A METHODOLOGY TO OBTAIN ANALYTICAL MODELS THAT REDUCE THE COMPUTATIONAL COMPLEXITY FACED IN REAL TIME IMPLEMENTATION OF NMPC CONTROLLERS

Abstract Model Predictive Control, MPC and NMPC, and real-time optimization, RTO and D-RTO, are known to help plant operability through the mitigation of impacts caused by external disturbances. However, the usage of these tools in industry requires overcoming some challenges, for instance: accurate models of the process, particularly in regard to nonlinearities; suitable computational time for obtaining the solution of large-scale problems and model mismatch between the RTO or D-RTO and NMPC. In this paper, we present a methodology to obtain analytical model predictions based on a Hammerstein structure to represent the process nonlinearities, reducing the computational effort in real-time applications. Unlike most common approaches that transform NMPC internal models, described by differential-algebraic equations (DAE), into an approximate system of nonlinear algebraic (NLA) equations using, for instance, orthogonal collocation, in the proposed approach, the obtained NLA is an exact description of the original DAEs system. The proposed algorithm was applied to a non-isothermal CSTR (continuous stirred tank reactor) integrated with an optimization layer. The results show that the proposed structure presented a significant reduction in computational time without performance loss, when compared with the NMPC using a rigorous model. Moreover, the proposed strategy demonstrated good performance in tracking the targets sent by the optimization layer, without model mismatches between layers.

抽象模型预测控制（MPC）与非线性模型预测控制（NMPC）、实时优化（RTO）与动态实时优化（D-RTO）等工具，通过缓解外部扰动对系统造成的影响，已被证实有助于提升工厂的可操作性。然而，这些工具在工业领域的应用仍面临诸多挑战，例如：对工艺过程的精确建模，尤其是针对非线性特性的建模；求解大规模问题所需的适宜计算时间，以及RTO或D-RTO与NMPC之间的模型不匹配问题。在本研究中，我们提出了一种基于Hammerstein结构来表征工艺非线性并获取分析模型预测的方法，从而降低实时应用中的计算工作量。与大多数将NMPC内部模型，即由微分代数方程（DAE）描述的模型，通过正交配置等方法转化为非线性代数方程（NLA）近似系统的常见方法不同，本方法中获得的NLA是对原始DAE系统的精确描述。所提出的算法被应用于一个非等温的连续搅拌槽反应器（CSTR），该反应器集成了优化层。结果显示，与使用严格模型进行NMPC相比，所提出的结构在计算时间上显著减少，且未损失性能。此外，所提出的策略在追踪优化层发送的目标时表现出良好的性能，且在层间不存在模型不匹配问题。