Datasheet

TMC4671 Datasheet • IC Version V1.00 | Document Revision V1.03 • 2018-Sept-06
50 / 158
The transfer function needs to be transformed to time discrete domain by Z-Transformation and coeffi-
cients need to be normalized. This is done by the following equations.
b_2_z = (b_0_cont · T
2
+ 2 · b_1_cont · T + 4 · b_2_cont)/(T
2
− 2 · a_1_cont · T + 4 · a_2_cont) (26)
b_1_z = (2 · b_0_cont · T
2
− 8 · b_2_cont)/(T
2
− 2 · a_1_cont · T + 4 · a_2_cont) (27)
b_0_z = (b_0_cont · T
2
− 2 · b_1_cont · T + 4 · b_2_cont)/(T
2
− 2 · a_1_cont · T + 4 · a_2_cont) (28)
a_2_z = (T
2
+ 2 · a_1_cont · T + 4 · a_2_cont)/(T
2
− 2 · a_1_cont · T + 4 · a_2_cont) (29)
a_1_z = (2 · T
2
− 8 · a_2_cont)/(T
2
− 2 · a_1_cont · T + 4 · a_2_cont) (30)
b_0 = round(b_0_z · 2
29
) (31)
b_1 = round(b_1_z · 2
29
) (32)
b_2 = round(b_2_z · 2
29
) (33)
a_1 = round(−a_1_z · 2
29
) (34)
a_2 = round(−a_2_z · 2
29
) (35)
while T is the sampling time according to PWM_MAX_COUNT · 10 ns and variables with index z are auxiliary
variables.
There are four biquad filters in the control structure. Figure 28 illustrates their placement in the control
structure.
Figure 28: Biquad Filters
The biquad filter for the position target value is intended to be used as a low-pass filter for smoothening
position input to the control structure. It is evaluated in every PWM cycle, or down-sampled according to
the down-sampling factor for the velocity and position controllers. After powering on it is disabled.
The biquad filter for the flux target value is also intended to be used as a low-pass filter for input values
from the user’s microcontroller. Sampling frequency is fixed to the PWM frequency.
The biquad filter for the torque target value can be used as a low-pass filter for bandwidth limitation
and noise suppression. Moreover, it can be designed to suppress a resonance or anti-resonance. Same
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