Hardware Reference
In-Depth Information
important role in the design of the servo controller. The next section provides
an optimal control scheme which results in a system with the highest TPI
possible in presence of all the NRRO sources. The limits on the servo control
loop's performance described so far can be broken using advanced techniques
such as sensor assisted feedforward control of disk's vertical vibration [63].
3.4 Optimal Control
Optimal control is a well known design technique in the control community. In
this approach, the controller design problem is first formulated as the problem
of optimizing certain norm of a pre-selected function (objective function) that
includes design specifications and description of noise and disturbances. The
controller is then identified such that the chosen norm of the objective function
is minimized. In this section, the problem of designing HDD track-following
servoisformulatedasastandardH
2
-optimal control problem. The objec-
tive of finding the minimum TMR budget is treated as an equivalent problem
of minimizing the H
2
norm of the corresponding transfer function. TMR or
Track Mis-Registration is an important metric that determines the track den-
sity (Tracks per inch or TPI) and, therefore, the achievable areal density of
the HDD.
As discussed before, the TMR during track following is defined as 3σ
pest
where
t
n−1
X
1
n
σ
pest
=
y
pest
(i)
2
.
(3.39)
i=0
Here n in equation (3.39) is the number of samples of the true PES. For a
given system with all the disturbances and noise described earlier, one must
minimize the value of 3σ
pest
in order to achieve the highest track density [83].
We can as so c i ate σ
pest
with the problem of designing the track-following
controller by considering the H
2
norm and H
2
-optimal control. The H
2
norm
of a system can be interpreted as the RMS value of the output when the
system is driven by independent zero mean white noise with unit power spectral
densities. In a hard disk drive servo as shown in Figure 3.34, all the disturbance
sources can be viewed as colored noise generated by filtering independent white
noises.
Let the true PES be the output of the system and the transfer function
from the vector of three independent white noise sources w =[w
n
]
tothetruePESy
pest
be defined as T
zw
. Then the H
2
norm of the transfer
function T
zw
is defined as
i
,w
o
,w
t
n−1
X
1
n
y
pest
(i)
2
,
T
zw
2
=
(3.40)
i=0
