Hardware Reference
In-Depth Information
Since the microactuator has a finite DC-gain, any limit on its input effec-
tively puts a limit on the displacement effectuated by the microactuator. This
limit on the microactuator's displacement can be incorporated in the design by
modifying the DMS controller structure. Figure 3.96 shows the modified DMS
structure which is similar to the DMS scheme (shown in Figure 3.90) except a
block marked sat(·) included in the controller. To see how incorporating the
microactuator model with saturation in the DMS controller helps to improve
the stability of the control loop in presence of microactuator saturation, let us
assume that r = 0, and the transfer function of a saturation section represented
as sat(·).
Breaking the VCM loop open at the point e
V
in Figure 3.96, we have the
open loop transfer function of the VCM path as
1
1+C
M
P
M
sat(·)
.
O
v
= C
V
P
V
(1 + C
M
P
M
sat(·))
(3.172)
Obviously, if P
M
= P
M
, and assuming that the microactuator P
M
and its
model P
M
have the same initial values, we have y
M
(k)=y
M
(k), resulting
effectively in
1
1+C
M
P
M
sat(·)
=1.
(1 + C
M
P
M
sat(·))
(3.173)
Consequently, the secondary stage actuator model does not appear in the VCM
path, thus its saturation will not affect the VCM control loop's stability.
In contrast, in the usual linear control configuration shown in Figure 3.90,
we have |y
M
(k)| |y
M
(k)| if the microactuator is saturated for sufficiently
long time. In this case, the effective open loop transfer function
1
1+C
M
P
M
sat(·)
O
v
= C
V
P
V
(1 + C
M
P
M
)
(3.174)
will have a higher effective gain than the case of equation (3.172), leading to
potential instability.
Next, we assume that the microactuator P
M
is represented by state space
equations:
½
x
M
(k +1) = F
M
x
M
(k)+Γ
M
u
M
(k),
(3.175)
y
M
= H
M
x(k),
and the estimator P
M
by
½
x
M
(k +1) = F
M
x
M
(k)+Γ
M
u
M
(k),
(3.176)
y
M
= H
M
x(k).
The error dynamics of the estimator is given by
x(k +1) = x(k +1)− x(k +1),
= F
M
x(k).
(3.177)
