User's Manual

PMAC User Manual
110 Closing the Servo Loop
For example, suppose a 55 Hz resonance has been identified in the mechanical coupling. To compensate
for this, put a lightly damped band-reject filter (damping ratio 0.2) at 50 Hz natural frequency, and a
heavily damped band-pass filter (damping ratio 0.8) at 80 Hz natural frequency to limit the high-
frequency gain of the filter. The servo update time is the default of 442 microseconds.
sec000442.0
sec
sec
6
10sec*442
s
T =
−
=
µ
µ
secrad2.314Hz50*2
nz
== πω
secrad7.502Hz80*2
np
== πω
2
s
T
2
nz
s
T
nzz
21
z
ωωζα ++=
2
000442.0*
2
2.314000442.0*2.314*2.0*21 ++=
0748.1
=
2
s
T
2
nps
T
npp
21
p
ωωζα ++=
2
000442.0*
2
7.502000442.0*7.502*8.0*21 ++=
4049.1
=
Next compute the filter coefficients:
()
(
)
912.1
0748.1
2000442.0*2.314*2.0*2
z
2
s
T
nzz
2
36Ix −=
+−
=
+−
=
α
ωζ
930.0
0748.1
1
z
1
37Ix ===
α
(
)
(
)
677.1
4049.1
2000442.0*7.502*8.0*2
p
2
s
T
npp
2
38Ix −=
+−
=
+−
=
α
ωξ
712.0
4049.1
1
p
1
39Ix ===
α
Finally, compute the DC gain adjustment, assuming for the example that the existing proportional gain
term Ixx30 had been 500,000:
169,979
4049.1
0748.1
2
2.314
2
7.502
000,500
p
z
2
nz
2
np
old
30Ix
new
30Ix ===
α
α
ω
ω
DC Gain Correction
Finally, multiply the old proportional gain (Ix30) by the reciprocal of the notch DC gain. If Ix30 was
100,000 before implementing the notch, to keep the same stiffness set:
Ix30 = 227000 ; 100,000 * 2.27
Play with Ix30 some more now to modify loop stiffness without affecting the characteristics of the notch.
Indeed, one of the important reasons for introducing a notch is to be able to increase the stiffness of the
loop without going unstable.
Other Uses of the Notch Filter
The notch filter is really a generalized second-order digital filter that can be put to uses other than creating
a notch. This can give great flexibility in tailoring the performance of the servo algorithm.