Eric S. Hamby

Noise Induced Loss of Tracking in Systems With Saturating Actuators and Antiwindup

This technical note is devoted to a recently discovered phenomenon that takes place in feedback systems with saturating actuators, proportional-integral (PI) control, and antiwindup. Namely, in such systems, measurement noise induces steady-state error in step tracking, which is incompatible with the standard error coefficients. We quantify this phenomenon using stochastic averaging theory and show that the noise induced loss of tracking occurs only if antiwindup is present. An indicator that predicts this phenomenon is derived, and a rule-of-thumb, based on this indicator, is formulated. An illustration using a digital printing device is provided. [DOI: 10.1115/1.4027163]

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

Development is one of the six key steps in xerographic printing processes. Under certain printing conditions, the “deveopability” of the toner particles tends to degrade resulting in a loss of image quality. Existing process controls have limited authority in compensating for this degradation, and, ultimately, a service operation may be required to install fresh toner. From a customer perspective, this machine maintenance results in productivity loss and added cost, both of which need to be minimized. In this paper, a control oriented model that characterizes “developability loss” is derived from an experimentally validated comprehensive statistical model. The resulting model considers the stress case of printing “low area coverage” documents (e.g., text pages) in a low relative humidity environment, and it maps the development voltage and toner dispensing rate actuators to the developed toner mass per unit area, which is the sensed output and is also used as a surrogate for print quality. Under these operating conditions, system analysis shows that developability loss is unavoidable. Given this result, a constrained time optimal control problem is formulated to determine the dispensing strategy to maximize the printer operating time while maintaining acceptable developability. Numerical solution shows that for the stress operating condition leading to developability loss, the optimal dispensing strategy increased the operating time by 170% compared with a conventional dispensing strategy.

Modeling and control of cyclic systems in xerography

This paper is devoted to the scientific study and engineering application of cyclic systems. Cyclic systems are non-traditional plants, containing devices with rotating dynamics along with actuators and sensors fixed in inertial space. The combination of rotating dynamics and inertially-fixed inputs and outputs leads to one-per-revolution (or stroboscopic) actuation and sensing. Control of cyclic systems amounts to designing a regulator that uses stroboscopic actuation and sensing to force the system into the desired regime. Although cyclic systems are periodic, the general theory of periodic control is not immediately applicable due to stroboscopic actuation and sensing. Because of rotating dynamics, the theory of impulsive control is not applicable as well. This work develops an approach to the control of systems with both rotating dynamics and stroboscopic instrumentation, and reports the initial application to a xerographic process.

Time maximum control for a class of single-input planar affine control systems and constraints

In some dynamic systems, it is desirable to keep the state trajectory within a predefined (constrained) subset of the state space, referred to as an operating region. However, for certain systems, state trajectories leave the operating region in finite time due to system dynamics. To keep the state trajectory in the operating region as long as possible, a constrained time optimal control problem can be formulated. The analytical solution to the optimal control problem can be derived for a class of single-input planar affine control systems and constraints, which exist in a wide range of processes in xerography, bio-reaction, etc. A numerical example from a development xerographic process is used to demonstrate the feasibility of the analytical solution.

System Analysis of a Hybrid Two-component Development Process for Xerography

In this paper, we will illustrate the utility of a control oriented model for a hybrid two component development process. More specifically, we will focus on the developability loss phenomenon observed in low throughput printings, where a monotonic increasing development voltage is required to achieve same amount of developed mass per unit area, which is highly correlated with the color appearance on the print images. For a given initial condition, the acceptable operating region for the development process is bounded by maximal and minimal toner mass levels as well as a maximal development voltage. We will demonstrate that the state trajectory will eventually leave the acceptable operating region in finite time for all continuous state feedback control involving dispensing input.