Using time-sequential sampling to stabilize the color and tone reproduction functions of a xerographic printing process

Abstract—Tone and color reproduction functions (TRC and CRC) characterize how a printer maps a desired tone or color into the actual printed output. TRC/CRC ideally, should be identity maps to achieve tone and color consistency. Whereas the TRC/CRC is potentially high or infinite dimensional, typically, only a small number of tone/color test patches for sensing can be printed and measured at a time and only a small number of actuators are available for control. Time-sequential sampling is proposed to address the sensing limitation issue in order to enable the time varying TRC or CRC to be reconstructed based on a small number of samples. A periodic Kalman filtering approach is employed for the reconstruction. A curve-fitting TRC stabilization controller based on linear quadratic (LQ) control with integral dynamics is proposed to address the actuation limitation issue. Two classic time-sequential sampling sequences are compared based on their spectral aliasing properties, and the reconstruction operations of the periodic Kalman filter is analyzed using Floquet theory. Simulations and experiments show that the proposed TRC/CRC stabilization system can be implemented practically and the control performance with one time-sequential sampled sensor is nearly as effective as using full sampling using sixteen fixed sensors. Index Terms—Curve-fitting, Kalman filter, optimal control, periodic system, signal reconstruction, time-sequential sampling, xerographic printing. I

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