Real-Time Nonlinear Model Predictive Control of a Transport-Reaction System

Abstract

Two real-time nonlinear model predictive control (NMPC) algorithms for a transport-reaction system are designed. The system is modeled by a hyperbolic partial differential equation and discretized by means of a two-time-level semi-implicit semi-Lagrangian scheme. For the resulting lumped-parameter system, a constrained optimal control problem is formulated and state constraints are implemented in the form of barrier functions. The NMPC algorithms perform a single step or several steps of an iterative solution routine of the optimal control problem at every sampling point. With this suboptimal solution strategy, a fixed maximum evaluation time and execution in real time are guaranteed. An analysis of the nominal stability is provided for one NMPC scheme. The robustness of the controllers is evaluated for an example problem, where a nonisothermal plug-flow reactor with irreversible exothermic reactions is considered. The control objectives are to limit the maximum reactor temperature (avoid hot spots) and to maximize the process output.