Perron-Frobenius theory

Interaction in Decentralized Control Systems: Application to Roll-to-Roll Systems

A procedure to analyze interaction in an experimental roll-to-roll system that uses a decentralized control strategy is presented in this paper. A Perron root based interaction metric is employed for the analysis. Experiments conducted on a roll-to-roll system are used to evaluate the interaction between different subsystems of the roll-to-roll system. To minimize interaction between subsystems of the roll-to-roll system, a procedure for designing pre-filters based on the Perron root of the system is also discussed in the paper. Experimental results with and without pre-filter clearly indicate the effectiveness of the pre-filter in minimizing interaction. Discussions regarding the roll-to-roll application, stability considerations and insights on using the Perron root based interaction measure for decentralized control applications are also given.

Modeling, Analysis and Control of Print Registration in Roll-to-Roll Printing Presses

Print registration in roll-to-roll (R2R) printing process is investigated in this dissertation. Print registration is the process of aligning multiple images that are printed in consecutive print units. The quality of the print output depends on the proper alignment of these images. A new mathematical model for print registration is developed by considering the effect of key process variables, such as web tension and transport velocity, print cylinder angular position and velocity, and the compensator roller position. Sources of machine induced disturbances and their effect on print registration are also investigated and machine design recommendations to mitigate these disturbances are given. Propagation of disturbances between print units due to web transport is investigated. The interaction, or the disturbance propagation behavior, between print units is studied by developing a new interaction metric called the Perron Root based Interaction Metric (PRIM). The new interaction metric, for large-scale interconnected systems employing decentralized controllers, is developed using tools from the Perron-Frobenius theory. A systematic procedure to minimize interaction is given by designing pre-filters for decentralized control systems. The disturbance propagation behavior with two registration control strategies is compared using the PRIM and it is found that a compensator based registration control (CRC) has smaller magnitude of disturbance propagation when compared to a print cylinder angular position based registration control (PARC). It is also found that a simple, decentralized, memoryless, state feedback controllers stabilizes print units with CRC. Results from a number of model simulations and experiments are provided to support the recommendations and conclusions.

Analysis and Minimization of Interaction in Decentralized Control Systems With Application to Roll-to-Roll Manufacturing

Analysis and minimization of interaction in multivariable systems employing decentralized controllers with application to roll-to-roll manufacturing systems are considered in this paper. A new interaction metric based on the Perron-Frobenius theory of nonnegative matrices is presented. This new metric may be used to quantify interaction in a large-scale interconnected system, establish constraints on closed-loop system stability, and provide a systematic design procedure for constructing decentralized pre-filters, which minimize interaction. The new interaction metric is applied to a roll-to-roll (R2R) manufacturing system, which utilizes decentralized control systems. R2R manufacturing is a continuous process in which flexible materials are transported on rollers through processing machinery where operations, such as printing, coating, lamination, etc., are performed to obtain finished products. Based on the Perron root interaction metric (PRIM), a comprehensive experimental study to analyze and minimize interaction on a large experimental R2R platform is presented. A representative sample of experimental results which demonstrate the applicability of PRIM is presented and discussed.