Hardware Reference
In-Depth Information
G
c
(z). This yields a F(z)=
(z
2
−1)×5.838×10
−
9
z
2
−0.1342z−0.06662
. Figure 3.61 shows the fre-
quency response of F(z) which is very much like a differentiator below 2 kHz.
In this case, F(s) can not totally cancel out the effects of the disk vertical mo-
tion because of the additional phase delay introduced by the low pass filters.
−150
−160
−170
−180
−190
−200
10
2
10
3
10
4
100
50
0
−50
−100
10
2
10
3
10
4
Frequency (Hz)
Figure 3.61: Frequency response of the feedforward controller.
Effect of the Feedforward Control
Figure 3.62 shows the PES spectrum after disk flutter is compensated using
F(z). We see in Figure 3.62 that the first mode is almost disappeared, while
the remaining 3 dominant modes are decreased in amplitude, though they are
still present. This is due to the phase lag of low-pass filter and phase lag of
digitization which can be seen in Figure 3.61.
We can conclude by comparing Figure 3.62 with Figure 3.57 which has the
same feedback controller G
c
(z) but without the feedforward control F(z), that
there is no obvious amplification of the modes above 1 kHz. The shape of the
baseline in PES spectrum has not change as well. This is due to the fact that
the feedforward compensation has no effect on the original feedback servo loop.
Furthermore, the amplitudes of the four dominant modes due to disk flutter
were significantly reduced. Table 3.5 summarizes the comparison results. As
can be seen from the table, the amplitudes of vibration modes decreased by
about 16% to 68%. The first four modes are attenuated by an average of 56%.
It is verified in this section that, at a number of disk resonance frequencies,
the disk flutter induced PES has a fixed phase and amplitude relationship
with the disk vertical vibration. Therefore, disk flutter induced TMR can
be compensated for by adding a feedforward control loop without modifying
the basic servo control loop. A simple, practical differentiator type feedforward
controller with the vertical direction vibration velocity measured using an LDV
