An Optimal Feedback Control Strategy for Nonlinear, Distributed-Parameter Processes

In this work, an optimal state feedback control strategy is proposed for non-linear, distributed-parameter processes. For different values of a given parameter susceptible to upsets, the strategy involves off-line computation of a repository of optimal open-loop states and gains needed for the feedback adjustment of control. A gain is determined by minimizing the perturbation of the objective functional about the new optimal state and control corresponding to a process 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, gas-based heavy oil recovery process controlled by the gas temperature 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 when the process has a pressure upset, the proposed strategy is able to determine control adjustments with negligible time delays and to navigate the process to the new optimal state.