Chapter 5 Classical Feedback Analysis
Xmath Control Design Module 5-12 ni.com
Each of these contributes a phase angle φ defined by:
with ω and pn expressed in the same units, either radians per second or Hz,
and using a four-quadrant arctangent function similar to that provided by
atan2( ) in Xmath. Thus the amount of phase contributed by a first order
pole at the frequency
(generally termed the corner frequency, because the asymptotes used to
draw different portions of the response intersect and form a corner) is –45°.
At frequencies beyond the corner frequency, the phase angle contributed by
that pole comes closer and closer to –90°. First-order zeros contribute phase
angle in the same manner except that the sign of the angle is positive.
margin( )[gnMargin,phMargin,dPdF,dGdF] = margin(H)
The margin( ) function is a useful tool for evaluating the stability margin
of a given system based on its frequency response. It returns PDMs
indicating the gain margin and the phase margin, as well as the rate of
change of gain and phase.
margin( ) is defined for SISO systems only. It takes as input either a
single PDM representing frequency response or a pair of PDMs containing
gain information in decibels and phase information in degrees. In either
case, the domain of the input is the set of frequency points, ω.
Within margin( ), as within bode( ), the frequency response is
converted to decibel magnitude and degree phase. All angles are converted
to four-quadrant angles between 0° and 360°. Use the following notation
for each point i in the frequency range:
φωpn
⁄()atan=
ωpn
=
Δxxi1+()xi()–=