Hardware Reference
In-Depth Information
when n is sufficiently large. As a result, the problem of controller design
for accurate tracking, which is to minimize ||T
zw
||
2
, can be solved using H
2
optimal control design method when an accurate noise and vibration model is
available. The solution formulae for both continuous-time and discrete-time
control cases are given next.
Figure 3.34: H
2
output feedback problem for an HDD servo system considering
noise and disturbance model [128].
3.4.1 H
2
Optimal Control: Continuous-time Case
Consider a stabilizable and detectable linear time-invariant system Σ with a
proper output feedback controller Σ
c
, shown in Fig 3.34 [166], where,
⎨
⎩
x = Ax+ Bu+ Ew,
Σ :
y = C
1
x
+ D
1
w,
(3.41)
z = C
2
x + D
2
u,
with x ∈
n
being the state, u ∈
n
the control input, w ∈
l
the disturbance
input, y ∈
p
the measurement output, and z ∈
q
the output to be controlled.
The problem of H
2
optimal control is equivalent to finding an internally
stabilizing proper controller such that the H
2
norm of the resulting closed-loop
transfer matrix T
zw
(Σ×Σ
c
) is minimized. A proper controller Σ
c
is said to
be an H
2
optimal controller if it internally stabilizes Σ and T
zw
(Σ×Σ
c
)
2
= γ
∗
2
.
