Uncertainty models for control of distributed actuator and sensor arrays

摘要

This paper considers control analysis approaches for systems incorporating large actuator and sensor arrays. Applications of such systems are increasingly common because of the development of micro-systems technology. Many imaging systems have large one-dimensional or two-dimensional arrays of actuators. This includes RF or optical reflectors, display, printing, and other systems. Signal processing for large sensor arrays has weel-established theory and applications, especially in imaging. At the same time, approaches to control of large distributed actuator and sensor arrays are much less developed. This paper considers one of the fundamental issues in design and anlaysis of large actuator and sensor array systems. The key notion in modern feedback control theory is the notion of uncertainty and associated notion of control robustness to this uncertainty. In control of dynamical systems evolving in time, structured uncertainty models are commonly accepted for theoretical analysis (Structured Singlular Value or mu -analysis) and practical control ddesign. In control of spatially distributed precesses, there is a need to testablish appropriate models of the uncertainty of the system spatial and dynamical characteristics. This paper discusses an extension of structured uncertainty models towards controlled systems with spatially distributed arrays of actuators and sensors. Unlike a dynamical uncertainty, spatial uncertainty is not causal in the spatial coordinate. This leads to related but different uncertainty models in the two cases. For spatial coordinates, boundary effects also contribute to the modeling error. By using the discussed uncertainty models, the existing methods of robust control design and analysis can be extended towards spatially distributed systems. As an illustrative example, this paper demonstrates an application of the developed approach to a one-dimensional model of a flexible reflector with a distributed acutator array for shape control.