Hardware Reference

In-Depth Information

where > 0. The constructed perturbed system

⎨

˜
Ew,

⎩
x = Ax+ Bu+

Σ :

D
1
w,

y = C
1
x

+

(3.51)

C
2
x +

D
2
u,

z =

is hence regular.

For the hard disk drive servo control design, we can formulate the following

H
2
-optimal problem [128],

⎨

⎩

x =( x

a
x

i
x

o
x

n
)

,

w =( w

i

w

o

w

n
)

,

⎛

⎝
A
a
000

⎞

0 A
i
00

00A
o
0

000A
n

⎠

A =

,

B =( B

a
000)

,

⎛

⎝

⎞

⎠

B
a
00

B
i
00

0 B
o
0

00B
n

(3.52)

E =

,

C
1
= C
a
C
i
C
o
C
n
) ,

D
1
=( D
i
D
o
D
n
) ,

C
2
=( C
a
C
i
C
o
0 ) ,

D
2
=

0.

Here the vector x =(x

n
)
represents the state variables from the

actuator G
p
(s), input disturbance filter G
I
(s), output disturbance filter G
O
(s)

and measurement filter G
N
(s) in Figure 3.34. The disturbance vector w =

(w

a
,x

i
,x

o
,x

n
)
includes the white noise sources that drive the process disturbance

filters and the measurement noise filter. Σ
a
(A
a
,B
a
,C
a
,D
a
), Σ
i
(A
i
,B
i
,C
i
,D
i
),

Σ
o
(A
o
,B
o
,C
o
,D
o
)andΣ
n
(A
n
,B
n
,C
n
,D
n
) denote the disk drive actuator, the

input disturbance filter, the output disturbance filter and the measurement

noise filter, respectively, and all these transfer functions are assumed strictly

proper.

Substituting the model parameters for HDD actuator, disturbance and

sensing noise parameters into equation 3.52 which in turn is substituted into

the Riccati equations 3.45 and 3.46, we can obtain an output feedback H
2

optimal control equation 3.42 which achieves the theoretically highest tracking

accuracy.

i
,w

o
,w