For ARx0 > 0 both roots are real and:
()()
()()
ωπ
x
x
ARx ARx
Q
ARx ARx
Arx ARx
=
=
+
201
01
01
For ARx0 < 0 roots are a complex pair and:
ωπ
x
x
ARx
Q ARx
=−
=
20
1
Note: When ARZ0 and ARZ1 are both zero, the numerator of
FvelErr
VelErr
s()
reduces to 1. If ARZ0 or ARZ1 is individually 0 the
numerator reduces to
s
ARZx2
1
π
+
Discrete time
transfer function
The velocity loop compensation is actually implemented as a
digital discrete time system function on the DSP. The continuous
time transfer function is converted to the discrete time domain by
a backward Euler mapping:
()
s
T
z
s
®
1
1
1
−
-
where T
s
= 250 µsec.
MA950 4-11
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