Hardware Reference
In-Depth Information
Figure 5.3: Noise and disturbances in a track propagation process.
noise. The position of the write head with respect to a perfectly circular track
on the disk is y(k) and the position error is pes(k).
Let us denote the period of one revolution of spindle by T
p
and the sampling
interval by T
s
.LetK = T
p
/T
s
,theny(k −K) represents the track pro
fi
le of
the previous track. Similarly, pes(k −K) represents the position error when
writing with reference to the previous track. The read head follows on the track
y(k −K) which is the reference input for the SSTW servo system, i.e., y(k)
from one revolution becomes the reference for the next written track. From
Figure 5.3, we see that
y(k)= [
CP
F
1+CP
]y(k −K)+
1
1+CP
d(k)+
P
1+CP
n(k)
1+CP
+
1+CP
v(k) −
F
CP
1+CP
d(k −K) −
PF
+
1+CP
n(k −K).
(5.2)
The control objectives can be de
fi
ned using the block diagram in Figure 5.4
as [45], which are,
a. to design a feedback controller C(z) to achieve a low TMR, i.e., to minimize
||Φ
yw
||
2
,theH
2
norm of the transfer function from noise vector w=[w
1
,
w
2
w
3
]' to track pro
fi
le y;
b. to design a feedforward compensator F(z) to contain the error propagation,
i.e., ||Φ
y(k)/y(k−K)
||
∞
< 1, the H
∞
norm of the transfer function from
y(k −K)toy(k) to be less than one;
While the H
2
optimal control is a standard one which has been discussed in
Section 3.4, a simple solution to make the magnitude of the transfer function
Φ
y(k)/y(k−K)
=
CP + F
1+CP
less than unity is
F(z)=Φ(1 + PC) −CP,