Modeling and Control of Color Xerographic Processes

The University of Michigan and Xerox\u27s Wilson Research Center have been collaborating on problems in color management systems since 1996, supported in part by an NSF GOALI grant. The paper is divided into three sections. The first discusses the basics of xerography and areas where systems methodology can have a potential impact. The second section describes the authors\u27 approach to the approximation of color space transformations using piecewise linear approximants and the graph intersection algorithm, with a brief review of some of the analytical and numerical results. The last section expounds on some of the benefits and difficulties of industry-university-government collaboration

Toward a Control Oriented Model of Xerographic Marking Engines

This paper presents some preliminary results from a research collaboration concerning the modeling and control of color xerography. In this first communication of our work, we describe our efforts to develop a model for a monochrome marking engine. We adopt the technique of principal component analysis for choice of output coordinates and demonstrate preliminary experimental evidence suggesting that this procedure yields accuracy in data reconstruction superior to present industry practice. Preliminary analysis of the experimental evidence suggests that the process has a nonlinear component that we seek to model using a mixture of physical and empirical insight

Particle tracking code of simulating global RF feedback

It is well known in the control community'' that a good feedback controller design is deeply rooted in the physics of the system. For example, when accelerating the beam we must keep several parameters under control so that the beam travels within the confined space. Important parameters include the frequency and phase of the rf signal, the dipole field, and the cavity voltage. Because errors in these parameters will progressively mislead the beam from its projected path in the tube, feedback loops are used to correct the behavior. Since the feedback loop feeds energy to the system, it changes the overall behavior of the system and may drive it to instability. Various types of controllers are used to stabilize the feedback loop. Integrating the beam physics with the feedback controllers allows us to carefully analyze the beam behavior. This will not only guarantee optimal performance but will also significantly enhance the ability of the beam control engineer to deal effectively with the interaction of various feedback loops. Motivated by this theme, we developed a simple one-particle tracking code to simulate particle behavior with feedback controllers. In order to achieve our fundamental objective, we can ask some key questions: What are the input and output parameters How can they be applied to the practical machine How can one interface the rf system dynamics such as the transfer characteristics of the rf cavities and phasing between the cavities Answers to these questions can be found by considering a simple case of a single cavity with one particle, tracking it turn-by-turn with appropriate initial conditions, then introducing constraints on crucial parameters. Critical parameters are rf frequency, phase, and amplitude once the dipole field has been given. These are arranged in the tracking code so that we can interface the feedback system controlling them

A General Control Model for Designing Beam Control Feedback Loops* A General Control Model for Designing Beam Control Feedback Loops

Abstract To control the beam in the synchrotron there may be six different primary feedback loops interacting with the beam at a given time. Three loops are local to the rf cavity. They are: high bandwidth cavity phase and amplitude loops used to minimize the effects due to beam loading and a low bandwidth cavity tuning loop. The loops global to the ring accelerating system are: a radial loop to keep the beam on orbit, a beam phase loop to damp the dipole synchrotron oscillations, and a synchronization loop to essentially lock with the succeeding machine. There are various ways in which these loops may be designed. Designs currently in use in operating machines are based on classical frequency domain techniques. To apply modern feedback controllers and study the interaction of all the feedback loops, a good mathematical model of the beam is extremely useful. In this paper we show the derivation of a non-linear tracking model in terms of differential equations obtained from a set of time varying finite difference equations. The model compares well with the results of thin element tracking codes

Interaction Between Beam Control and RF Feedback Loops for High Q Cavities an Heavy Beam Loading

An open-loop state space model of all the major low-level rf feedback control loops is derived. The model has control and state variables for fast-cycling machines to apply modern multivariable feedback techniques. A condition is derived to know when exactly we can cross the boundaries between time-varying and time-invariant approaches for a fast-cycling machine like the Low Energy Booster (LEB). The conditions are dependent on the Q of the cavity and the rate at which the frequency changes with time. Apart from capturing the time-variant characteristics, the errors in the magnetic field are accounted in the model to study the effects on synchronization with the Medium Energy Booster (MEB). The control model is useful to study the effects on beam control due to heavy beam loading at high intensities, voltage transients just after injection especially due to time-varying voltages, instability thresholds created by the cavity tuning feedback system, cross coupling between feedback loops with and without direct rf feedback etc. As a special case we have shown that the model agrees with the well known Pedersen model derived for the CERN PS booster. As an application of the model we undertook a detailed study of the cross coupling between the loops by considering all of them at once for varying time, Q and beam intensities. A discussion of the method to identify the coupling is shown. At the end a summary of the identified loop interactions is presented