GOALI: Control of Cyclic Systems - Theory, Applications, and Experiments

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

The research objective of this award is the development of a control theory for cyclic systems and its application and experimental verification. Cyclic systems contain mechanical devices that rotate, along with actuators and sensors that are fixed in inertial space. The combination of rotating motion and inertially-fixed inputs and outputs leads to one-per-revolution (or stroboscopic) actuation and sensing. The research will result in methods that are applicable to xerographic processes, drilling and milling machines, and turbomachinery. The approach of the research is based on so-called circulant matrices, which describe cyclic systems. Each row of a circulant matrix is a circular permutation of the previous row. Fundamental properties of circulant matrices constitute the foundation of the theoretical part of the research; the experimental part is based on the xerographic process. Deliverables include: (1) Methods for mathematical modeling of cyclic systems; (2) Methods for stabilizability, controllability, and observability of cyclic systems; (3) Methods for designing reference tracking and disturbance rejection controllers for cyclic systems; (4) Application of the results obtained to the photoreceptor charging system in xerography to reduce color variation; (5) Experimental verification of the techniques developed; (6) Documentation of the research results; (7) Engineering student education. If successful, the results of this research will provide a methodology for improving performance of rotating devices using feedback control. Indeed, in many instances, high performance of rotating devices is achieved using expensive high quality hardware. Based on the methods to be developed, high performance will be achieved using inexpensive low quality hardware but with stroboscopic feedback control. The results of this research will be disseminated to industrial audiences through short courses. Graduate students involved in this GOALI project will be exposed to industrial environment at Xerox Research Center. Efforts will be made to involve under-represented minorities and women to this project as well as high school students.