For ARx0 > 0 both roots are real and:
(
)(
)
(
)(
)
ω
π
x
x
ARx ARx
Q
ARx ARx
Arx
ARx
=
=
+
2
0
1
0
1
0
1
For ARx0 < 0 roots are a complex pair and:
ω
π
x
x
ARx
Q
ARx
= −
=
2
0
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
ARZx
2
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
µ
sec.
MA950
4 - 11