Optimal control of counterflow diffusion processes.

This work is concerned with the optimal conditions of flow control of countercurrent chemical processes. Such processes abound in chemical engineering, in a number of forms. A parallel treatment of both continuous and discrete systems is pursued, largely under the mantle of distributed control system theory. Examination of common features of counterflow processes yields performance criteria and control constraints which may be chosen as a measure of controller efficiency. Based on these criteria a standardised system is investigated according to several distinct approaches, each tested practically against a particular physical countercurrent system. The derivation of transfer functions relating exit boundary conditions to input flow and input boundary conditions is extended, in order to cover the case of spatially dependent flow dynamics, with reference to a solvent extraction process. The complexity and role of terms entering into the transfer function is assessed from a viewpoint of sub-optimal regulatory control. A more general approach surveys the theory of partial differential equations, in order to investigate approximate means of representation. Out of a number of variational approximation methods, it is shown that a discrete Fourier series provides the most suitable reduction to a lumped system. Using distributed gradient techniques, it is possible to obtain optimal flow profiles corresponding to regulatory and maximum extraction cost functions. Such a method is shown to extend to the case of spatially varying flow dynamics. Indirect optimal control methods are also applied to the distributed problem, when both dynamics and performance criteria are expressed in lumped system form. The multiplicative role of flow parameters is found to persist through both the direct and indirect methods of optimal control.