Browsing by Subject "Lattice theoretic framework"

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    Sensing and control for color consistency of the xerographic printing process.
    (2009-09) Sim, Teck Ping
    This dissertation deals with the formulation, design, and implementation of the sensing and control system for maintaining color consistency of a xerographic color printing process. It involves stabilization of the tone reproduction curves (TRC) of all the primary color separations or directly on the color reproduction characteristics (CRC) function. Color prints quality and consistency are sensitive to disturbance induced variations due largely to the complexity of the print process itself and the small margin of perceptual color variations. In this dissertation a process level control is proposed to directly stabilize the printed colors. Implementing such a control system is difficult because while it is desirable to control all the reproducible colors, we have limited sensing and actuation authorities. To effectively stabilize the printed colors, all reproducible color information (potentially infinitely many colors) needs to be available at each time instance. However, only small number of color patches (3 to 5 color patches) can be printed and measured at every print cycle. Therefore, unlike typical sensing in control system, we need to sample in both time and in the spatial (or color) domains. Additionally unlike typical sensing of temporal-spatial signal, we are constrained by the availability of sensors to measure the spatial (color) samples and we need to sample these spatial samples in as temporally sparse manner as possible. The proposed solution consists of sampling a small number of n different colors at different time instances, a method known as time-sequential sampling. With time-sequential sampling, we need to decide which colors, in what order and at what time instance to sample? In this dissertation, an algorithm is proposed to design the time-sequential sampling in the lattice theoretic framework for n samples at each sampling instance known as TS(n) sampling such that we achieved the largest possible inter-sampling time, while effectively resolving the highest frequencies of the temporal-spatial signal in between samples (i.e. avoids aliasing). We verified that the designed TS(n) sampling approach is efficient and performs as well as if we have full color information and has better performance than equivalent classical time-sequential sampling approaches. Specifically, the key contributions in the design of the TS(n) sampling include; 1) proposed a framework to parameterize the space of all non-aliasing TS(n=1) sampling lattices; 2) showed that the space of all possible non-aliasing TS(1) sampling is compact. Hence an optimization algorithm that guarantees to terminate can be proposed and has been developed; 3) proposed restriction conditions to reduce the computational complexity of the optimization algorithm; 4) showed that when the temporal-spatial signal is not undersampled temporally by more than a factor of 2, if an optimal TS(1) sampling can be found under this restriction, the optimal lattice sampling will be as good as any unconstrained optimal TS(1) sampling; and 5) proposed construction of the TS(n), n>1 sampling design from the designed optimal TS(1) sampling. The main benefit of the TS(n), n>1 sampling design is the ability to tradeoff sensor hardware and inter-sampling time requirements, an important requirement for implementation in practical system where the inter-sampling time is typically fixed. In order to achieve color consistency, we need a control system that can constantly maintain a small error between the printed colors and the desired colors at all times. However, the number of colors to be stabilized in this manner far outnumbered the number of actuators in the print process. The proposed solution finds the control input to the actuators that minimize the perceptual error between the printed colors and the desired colors. This approach is akin to finding the best fit printed colors to the desired colors and therefore, all the reproducible colors are "approximately" similar to the desired colors. With the process under control, any residual deviations can now be accounted for with a feed-forward compensation strategy. This control strategy makes use of the known colors deviation and continuously re-coordinate the input colors to the printer such that the desired output colors are achieved. In addition, control approaches were proposed to coordinate and stabilize the tone reproduction of multiple print systems. Both simulation and hardware-in-loop experimental studies were conducted and presented in this dissertation to verify the performance and validity of the proposed approaches.