Hardware Reference
In-Depth Information
different methods to implement this correction of RRO such as
1. calculating the signal required to be injected at each frequency of RRO
and storing the information in a lookup table which can be used for
feedforward compensation, or
2. using an Adaptive Feedforward Control (AFC) scheme [206].
These methods are explained in the following sub-sections. Another method,
that includes simultaneous multiple frequency RRO compensation using peri-
odic signal generator with a delay term, is explained later in this section.
Compensation of RRO using Inverse Signal
Since RRO is a repeatable signal, it can be decomposed as a sum of a series of
sine and cosine waves, which can be represented in the following formats:
X
L
A
i
sin(
2πi(n
−
1)
N
R
y
(n)=
+φ
i
),
i=1
X
L
−jφ
i
,
=
A
i
e
i=1
X
L
[a
i
sin(
2πi(n
−
1)
N
)+b
i
cos(
2πi(n
−
1)
N
=
)],
i=1
"
#
, ···, sin
2π
2
(n
−
1)
N
sin
2π(n
−
1)
N
=
, ···, cos
2π
2
(n
−
1)
N
cos
2π(n
−
1)
N
∙
¸
T
a
1
, ···,a
N/2
b
1
, ···,b
N/2
·
.
(3.85)
L =0.5 ∗F
s
/rpm/60 = N/2 is number of frequencies which is half of the
∙
¸
T
a
1
, ···,a
N/2
b
1
, ···,b
N/2
number of sectors, ∆t is the sampling period. Let θ
a
=
,
expanding the above equations we have
"
#
, ···, sin
2π
2
(1
−
1)
N
sin
2π(1
−
1)
N
R
y
(1) =
θ
a
,
, ···, cos
2π
2
(1
−
1)
N
cos
2π(1
−
1)
N
"
#
, ···, sin
2π
2
(2
−
1)
N
sin
2π(2
−
1)
N
R
y
(2) =
θ
a
,
, ···, cos
2π
2
(2
−
1)
N
cos
2π(2
−
1)
N
.
.
(3.86)
"
#
, ···, sin
2π
2
(N
−
1)
N
sin
2π(N
−
1)
N
R
y
(N)=
θ
a
.
, ···, cos
2π
2
(N
−
1)
N
cos
2π(N
−
1)
N
(3.87)
