Hardware Reference
In-Depth Information
Figure 3.60: Feedforward compensation scheme for disk flutter.
the transfer function is simple to design and easy to implement. From Fig-
ure 3.60, the feedforward compensator F(s) whose output is added to the
normal feedback controller G
c
(s) can be obtained by letting:
S
h
(s)F(s)=S(z)
1
s
K,
(3.135)
where
1
1+G
P
(s)G
c
(s)
,
S(s)=
(3.136)
is the sensitivity transfer function and
G
p
(s)
1+G
p
(s)G
c
(s)
,
S
h
(s)=
(3.137)
is the shock transfer function. Substituting equations 3.136 and 3.137 into
equation 3.135, we immediately have
F(s)=
S(s)
S
h
(s)
1
s
K =
P
den
(s)
1
s
K,
(3.138)
P
num
(s)
provided F(s) is realizable.
For the system described above, G
(
s)=
P
num
(s)
P
den
(s)
has a relative degree of
2. Therefore, is a first order low pass filter added to the right hand side
of equation 3.138 makes F(s) realizable. A feedforward compensator can be
designed as
2π× 12000
s +2π× 12000
,
which contains a second low pass filter. The feedforward controller is dis-
cretized at 25.28 kHz which is two times as fast as the feedback controller
F(s)=
1.4596
×
10
−8
s
s +2π× 4000
