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)