Control of distributed parameter systems

• Main Author: McCann, Michael John
• Other Authors: Westcott, J. H.
• Published: Imperial College London 1963
• Subjects: 660
• Online Access: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.602254

Many industrial processes are shown to have a common underlying form involving transport of energy and matter by flow and dispersion or diffusion. Mathematical models using the Laplace transform and root-locus methods produce space parameter dependant transfer functions, and explain resonance like phenomena characteristic of distributed forcing of flow systems. Harmonic or functional analysis depends on having eigen functions for the differential operators for the system. The number of sections required for a lumped parameter model produced by spatial quantization was found (on a digital computer) to depend on the disturbances being considered and a parameter characterizing the system. A cheap, simple, special purpose electronic analogue was developed. Control design by conventional methods yields a useful standard of comparison. The absolutely optimal solutions from the calculus of variations (etc.) are shown to present major computational difficulties especially when the theory is extended to partial differential and integral equations. Practical use of sub-optimal control design methods and the analytical development of a direct feedback controller all depend on having a state-space of low dimensionality. A correlation coefficient criterion for instrumentation gives a method for specifying instrumentation for protection purposes but not for control or performance measure. Control based on instantaneous computation on a measure of state is shown to need only small amounts of instrumentation but sensitivity to parameter changes has to be taken into account. Spatially distributed control can deal with disturbances arising anywhere in the system, and sensitivity to parameter changes is reduced at the cost of greater complexity The structure of the control scheme and its instrumentation is largely determined by the spatial location of the measure or measures used for performance assessment and the relationship between spatial displacement and time delays in the distributed systems.