Hardware Reference

In-Depth Information

bance power is concentrated so that the sensitivity transfer function S(s)has

notch at those frequencies. If the loop gain is increased in the band of frequen-

cies where the disturbance spectrum is concentrated, the vibration is more ef-

fectively rejected though the servo loop bandwidth is not increased. Inclusion

of peak filter is an example of this approach. The sensitivity and complemen-

tary sensitivity functions shown in Figure 3.32 underscores the effectiveness of

addingapeakfilter with center frequency at 360 Hz. The peak filter improves

vibration suppression at its central frequency, but amplifies vibration at other

frequencies. This limitation can be understood better with the help of waterbed

effect discussed later.

Bode plot measures a system's steady state responses when the input is

pure sinusoids of different frequencies. When we analyze the performance of

theclosedloopsystemusingtheBodeplots,itshouldbekeptinmindthatit

takes suﬃciently long time for the closed-loop to attenuate the pure sinusoid

disturbances. If the peak filter is designed for narrow band NRROs (and thus

not pure sinusoid of suﬃciently long duration), the vibration reduction may

notbeasgoodaswhatisexpectedfromtheanalysisoftheBodeplot.

As the recording density continues to increase, each bit consists of less num-

ber of magnetic grains. This causes a possible decrease in the SNR (Signal-

to-Noise Ratio) of the read back signal. The position feedback in HDD servo-

mechanism is generated from the read back waveform produced by the servo

patterns on the disks. Low SNR of the readback waveform thus has a detri-

mental effect on the performance of the HDD servomechanism. The spectrum

of the noise in PES generation lies in the higher range of frequencies. Increased

bandwidth of the servo loop means higher magnitude of measurement noise in

the PES. Therefore, the PES noise puts a limit on the achievable bandwidth.

Study of low noise PES generation is important so that the servo system can

effectively utilize the high bandwidth servo to achieve high tracking accuracy.

3.3.2 Waterbed Effect

The continuous time Bode's Integral Theorem is given as follows:

Let L(s) be a stable open-loop transfer function of a continuous-time,

single-input-single-output (SISO), linear time-invariant (LTI). Then the sensi-

tivity function is S(s)=1/(1 + L(s)). When the closed-loop system is stable

and k
s
= lim

s→∞
sL(s), then

1

π

Z

∞

ln |S(jω)|dω = −
1

2
k
s
.

(3.37)

0

When the relative degree of L(s)isnolessthan2,k
s
=0,then

1

π

Z

∞

ln |S(jω)|dω=0.

(3.38)

0