Hardware Reference
In-Depth Information
and phase delay of about 93
◦
at f
m
. At the 0-dB crossover frequency, which
is approximately 2020 Hz, the phase is about 80
◦
above −180
◦
.
However, one can notice that the frequency at which the magnitude re-
sponses of the two paths cross each other, the overall gain drops to a value
lower than the gain of either of the two loops. It indicates that the two actua-
tors are conflicting with each other at the hand-off frequency. This is because
of the phase difference between the two loops at the hand-off frequency. To re-
duce the phase difference between the microactuator output and VCM output
at the hand-off frequency, it is necessary to change the loop gains by reselecting
the controller parameters.
In the next example, a controller is designed for the parallel structure using
optimal control approach.
Direct MIMO Design
State space method is another popular method for designing controller, espe-
cially for plants with multiple inputs and multiple outputs. In this approach,
a state feedback controller is first designed to achieve desired system dynamics
assuming all states of the plant are available for feedback. This is followed by
the design of an estimator that reconstructs the unavailable states of the plant.
Let the state space model of the dual-stage actuator be
½
x
p
(k +1) = A
p
x
p
(k)+B
p
u
p
(k),
y
p
(k) =y
m
(k)+y
v
(k)=C
p
x
p
(k),
(3.151)
where
∙
¸
∙
¸
A
m
0
B
m
0
A
p
=
,B
p
=
,
0
A
v
0
B
v
£
¤
C
p
=
C
m
C
v
.
£
¤
T
x
T
m
x
v
Here the vector x
p
=
is the state vector and y
p
is the displace-
©
ª
©
ª
ment output of dual actuator, and
,
x
m
, x
v
, y
m
, y
v
, u
m
and u
v
are the system matrices, states, displacement out-
puts and control inputs of micro-actuator model and VCM, respectively.
State feedback design does not include any integral action. However, we are
interested to have integral control for the HDD servomechanism to overcome
the effect of input bias. This can be achieved by augmenting the state space
model by including two more states, i.e., the tracking errors of the secondary
stage and the VCM [68],
A
m
,B
m
,C
m
,
A
v
,B
v
,C
v
x
pi
(k +1) = x
pi
(k)+r(k) −y
p
(k),
(3.152)
x
vi
(k +1) = x
vi
(k)+r(k) −y
v
(k).
(3.153)
Then it follows that the generalized system is
½
x(k +1) = Ax(k)+Bu(k)+B
r
r(k),
y(k) =Cx(k),
(3.154)
