Economic model predictive control of a first-order hyperbolic PDE system

This work focuses on economic model predictive control (EMPC) of a system of two quasi-linear first-order hyperbolic partial differential equations (PDEs) arising in the first-principles modeling of a non-isothermal plug-flow reactor where a second-order reaction takes place. Owing to the hyperbolic nature of the PDE model, a suitable finite-difference scheme is initially used to carry out spatial discretization and construct an accurate ordinary differential equation (ODE) model in time, which is subsequently used for the design of an EMPC system that manipulates the feed reactant concentration to directly maximize the production rate of the product species along the length of the reactor; both state and output feedback implementations of the EMPC are presented. Extensive simulations studies are carried out by applying the EMPC schemes to a high-order approximation of the PDE process model to evaluate economic performance improvement over steady-state operation, computation time EMPC requirements versus the sampling time, and impact of EMPC horizon length on economic performance and number of measurement points on state estimation accuracy.