User's Manual

Turbo PMAC User Manual
158 Motor Compensation Tables and Constants
Second-Order Filter: To calculate a second-order low-pass filter, we consider the continuous transfer
function for a generalized second-order filter:
()
2
n
n
2
2
s
2
n
sF
ωζω
ω
++
=
where ω
n
is the cutoff frequency of the filter in radians per second, and ς is the damping ratio – a value of
0.707 produces a Butterworth filter here.
First, compute the following intermediate value:
2
s
T
2
n
s
T
n
21 ωζωα ++=
Then compute the filter coefficients:
(
)
α
ζω
2
s
T
n
2
38Ixx
+−
=
α
1
39Ixx =
Ixx36 and Ixx37 should be set to 0 if no other use is made of this filter.
Finally, modify your proportional-gain term to compensate for the DC-gain change that the filter creates:
α
ω
2
s
T
2
n
old
30Ixx
new
30Ixx =
For example, to implement a second-order low-pass filter with a cutoff frequency of 60 Hz and a damping
ratio of 0.707 on a Turbo PMAC with a servo update time of 250 µsec, we compute the following:
0942.0000250.0*60**2
s
T
n
== πω
146.10942.00942.0*707.0*21a
2
=
+
+=
(
)
861.1
146.1
20942.0*707.0*2
38Ixx −=
+−
=
873.0
146.1
1
39Ixx ==
old
30Ixx*00774.0
146.1
2
0942.0
old
30Ixx
new
30Ixx ==
037Ixx,36Ixx
=
Use to Create a Velocity-Loop Integrator
This filter can also be used to create an integrator inside the velocity loop, independent of the integral
gain term in the position loop. This additional integrator can provide additional stiffness and disturbance
rejection. However, it may hinder quick response to acceleration commands.
Manual Specification
Consider a PI filter in the velocity loop with transfer function:
()
1
iv
pv
z
1
K
KzV
−
−
+=
where K
pv
is the velocity-loop proportional gain, and K
iv
is the velocity-loop integral gain. This can be
manipulated to produce:
()
()
()
1
1
ivpv
pv
ivpv
1
1
pvivpv
1
iv
1
pv
z
1
z
KK
K
1
KK
z
1
zKKK
z
1
Kz1K
zV
−
−
−
−
−
−
−








+
−
+=
−
−+
=
−
+−
=
In Turbo PMAC terms, the gain term (K
pv
+K
iv
) is multiplied into the existing gain term Ixx30: