Hardware Reference
In-Depth Information
O has positive real part in low excitation frequency range, the system is stable
for sufficiently small adaptive gain g
i
. At excitation frequency where O has a
negative real part, the adaptation gain can be a negative small value. Note
that very often O is the closed-loop servo system with the baseline servo control
while C
r
or AFC is the compensator added for canceling the RROs.
The discrete-time representation of the adaptive control and transfer func-
tion equivalent are as follows,
a
i
[k]=a
i
[k −1] + g
i
y[k]cos(ω
i
T
k
),
(3.97)
b
i
[k]=b
i
[k −1] + g
i
y[k]sin(ω
i
T
k
),
(3.98)
½
¾
z
2
−cos(ω
i
T
k
)z
z
2
−2cos(ω
i
T
k
)z +1
C
r
(z)=g
i
,
(3.99)
where T
k
is the sampling period.
Figure 3.48: Simplified block diagram for analyzing the RRO compensation
effectiveness. O
−1
istheapproximateinverseoftheplantO for improving the
effectiveness of the RRO compensation.
Now, to enhance the effectiveness of RRO compensation for the known
closed-loop servo system O(s), consider an alternative equivalent RRO distur-
bance D
O
−1
is the approximate inverse of
O for reasons to be discussed below. The transfer function from D
(s) as shown in Figure 3.48 where
(s)toY (s)
can be written by:
1
1+C
r
(s) O
−1
(s)O(s)
.
R(s)=
(3.100)
When R(jωT ) = 1, the loop gain at runout frequency ω equals to 1 meaning
there is no runout compensation. When R(jωT ) < 1or> 1, the closed-loop
will attenuate or amplify the corresponding frequencies respectively.
