Late lumping controlled variable design for transport reaction processes

Abstract

Transport reaction processes (TRPs) are inherently infinite-dimensional in space, and achieving optimal distributions of their physical quantities under disturbances is a common challenge. Discretizing such systems into finite-dimensional models and then devising an optimization scheme, is the mainstream route. Among these strategies, a relatively new distributed parameter self-optimizing control (SOC) yields acceptable losses by maintaining controlled variables (CVs) designed offline at constants, which avoids repeated online optimization and is suitable for sufficiently precise discrete TRPs without incurring significant online computational costs. However, any model reduction can cause the loss of critical system information and compromises the optimality of SOC. In this work, a late lumping SOC method that avoids spatial approximation entirely during design phases is developed for TRPs. Using the late lumping null space theorem and the analytical derived sensitivity operator, optimal CVs can be identified to achieve a near-zero loss. The sensitivity for typical TRPs is determined analytically through the theories of differential equations and adjoint operators. Two simulation experiments involving TRPs with convection and diffusion phenomena demonstrate the effectiveness of the proposed method.