Abstract
Machine learning has attracted extensive interest in the process engineering field, due to the capability of modeling complex nonlinear process behavior. This work presents a method for combining neural network models with first-principles models in real-time optimization (RTO) and model predictive control (MPC) and demonstrates the application to two chemical process examples. First, the proposed methodology that integrates a neural network model and a first-principles model in the optimization problems of RTO and MPC is discussed. Then, two chemical process examples are presented. In the first example, a continuous stirred tank reactor (CSTR) with a reversible exothermic reaction is studied. A feed-forward neural network model is used to approximate the nonlinear reaction rate and is combined with a first-principles model in RTO and MPC. An RTO is designed to find the optimal reactor operating condition balancing energy cost and reactant conversion, and an MPC is designed to drive the process to the optimal operating condition. A variation in energy price is introduced to demonstrate that the developed RTO scheme is able to minimize operation cost and yields a closed-loop performance that is very close to the one attained by RTO/MPC using the first-principles model. In the second example, a distillation column is used to demonstrate an industrial application of the use of machine learning to model nonlinearities in RTO. A feed-forward neural network is first built to obtain the phase equilibrium properties and then combined with a first-principles model in RTO, which is designed to maximize the operation profit and calculate optimal set-points for the controllers. A variation in feed concentration is introduced to demonstrate that the developed RTO scheme can increase operation profit for all considered conditions.
Highlights
In the last few decades, chemical processes have been studied and represented with different models for real-time optimization (RTO) and model predictive control (MPC) in order to improve the process steady-state and dynamic performance
A Lyapunov-based model predictive controller (LMPC) is designed to bring the process to the steady-state calculated by the RTO
The RTO of Equation (10) is solved at the beginning of each RTO period to achieve a set of improved set-points, which will be tracked by the MPC of Equation (12)
Summary
In the last few decades, chemical processes have been studied and represented with different models for real-time optimization (RTO) and model predictive control (MPC) in order to improve the process steady-state and dynamic performance. First-principles models are used to represent the well-known part of the process and embedding physical knowledge in the formulation, while the complex nonlinear part of the process is represented with neural networks. This proposed hybrid formulation is applied in the context of real-time optimization and model predictive control in two chemical processes. This work demonstrates the implementation of a hybrid approach of combining a first-principles model and a neural network model in the RTO and MPC optimization problems. The combined model is used in RTO to investigate the performance of the proposed methodology
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