Real Time Optimal Control of Distributed-Parameter Systems

An optimal state feedback control strategy is proposed for processes described by non-linear, distributed-parameter models. For different values of a given parameter susceptible to upsets, the strategy involves off-line computation of a repository of optimal open-loop control, state, and the gain needed for the feedback adjustment of control. The gain is determined by minimizing the perturbation of the objective functional, state and control due to an upset. When an upset is encountered in a running process, the repository is utilized to obtain the control adjustment required to steer the process to the new optimal state. The strategy is successfully applied to a highly non-linear, heavy oil recovery process with the state depending non-linearly on time and two spatial directions inside a moving boundary, and subject to pressure upsets. The results demonstrate that the proposed strategy is able to determine control adjustment with negligible time delay, and navigate the process to the new optimal state when disturbed by a pressure upset.