Spatial Filtering Concepts in Distributed Parameter Control

Abstract

A new method of analyzing distributed parameter control systems is presented, based upon their input/output representation in a spatially and temporally transformed frequency space. The classes of distributed systems amenable to the analysis are described in terms of their Green’s functions. The plants’ input/output relations are studied in the transformed space using the singular value decomposition to determine the system’s spatial performance. Performance is quantified in terms of generalized command following, disturbance rejection, noise rejection, controllability, and observability over spatial and temporal bandwidths, with suitable design measures presented. The analysis provides insight into the performance of sensor and actuator distributions in achieving spatial frequency performance specifications, determines spatial regimes where the response is directional, and quantifies sensor and actuator placement with respect to limitations of system and transducer spatial modelling. The analysis is shown to be applicable to discrete as well as distributed sensors and actuators, and utilizes commonly available numerical analysis techniques. An example problem is considered.