Internal Process Controls - Control of Color Imaging Systems: Analysis and Design - page 492

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Area coverage

FIGURE 9.14 Development TRCs for the actuator space shown in Figure 9.12.

output data is used for determining the Jacobian matrix. A numerical
3-D model is constructed through interpolation. Nearest neighbor, linear, spline, or
cubic interpolation methods can be used, depending on the input

The input -

output data. Key
steps in determining the Jacobian matrix at the nominal operating points are

-

1. Set the actuator vector, U 0 ¼ [ U ho U lo U bo ] 0 to the desired nominal value.
2. Vary U h to some value about the nominal value of U ho (increase by that
value and decrease by that value) while keeping other actuator values at
their nominal operating points. Record the difference DMA vector for these
actuator settings obtained using the numerical model. This step gives the

first column vector of the Jacobian matrix.
3. Vary U l to some value about the nominal value of U lo while keeping other
actuator values at their nominal operating points. Record the difference
DMA vector for these actuator settings obtained using the numerical model.
This step gives the second column vector of the Jacobian matrix.
4. Vary U b to some value about the nominal value of U bo while keeping other
actuator values at their nominal operating point. Record the difference
DMA vector for these actuator settings obtained using the numerical
model. This step gives the last column vector of the Jacobian matrix.

Example 9.5

Test the following developability control system for complete controllability. The
system is given at the nominal operating point {U ho ¼

600 V, U lo ¼ 100 V,

U bo ¼ 300 V}.