Image Processing Reference
In-Depth Information
first compute the area coverage from the pixel counter. The estimated
amount of developed mass, v(k), in grams, can be found using following equation:
We
v ( k ) ¼ image size toner mass
1000
area coverage ( k )
(
9
:
97
)
where toner mass is the amount of toner developed in milligrams = square centimeters.
Image size is the size of the image (e.g., 21.59
27.94
10 square centimeters for a
8.5 00
11 00 page with 10 pages being printed per one TC cycle). Area coverage
¼ P c ,
is the ratio of the total area where there is toner to the total image area, which is
calculated for each image using the pixel counter. In the actual implementation of the
feedforward compensation function, the pixel counter data is multiplied by a con-
stant, K ff , and the resulting signal is advanced by
cycles to account for the
dispenser lag. If the area coverage of each image is known
m
cycles ahead of actual
print, and the estimated toner mass is known accurately (which is included in the
feedforward gain, Kff), ff ), perfect cancellation for image disturbance can be achieved.
The control input (Equation 9.91) is modi
m
ed with feedforward compensation as
shown below:
z
z
1 K i e s ( z ) þ K ff z m p c ( z )
u ( z ) ¼ K p e s ( z ) þ
( 9 : 98 )
9.11.5 D ESIGN OF TC C ONTROL L OOP WITH S TATE F EEDBACK C ONTROLLER
AND S TATE E STIMATOR
To improve the overall TC performance, the following three major system compon-
ents need to be optimized: (1) the open-loop toner replenishment (dispense) and
mixing system (i.e., plant itself), (2) the TC measurement system (i.e., sensor), and
(3) the closed-loop control algorithm. Optimization of the toner replenishment
system and measurement system is related to the system hardware. Optimization of
the feedback controller is a software function which is easy to be incorporated even
after the hardware system is fully commissioned.
In this section, a new state-based feedback control algorithm (i.e., a set of
instructions implemented via a computer code) is discussed. In this algorithm, the
time delay in the toner dispense is replaced by states, and each state is estimated
using measurements from the TC sensor. States are de
ned by creating an open-loop
state-based model of the system. States are estimated from the sensor output using a
state estimator. As the system and each of the states is controlled, an improved
dynamic performance is expected as compared with the Smith predictor implemen-
tation. In addition to this bene
t, since the controller does not use an integrator, an
antiwindup compensator will not be required if the TC loop were to operate under
limited actuator (Section 9.12).
The system described by Equation 9.63 has a delay of
m
cycles. This is split into
m
states as in Figure 9.39. Formations of these states can be understood when the
system equation is expressed in terms of z-transforms.
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