Profile control in distributed parameter systems using lexicographic optimization based MPC

Process equipment that exhibits significant spatial variation of system properties, such as temperature or concentration in a fixed bed reactor, are typically modeled as distributed parameter systems. While some properties of the final product exiting the equipment may depend on the states concerning the endpoint, others may be a function of the history of processing within the equipment. In such instances, control of the spatial property profile may be beneficial. In this work, we explore the idea of profile control using extended MPC and outline the additional challenges that must be addressed in this context. In case that the target profile is unachievable, we present an MPC formulation that uses lexicographic optimization to prioritize the different sections of the profile. Simulation of a simple representative system namely a hypothetical plug flow reactor is used to demonstrate that the lexicographic optimization based MPC provides a systematic approach to profile control and spans between the endpoint control strategy and the whole profile control strategy. The benefits of lexicographic optimization based MPC were also demonstrated on a large-scale distributed parameter system of industrial size, namely the continuous pulp digester.