Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 355

100 100

80 50

o

o

60 0

40 -50

20 -100

0 50 100 0 50 100

Cyan (%) Cyan (%)

40

20

M = 50%; Y = 50%
M = 10%; Y = 50%

o

0

o Nominal point

-20

-40

0 50 100

Cyan (%)

FIGURE 7.30 Diagram representing L*a*b* values when C separation is varied at constant

M and Y.

B is the Jacobian matrix computed around the initial CMY value (or measured
using techniques outlined in Ref. [95])
u(k) is the control law applied to the input of the printer

The Jacobian matrix B is different for each node color and computed as follows:

2 3

@ L*
@ C

@ L*
@ M

@ L*
@ Y

4 5

@ a*
@ C

@ a*
@ M

@ a*
@ Y

B ¼ ( 7 : 88 )

@ b*
@ C

@ b*
@ M

@ b*
@ Y

The control law is designed using MIMO state-feedback controllers (based on linear
quadratic regulator [LQR] or pole-placement as shown in Chapter 6 or any other
multivariable digital control techniques [96 ¼ Ke(k), where e(k)

is the error between the target L*a*b* and the model L*a*b* at iteration k. In pole-
placement design (Chapter 6), the gain matrix K is derived based on the pole values
speci

- 100]). Thus, u(k)

ed such that the closed-loop system model shown in Figure 7.29 is stable. This
is achieved by assigning pole values within the range [0,1) in the Z-domain. For the
loop to be stable, the eigenvalues of the closed-loop system should remain inside
the unit circle of the Z-domain even when the printer drifts. Hence, the pole values