### Abstract

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.

Original language | English |
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Title of host publication | Proceedings of 6^{th} International Conference on Advances in Control and Optimization of Dynamical Systems |

Publisher | Elsevier |

Publication date | 2020 |

Pages | 500-505 |

Publication status | Published - 2020 |

Event | 6^{th} International Conference on Advances in Control and Optimization of Dynamical Systems - IIT Madras, Chennai, IndiaDuration: 16 Feb 2020 → 19 Feb 2020 |

### Conference

Conference | 6^{th} International Conference on Advances in Control and Optimization of Dynamical Systems |
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Location | IIT Madras |

Country | India |

City | Chennai |

Period | 16/02/2020 → 19/02/2020 |

### Keywords

- Nonlinear model predictive control
- Multiple steady states
- Adiabatic continuous stirred tank reactor
- Exothermic reaction
- Stochastic diﬀerential equations

## Cite this

Wahlgreen, M. R., Schroll-Fleischer, E., Boiroux, D., Ritschel, T., Wu, H., Huusom, J. K., & Jørgensen, J. B. (2020). Nonlinear Model Predictive Control for an Exothermic Reaction in an Adiabatic CSTR. In

*Proceedings of 6*(pp. 500-505). Elsevier.^{th}International Conference on Advances in Control and Optimization of Dynamical Systems