Delta Tau GEO BRICK LV User Manual
Turbo PMAC User Manual
Motor Compensation Tables and Constants
155
Filter Structure
For those familiar with control theory (not necessary to use the filter!), the form of Turbo PMAC’s notch
filter system is:
filter system is:
2
z
39
Ixx
1
z
38
Ixx
1
2
z
37
Ixx
1
z
36
Ixx
1
2
z
2
D
1
z
1
D
1
2
z
2
N
1
z
1
N
1
)
z
(
D
)
z
(
N
−
+
−
+
−
+
−
+
=
−
+
−
+
−
+
−
+
=
The I-variables Ixx36, Ixx37, Ixx38, and Ixx39 each have a range of -2.0 to +2.0; they are 24-bit values,
with one sign bit, one integer bit, and 22 fractional bits.
with one sign bit, one integer bit, and 22 fractional bits.
Use to Create a Notch
In feedback controls, a notch filter is an anti-resonance filter used to counteract a physical resonance.
While there are many different philosophies as to how to set up a notch filter, we recommend setting up a
lightly damped band-reject filter at about 90 percent of the resonant frequency, and a heavily damped
band-pass filter at a frequency somewhat greater than the resonant frequency (to reduce the high-
frequency gain of the filter itself). The band-reject filter is implemented in the numerator of the filter
[N(z)], creating zeros in control terms; the band-pass filter is implemented in the denominator of the filter
[D(z)], creating “poles” in control terms.
While there are many different philosophies as to how to set up a notch filter, we recommend setting up a
lightly damped band-reject filter at about 90 percent of the resonant frequency, and a heavily damped
band-pass filter at a frequency somewhat greater than the resonant frequency (to reduce the high-
frequency gain of the filter itself). The band-reject filter is implemented in the numerator of the filter
[N(z)], creating zeros in control terms; the band-pass filter is implemented in the denominator of the filter
[D(z)], creating “poles” in control terms.
Automatic Notch Specification
The Turbo PMAC Executive program allows you to set up a notch filter very simply, without the need to
understand how a notch filter works. The easiest way is to enter the frequency of the mechanical
resonance that you wish to control. 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 you to set up a notch filter very simply, without the need to
understand how a notch filter works. The easiest way is to enter the frequency of the mechanical
resonance that you wish to control. 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.
Alternatively, you can individually specify the desired characteristics of the band-reject and band-pass
filters. The two characteristics for each part of the filter are the natural frequency
filters. The two characteristics for each part of the filter are the natural frequency
ω
n
and the damping
ratio
ζ
. The Executive program will compute the coefficients to achieve those characteristics, and
download them to Turbo PMAC.
Manual Notch Specification
To calculate the notch filter coefficients manually, consider the continuous transfer function for a notch
filter:
To calculate the notch filter coefficients manually, consider the continuous transfer function for a notch
filter:
( )
2
np
np
p
2
2
s
2
nz
nz
z
2
2
s
s
G
ω
ω
ζ
ω
ω
ζ
+
+
+
+
=
Start with five parameters for the filter:
•
ω
nz
: the natural frequency of the zeroes in radians/second (not in Hertz)
•
ζ
z
: the damping ratio of the zeroes
•
ω
np
: the natural frequency of the poles in radians/second (not in Hertz)
•
ζ
p
: the damping ratio of the poles
•
T
s
: the servo-loop sampling period in seconds (not in msec)
To compute radians/second from Hertz, multiply by 2
π (6.283). To compute the sampling period in
seconds from the sampling rate in kHz, first multiply the rate by 1000 to get Hz, and then take the
reciprocal. Remember that the sampling period is equal to (Ixx60+1) times the servo-interrupt period.
First, compute the following intermediate values:
reciprocal. Remember that the sampling period is equal to (Ixx60+1) times the servo-interrupt period.
First, compute the following intermediate values:
2
s
T
2
nz
s
T
nz
z
2
1
z
ω
ω
ζ
α
+
+
=
2
s
T
2
np
s
T
np
p
2
1
p
ω
ω
ζ
α
+
+
=