any of
a number, the associated frequency in hertz, or an empty matrix if the gain margin does not exist.
Given a SISO linear system in continuous or discrete time,
gain margin in dB of
fr, the achieved corresponding frequency in
The gain margin, if it exists, is the minimal value of the
system gain at points where the nyquist plot crosses the negative
real axis. In other words the gain margin is
g is the
open loop gain of
h when the frequency response
h equals -180°
The algorithm uses polynomial root finder to solve the equations:
for the continuous time case.
for the discrete time case.
h=syslin('c',-1+%s,3+2*%s+%s^2) //continuous time case [g,fr]=g_margin(h) [g,fr]=g_margin(h-10) nyquist(h-10)
h = syslin(0.1,0.04798*%z+0.0464,%z^2-1.81*%z+0.9048);//discrete time case [g ,fr]=g_margin(h); show_margins(h)
- p_margin — phase 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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