Image Processing Reference
In-Depth Information
Filtered sensor output
(Low, mid, and high DMAs), x ( k )
-
v ( k )
u ( k )
e ( k )
U ( k )
Xerographic
system with
level 1
Gain
matrix,
K
+
Integrator
+
Targets
(Low, mid, and
high DMAs), x d
Nominal actuator
values, U 0
Actuations to level 1
and development system
FIGURE 9.11
MIMO level 2 developability controller.
signal. The
filtered DMA vector is compared to the desired DMA target vector
and the error vector is processed by the feedback controller to generate the
actuator values. The choice of actuators depends on the control hierarchy and
the ease of implementation. In a time hierarchical control architecture, since the
electrostatic control loop is fully settled before closing the outer level 2 control
loop, the set points for the level 1 loop Vl} h and V l } act as two actuators. The
developer bias, V bias , which affects how much toner is transferred to the photo-
conductor, is used as the third actuator. Numerous additional architectures use
combinations of process parameters as actuators [16
-
21] in order to optimize for
cost and performance. For a three patch sampling system, in which the sensed
signals are coupled to all of the actuators, the simplest controller would be a
three-input three-output state feedback controller whose gains are determined
from the Jacobian matrix. Elements in the matrix represent the
first-order deriva-
tives of the DMA of the three patches with respect to the three actuators. The
design of a MIMO controller is described in Figure 9.11.
Let D l (k), D m (k), and D h (k) represent the three different DMA measurements
(output of the
filter) at the sample time de
ned by the parameter k. These DMA
measurements are basically identi
ed as three different points on the TRC. k is a
parameter used to describe the iteration of the level 2 control loop. This parameter is
different from the iteration number of the level 1 loop. The hierarchical structure
contains nested loops: an inner loop (level 1) operating within the body of an outer
loop (level 2). Several iterations of the inner loop are required to reach steady
performance before the outer loop is closed. One iteration pass for a level 2 loop
comprises of a sensing-processing-actuation update cycle. Normally, 10
-
30 prints
are made for every level 2 iteration.
Let the corresponding target values of the toner mass be represented by the vector,
x d ¼ [ D l
D m
D h ] T . The target vector does not depend on k since there is no higher
level
loop used to update the target vector. The actuator signals U h ( k ) ¼
V h ( k )
, U l ( k ) ¼ V l ( k )
are captured by the actuator vector
U ( k ) ¼ [ U h ( k ) U l ( k ) U b ( k )] T .LetU 0 ¼ [ U ho U lo U bo ] T be the corresponding
static nominal actuator vector that does not depend on the sample time. The linear state
feedback controller will have the architecture shown in Figure 9.11.
,andU b ( k ) ¼ V bias ( k )
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