Nonlinear Model Predictive Control for an Exothermic Reaction in an Adiabatic CSTR

We model and simulate an exothermic reaction conducted in an adiabatic continuous stirred tank reactor (CSTR). The system has multiple steady states in part of its operating window. We demonstrate that the three-state model representing the mass and energy balances of the system can be well approximated with a two-state as well as a one-state model. The reduced-order models are relevant for efficient implementation of nonlinear model predictive control (NMPC). We extend the drift term in the system of deterministic ordinary differential equations (ODEs) with a diffusion term such that the process is modeled by a system of stochastic differential equations (SDEs). The SDE representation is well-suited for development of the NMPC that is based on a continuous-discrete extended Kalman filter (CD-EKF) and an optimal control problem. The optimal control problem (OCP) is solved using a multiple-shooting algorithm as the NMPC must be able to stabilize the system at stable as well as unstable steady states. Simulations demonstrate that the NMPC based on a one-state reduced SDE can track any reactor temperature setpoint at stable as well as unstable steady states.