Image Processing Reference
In-Depth Information
iii. Compare the results of step ii by running the control simulation with the
charge and development models from Chapter 10.
iv. Are there other reasons why this type of control approach is more suitable
than level 1 and 2 architecture? Justify your answers.
S
OLUTION
Case (i): Gain matrix from Equation 9.43 for pole values p
1
¼p
2
¼p
3
¼
0.3 is
given by
2
4
3
5
10
4
3
:
9405
1
:
2977
0
:
2317
K ¼
0
:
7855
0
:
1988
0
:
0592
0
:
1578
0
:
0475
0
:
0055
Gain matrix from Equation 9.43 for pole values p
1
¼
0.3; p
2
¼
0.3; p
3
¼
0.7 is
given by
2
4
3
5
10
4
3
:
9405
1
:
2977
0
:
0993
K ¼
0
:
7855
0
:
1988
0
:
0254
0
:
1578
0
:
0475
0
:
0023
Case (ii): Step responses for the DMA states were created by changing the DMA
vector from [0.0384 0.1301 0.3398] to [0.0384 0.1301 0.3738]. The DMA vector
shown in Figure 9.16a converges to the desired steady-state value for the two
different gain matrices. The actuator response is shown in Figure 9.16b.
Solutions for cases (iii) and (iv) are left to the reader.
9.9 LEVEL 3 CONTROL LOOPS
At level 3, the TRCs of the individual separation are maintained in such a way that
they correspond to a reference tone curve on the photoconductor or on the paper
with the fused toner. The tone curve on the photoconductor (called
developed
''
reproduction curve
) is a function that maps digital contone values of a color separated
image to DMA values on the photoconductor. Similarly, the tone curve on the paper is
a function that maps a color separated image to an optical density on the paper after
fusing. For black and white printers, what matters is the tone curve on the paper. To
achieve good reproduction, it is important that the desired curve be linear. Often, users
request different tone curves depending on the overall appearance of the image. For
four-color digital reproduction, the complex interaction of each of the tone curves on
the paper makes it difficult to specify the exact shape of the desired tone curves.
A linear reference curve is more widely used in the industry. By design, the DMA
at 100% area coverage is generally limited to a set point and density control loops try
to maintain solids at those points. As a result, the available control space is externally
limited for level 2 process controls, which involves achieving the desired linear tone
response on the photoconductor or paper. The controllable space is illustrated con-
ceptually in Figure 9.17. In this
''
figure, level 2 targets are in the controllable space that
is outside the space where the desired reference TRC curve, which is linear in this
illustration. Thus, the desired tone curve is uncontrollable by levels 1 and 2 actuators.
For such situations, a preferred way to achieve the desired tone response is through
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