Справочник Пользователя для Delta Tau GEO BRICK LV
Turbo PMAC User Manual
Motor Compensation Tables and Constants
157
169
,
979
4049
.
1
0748
.
1
2
2
.
314
2
7
.
502
000
,
500
p
z
2
nz
2
np
old
30
Ixx
new
30
Ixx
=
=
=
α
α
ω
ω
Use to Create a Low-Pass Filter
It is also possible to use this filter component as a low-pass filter if reducing roughness of operation is
more important than high system bandwidth. Typically, the low-pass filter is used if a low-resolution
position sensor is used.
more important than high system bandwidth. Typically, the low-pass filter is used if a low-resolution
position sensor is used.
Automatic Specification
The Turbo PMAC Executive program allows the set up of a low-pass filter easily, without the need to
understand how it works. Enter the cutoff frequency of the filter (the frequency above which should not
pass much signal strength) and choose whether to create a first-order or second-order filter. The
Executive program will compute the desired characteristics of the band-reject and band-pass filters,
compute the coefficients, and download them to Turbo PMAC.
The Turbo PMAC Executive program allows the set up of a low-pass filter easily, without the need to
understand how it works. Enter the cutoff frequency of the filter (the frequency above which should not
pass much signal strength) and choose whether to create a first-order or second-order filter. The
Executive program will compute the desired characteristics of the band-reject and band-pass filters,
compute the coefficients, and download them to Turbo PMAC.
Manual Specification
To calculate a low-pass filter manually, specify the cutoff frequency in radians per second, and the servo-
update frequency in seconds.
To calculate a low-pass filter manually, specify the cutoff frequency in radians per second, and the servo-
update frequency in seconds.
First-Order Filter: To calculate a first-order low-pass filter, consider the continuous transfer function
for the filter:
for the filter:
( )
ω
ω
ω
+
=
+
=
s
1
/
s
1
s
F
where
ω
is the cutoff frequency in radians per second (equal to 2
π
f, where f is the cutoff frequency in
Hertz). This value
ω
is equal to 1/
τ
, where
τ
is the time constant of the filter.
Next, convert this to a discrete-time transfer function using the approximation s=(1-z
-1
)/T
s
, where T
s
is the
servo update time in seconds.
( )
1
z
s
T
1
1
1
1
*
s
T
1
s
T
s
T
1
z
1
s
T
s
T
1
z
1
z
F
−
+
−
+
=
+
−
−
=
+
−
−
=
ω
ω
ω
ω
ω
ω
ω
In Turbo PMAC terms, the gain term is multiplied into the existing gain term Ixx30:
s
T
1
s
T
*
old
30
Ixx
new
30
Ixx
ω
ω
+
=
The pole term uses the first-order notch filter pole parameter Ixx38. The other filter parameters Ixx36,
Ixx37 and Ixx39 are set to zero if the filter is used only as a low-pass filter.
Ixx37 and Ixx39 are set to zero if the filter is used only as a low-pass filter.
s
T
1
1
38
Ixx
ω
+
−
=
For example, to implement a first-order low-pass filter with a cutoff frequency of 50 Hz on a Turbo
PMAC with a servo update time of 442 µsec, we compute:
PMAC with a servo update time of 442 µsec, we compute:
139
.
0
000442
.
0
*
50
*
*
2
s
T
=
=
π
ω
old
30
Ixx
*
122
.
0
139
.
0
1
139
.
0
*
old
30
Ixx
new
30
Ixx
=
+
=
877
.
0
139
.
0
1
1
38
Ixx
−
=
+
−
=
0
39
Ixx
,
37
Ixx
,
36
Ixx
=