Hardware Reference
In-Depth Information
Figure 3.26: Control schemes for disturbance rejection using peak filter.
channel in such a way that the extended system is exponentially stabilizable
via output feedback. A peak
fi
lter consisting of a pair of lightly damped poles
canbeusedtomodelthenarrowbanddisturbance, for example the RRO or
narrow band NRRO, present in HDD servomechanism [48],[183],[229]. The
peak filter transfer function is the inverse of a notch filter transfer function.
There are two possible ways to implement a controller that rejects narrow-
band disturbances. In the first method, an internal model of the disturbance
is embedded into the open loop to form an augmented model and the distur-
bance is eliminated via feedback control of the augmented model. The second
approach, on the other hand, detects the disturbance and cancels it via active
feedforward control [63]. The method involving internal disturbance model is
discussed here. In the frequency domain, the compensator that includes an
internal model of the narrow band disturbance exhibits a large peak at the
disturbance frequency. That is why such compensator is commonly known as
peak
fi
lter . Figure 3.26 shows the block diagram of the closed loop system
using peak filter.
Consider the HDD servo control loop shown in Figure 3.26. The transfer
functions of the plant and the nominal, appropriate and stabilizing controller
are G
p
(s)andG
c
(s), respectively. A peak filter C
p
(s) with center frequency
coinciding with the frequency ω
i
of a narrow band disturbance represents the
internal model of the disturbance. The input disturbance i
d
may have periodic
components. The reference signal, plant output, and the tracking error are
represented in this figure by r, y and pes, respectively.
With the peak filter C
p
(s) included in the loop configuration shown in
Figure 3.26, the open-loop transfer function L(s) and the error rejection (or
sensitivity) transfer function S(s)are
L(s)=(1+C
p
)G
c
G
p
,
1
1+G
p
G
c
(1 + C
p
)
,
S(s)=
1
1+G
p
G
c
1+G
p
G
c
1+(1+G
p
G
c
)C
p
,
=
= S
0
S
F
,
(3.25)
