One-Dimensional, Two-Dimensional, and Spot-Color Management and Control Methods - Control of Color Imaging Systems: Analysis and Design - page 466

controller regarding the actuators when the spot colors under consideration are
common to two or more gamut classes, and (d) a unique solution for each spot
color once a gamut class has been chosen.

8.7.3 C ONTROL A LGORITHM
Once a gamut class is selected, we know which of the three color separations to use
to find the recipe for a given spot color. For out-of-gamut colors, choice of gamut

class not only depends on the color, but also depends on the gamut mapping
strategy used to map the colors to the printer

s gamut. The ICI (Section 6.4.3)
or moving-matrix (Section 6.3.2) algorithms can be used to

'

find the estimated
tricolor recipe associated with each mapped or in-gamut spot-color target using the
printer model (analytical or empirical, obtained using experimental data) associated
with each gamut class. Accuracy of this recipe depends on (a) accuracy of the
printer model and (b) accuracy of the inversion algorithm. To further re

ne
the accuracy, a three-input three-output MIMO state-feedback controller described
in Section 7.5.2.2 is used. The approach is shown in Figure 8.29 for CMY gamut
class, but the same method applies to the rest of the gamut classes. The recipe
obtained from the ICI or moving-matrix algorithms are used as nominal CMYK
values while working with the iterative feedback loop corresponding to the
gamut class under use. Iterations can also be carried out directly on the printer
with an in-line color sensor.
The control law can be designed using MIMO state-feedback methods or LQR or
model predictive control [13] approaches. Thus, u(k) ¼þ Ke(k), where e(k) is the

error between the target and the measured L*a*b* at iteration k. The gain matrix, K,
is derived based on the pole values speci ed such that the closed loop shown in

Figure 8.29 is stable. This is achieved by assigning pole values in the range [0, 1),
which will place the eigenvalues of the closed-loop system inside the unit circle.
During iterations, if the error, e (shown in Figure 8.29 for CMY gamut class), for
the spot color at or near the gamut boundary is higher than the previous one, then a
best CMY selection algorithm (see Figure 7.32) can be used because the CMY values
near the boundary may reach saturation (i.e., the CMY values may go to outside the
range 0 or 255).

8.7.4 C ONTROL A LGORITHM WITH I NK L IMITS
Often the tricolor gamut class does not give full gamut coverage in the dark part of
the gamut since those colors cannot be produced with only three separations. To
reproduce spot colors accurately with full gamut coverage, often a four-color gamut
class is introduced. A GCR-constrained 4-to-3 control-based inversion, as described
in Figure 7.41, can be used. Ink limiting constraints are often required in a four-color
system due to limitation on the fuser. Constraints for ink limits can be applied during
iteration while finding the recipe automatically. This would require more complex

control algorithms.