Modeling and control of a two component development process for xerography

Feng Liu, Purdue University

Abstract

Development is one of the six key steps in xerography. It has been observed that during operation, toner particles tend to lose their developability that degrades image quality. For certain low area and low relative humidity operating condition, this degradation cannot be reversed with existing process control actuators without a service operation that is both time consuming and expensive. In this work, a control oriented model that characterizes this phenomenon is derived from an experimentally validated comprehensive statistical model. The resulting model maps the development voltage and toner dispensing rate to the developed mass per unit area that characterizes the print quality of the printer. System analyses show that the developability loss for low area coverage printing is unavoidable. In addition, development voltage and toner dispense rate have limited impact in reversing the loss of developability. Based on these observations, two constrained optimal control problems are formulated to determine the dispense strategy to maximize the operating time while maintaining acceptable developability within a given range of allowable development voltage and acceptable toner concentration. The first problem deals with the full state dynamics (i.e. the toner mass, sump state and donor state), the state constraints are put on the toner mass and donor state. The second problem deals with the reduced dynamics (i.e. the toner mass and the sump state only), the state constraints are put on the toner mass and sump state. For the first problem, numerical solution shows that for a given operating condition, with bounded toner concentration and development voltage, the optimal dispense strategy is a concatenation of the minimal allowed dispensing rate and a controlled dispensing rate associated with operating the development voltage at its maximum value. For the reduced dynamics of the process, we derive an analytical solution to a more generic class of single input planar affine control systems. Based on the existence of the optimal control and the first-order necessary conditions of optimality, the analytical solution is derived without solving for the costate dynamics explicitly. The analytical solution can be directly applied to the second problem and is supported by the solution from numerical approach.

Degree

Ph.D.

Advisors

Chiu, Purdue University.

Subject Area

Mechanical engineering

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