Hardware Reference
In-Depth Information
where x
o
is the estimation of x
p
. The observer gain L can be obtained
by
L = −A
p
QC
p
(V
2
+ C
p
QC
p
)
−1
(3.159)
where V
1
and V
2
are some weighting matrices, and Q>0 is the unique
stabilizing solution of the following Riccati equation:
A
P
QA
P
−Q + V
1
−A
P
QC
p
(V
2
+ C
p
QC
p
)
−1
C
p
QA
p
=0.
(3.160)
Following equations 3.156 and 3.159, the desired controller can be obtained
with the following state space description:
⎨
x
k
(k +1) = A
k
x
k
(k)+B
k
u(k),
+B
kr
r(k)+B
ky
y(k),
u(k) =C
k
x
k
(k),
(3.161)
⎩
where
⎡
⎤
A
p
+ LC
p
00
0
⎣
⎦
A
k
=
1
0
,
£
¤
0 −C
v
01
⎡
⎤
⎡
⎤
⎡
⎤
B
p
0
0
0
1
1
−
−1
0
⎣
⎦
⎣
⎦
⎣
⎦
B
k
=
,B
kr
=
,B
ky
=
.
Figure 3.75: Dual-stage actuator system block diagram.
The simulation results presented here are obtained using the MATLAB
TM
SIMULINK. The SIMULINK model is shown in Figure 3.75.
Using the controller given above, the frequency responses of the closed-
loop system are shown in Figure 3.76.
It is obvious that the bandwidth of
closed-loop system is about 2 kHz.
Figure 3.77 and Figure 3.78 show the simulation results of the closed-loop
system with a reference input of 0.5 sin(200πt)+sin(8000πt). As expected, the
dual-stage system follows the reference input closely. The VCM mainly tracks
the low frequency input, and the microactuator tracks the high frequency one.
