Gain margin and associated crossover frequency (original) (raw)

Scilab 5.3.3

Please note that the recommended version of Scilab is 2026.0.1. This page might be outdated.
See the recommended documentation of this function

Scilab help >> CACSD > g_margin

g_margin

gain margin and associated crossover frequency

Calling Sequence

gm=g_margin(h) [gm,fr]=g_margin(h)

Arguments

h

a SISO linear system (see :syslin).

gm

a number, the gain margin (in dB) if any ofInf

fr

a number, the associated frequency in hertz, or an empty matrix if the gain margin does not exist.

Description

Given a SISO linear system in continuous or discrete time,g_margin returns gm, the gain margin in dB of h andfr, the achieved corresponding frequency in hz.

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 is20*log10(1/g) where g is the open loop gain of h when the frequency response phase of h equals -180°

The algorithm uses polynomial root finder to solve the equations:

h(s)=h(-s)

for the continuous time case.

h(z)=h(1/z)

for the discrete time case.

Examples

h=syslin('c',-1+%s,3+2*%s+%s^2) [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); [g ,fr]=g_margin(h); show_margins(h)

See Also

Authors

Serge Steer, INRIA