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Appendix H-4
page 4 of 4
To mitigate encoder velocity quantization noise, the derivative function is followed by an “n-point
averager”, which averages velocity information over a range of samples to provide finer resolution.
However, this low pass filter also introduces phase lag proportional to n that counteracts the desired
phase lead generated by the differentiator. To balance these two constraints, n is set equal to two, which
effectively doubles encoder resolution per sample interval. The derivative stage transfer function is:
VELOCITY =
(
z-1
Tz
)( 21 + 2z1 )
The following diagram illustrates the PID controller as well as the transfer functions of parasitic effects
found in the system.
PID System Block
DSP
Accumulator
+
+ +
P
Calculation
Delay
PWM Limit
OUT
EXP(STc )
IN
Sample and
Hold
z-1
I
S
Tz
K1
Commanded
Position
+
-
Integrator
Limit
OUT
Position
Error
IN
-D
Motor
I
4 Point
Averager
Volts
PWM
G (S)
Radians
Volt
2 Point
Averager
Integrator
Output
Position
Tz
z-1
Differentiator
On/Off
Profiler
Threshold
Switch
Encoder Position
z-1
Tz
K2
Counts
Radian
The default parameters for the digital filter have been calculated to provide stable operation in most
applications. It should not be necessary to adjust the derivative term. In many cases, especially when
using small, high speed motors, the proportional and integral terms are set to relatively low values and
should be increased to provide the desired system response.
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