VIBRATING CONDUIT PARAMETER SENSORS AND METHODS OF OPERATION THEREFOR UTILIZING SPATIAL INTEGRATION

A process parameter sensor for a material processing system includes a conduit configured to contain material from the material processing system. A plurality of motion transducers is operative to produce a plurality of motion signals representing motion at a number of locations on the conduit. An overdetermined process parameter estimator is responsive to the plurality of motion transducers and configured to receive the plurality of motion signals. The overdetermined process parameter estimator is operative to resolve conduit motion into motion attributable to each of a predetermined number of forces and to estimate a process parameter associated with a material in the conduit according to the resolved motion, wherein the number of locations exceeds the number of forces such that the plurality of motion signals provides an overdetermined information set for resolution of conduit motion into motion attributable to the predetermined number of forces. According to one aspect, a process parameter is estimated from a spatially averaged motion signal using, for example, a conventional Coriolis measuring circuit. According to another aspect, a plurality of motion signals is produced representing motion at a number of locations exceeding a predetermined number of real or complex modes such that the plurality of motion signals represent an overdetermined information source for resolution of motion of the conduit into motion in each of the modes. An estimate of modal motion attributable to a Coriolis force may be generated from the plurality of motion signals, and an estimate of a process parameter may be estimated from the estimate of modal motion.