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