Image Processing Reference
In-Depth Information
Hence,
taking u(t)
¼þ
Kx(t), where K is a constant gain matrix chosen to
satisfy the speci
cations (i.e., so that the closed-loop system has the desired eigen-
values) we get
X
(
s
) ¼ (
sI
A
BK
)
1
x
(
)
Y
(
s
) ¼ (
C
þ
DK
)(
sI
A
BK
)
1
x
(
0
(
9
:
32
)
)
0
or in the discrete case:
X
(
z
) ¼ (
zI
A
BK
)
1
x
(
)
Y
(
z
) ¼ (
C
þ
DK
)(
zI
A
BK
)
1
x
(
0
(
:
)
9
33
0
)
that is, again s is replaced with z. Therefore, we can use the same pole-placement
algorithms developed for continuous-time LTI systems. Of course, to achieve sta-
bility of the closed-loop system, the poles have to be placed in the left-hand side of
complex s-plane for continuous-time systems and inside the unit circle of the
complex z-plane for discrete-time systems.
9.6 LEVEL 2 DEVELOPABILITY CONTROLLER
Control of the
field strength and the uniformity of the charge on the photoconductor is
very important because high-quality prints are produced when a uniform charge with
the desired magnitude is maintained on the photoconductor. If the photoconductor is
not well controlled for both fully exposed (V
1
—
the voltage on the discharged region)
and unexposed levels (V
h
—
the voltage on the charged area), then the electrostatic
latent image obtained upon exposure of the image (e.g., the development voltage, for a
discharged area development, V
dev
, shown in Equations 10.29 and 10.30) will be
relatively weak and the resulting deposition of toner material will be weakened. As a
result, the copy produced by an underexposed photoconductor would look faded since
V
dev
will not be suf
cient for good development. If, however, the photoconductor is
overcharged, there will be too much developer material that is deposited on the
photoconductor. This results in a higher cleaning voltage, V
clean
which affects the
background and dot growth of the image on the photoreceptor. A copy produced by an
overcharged photoconductor will have a gray or dark background instead of the white
background of the paper. In addition to the background effect, areas intended to be
gray will be black and the tone reproduction will be poor. Moreover, if the photo-
conductor is excessively overcharged, it can be permanently damaged.
In a digital printing machine such as an electrophotographic engine, each tone of
a contone image is produced by a certain spatial combination of the available tone
levels produced by the halftone screening process. A binary printer uses two levels
with a dot
; that is, toner is developed on an exposed dot to create a
solid cyan, magenta, yellow, or black dot for a discharge area development.
These levels are used to reproduce the contone image. In some machines multiple
exposure levels are obtained by performing intensity modulation during exposure.
on
or
off
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