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Control Oriented Modeling of a Hybrid Two-Component Development Process for Xerography

This paper presents a methodology for developing a control oriented model for a hybrid development architecture. The resulting model is suited for multivariable controller design and analysis to stabilize and improve the development process. The proposed methodology extracts relevant characteristics from an experimentally validated complex model based on toner age distribution and development probability. Three lumped state variables are proposed to characterize the macroscopic properties of the process. Ordinary differential equations of the proposed states are then derived to characterize the system dynamics of the process. Simulation results show that, for the properties of interest, the control oriented model yields similar results as the complex model for a wide range of operating conditions. Although the results presented are for a development process, the methodology can also be extended to other xerographic processes. Introduction Xerography is the “dry-marking” process used in the majority of laser printers and copiers. A typical xerographic process includes 6 sequential steps around a photoreceptor (PR): charge, expose, develop, transfer, fuse and clean. Detailed description of the steps involved in a xerographic process can be found in [1]-[3]. In this study, we will focus on the development step. The development step is one of the most important and challenging steps in xerography. It is a key factor in determining marking engine productivity and image quality. A hybrid two-component development approach was introduced in 1975 by Liebman [4]. This approach is called hybrid since it uses both single-component and two-component development processes, where two-component development refers to a process that uses combination of toner and carrier particles. The hybrid twocomponent approach has since been used in various products for its high reliability and low operating cost [5,6]. In this paper, we will investigate an example of a hybrid twocomponent development system as given in Fig. 1. To work through the system, we begin with toner and carrier particles that are dispensed from the dispenser to the sump area, where the toner and carrier particles are mixed and transported through an auger. An important aspect of this mixing is that it facilitates tribocharging between the toner and carrier, which causes the toner to attach to the surface of the carrier. To further assist charging and particle flow, additives are typically blended with the toner prior to being dispensed. Eventually, the toner/carrier mixture is transported by the auger within proximity of the mag roll, where this combination of particles becomes electromagnetically attached to the mag roll. The toner particles are then detached from the carrier particles and are electrostatically transferred to the donor rolls. As the donor roll rotates and aligns with the development electrostatic field formed by the latent image on the PR and the development electrode, the field strength detaches the charged toner particles from the donor roll and moves them on to the PR surface. Typically, models of the development process have been constructed from a physics perspective to provide phenomenological understanding, predict system behavior, and diagnose system defects. Although accurate, these first-principles based models are typically complex and computationally intensive. They tend to be difficult to use for process control synthesis and analysis. Control oriented models for printer calibration have also appeared in the literature [7]-[9]. These models treat the development step as a static, nonlinear mapping between the development voltage Vdev and the developed mass per area (referred to as DMA) on the PR. One of the widely used models is the “solid area development curve” model [1], which takes the form 0 [1 ] dev D V V DMA e (1) where VD0 is the potential required for the onset of the development, is the slope of the development curve at VD0, represents the maximum achievable DMA. For process control purposes, under specific operating conditions, , and VD0 are typically assumed to be constant. However, in practice, customer usage (e.g. area coverage of a print job) and the ambient conditions cause substantial change in and , indicating that the constant-parameter model is limited. This limitation is more prominent for “low” area coverage (e.g., less than 10%). Figure 1. Schematic of a hybrid two-component development process With more stringent requirements on image quality, it is necessary to develop a methodology for deriving a model that captures the dynamic behavior more comprehensively, but is still manageable for controller analysis and synthesis. In this paper, we Trim Blade