D2 Series Servo Drive User Manual Operation Principles
HIWIN MIKROSYSTEM CORP. 3-9
3.6 Gain margin and phase margin
3.6.1 Nyquist diagram
Gain margin (GM) is defined as that the loop gain, calculated by dB, can be increased before the
close-loop system becomes unstable. On the other hand, phase margin (PM) is defined as that the phase
delay can be increased before the close-loop system becomes unstable.
Gain margin
Denote G(jω
p
) as the relative distance from the intersection of Nyquist diagram and the negative real
axis to the point (-1, j0), where ω
p
is the frequency at the phase crossover. The example of G(jω
p
)
= 180° is shown in figure 3.6.1.1. For the transfer function G(s) in a loop system, gain margin = GM =
dB.
Following results can be derived from figure 3.6.1.1 and characteristics of Nyquist diagram.
a If G(jω) does not intersect with the negative real axis, |G(jω
p
)| = 0 and GM = dB. When the
Nyquist diagram does not intersect with the negative real axis at any non-zero and finite
frequency, GM =
dB. Theoretically, the loop gain can be increased to be infinite before the
system becomes unstable.
b If G(jω) intersects with the negative real axis between 0 and -1, 0 < |G(jω
p
)| < 1 and GM > 0 dB.
When the Nyquist diagram intersects with the negative real axis between 0 and -1 at any
frequency, the system is stable as increasing loop gain.
c If G(jω) is at the point (-1, j0), |G(jω
p
)| = 1 and GM = 0 dB. When the Nyquist diagram G(jω) is at
the point (-1, j0), GM = 0 dB. This means that the system reaches the unstable boundary and the
loop gain cannot be increased any more.
d If G(jω) passes by the point (-1, j0), |G(jω
p
)| > 1 and GM < 0 dB. When the Nyquist diagram
G(jω) passes by the point (-1, j0), GM < 0 dB. At this time, GM must be reduced to achieve the
steady state of loop gain.
)(log
)(
log
p
p
j
G
jG
ω
ω
1010
20
1
20 −=
To Next Page
Loading...
Need help?
General
