论文标题
基于SS的MPC和基于ARX的MPC等效性
Equivalence of SS-based MPC and ARX-based MPC
论文作者
论文摘要
MPC中使用的两种面向控制的模型是状态空间（SS）模型和输入输出模型（例如ARX模型）。从建模范式获得时，SS模型具有可解释性，并且ARX模型是黑框但适应性的。本文旨在将可解释性引入ARX模型，从而提出了一种基于第一原则的建模范式，用于获取面向控制的ARX模型，以替代现有数据驱动的ARX识别范式。也就是说，首先通过在有趣的点上线性化基于第一原理的模型，然后通过SS-to-ARX变换将解释性SS模型进行线性化，然后将解释性SS模型转换为等效的ARX模型。本文介绍了基于SS-ARX转换的Cayley-Hamilton，观察者理论和Kalman滤波器的转换，进一步表明，选择ARX模型顺序应取决于过程噪声以实现良好的闭环性能，而不是数据驱动的ARX ARX ARX识别范式中的拟合标准。 AFTI-16 MPC示例用于说明基于SS的MPC和基于ARX的MPC问题的等效性，并研究不同SS-to-ARX转换对噪声的鲁棒性。
Two kinds of control-oriented models used in MPC are the state-space (SS) model and the input-output model (such as the ARX model). The SS model has interpretability when obtained from the modeling paradigm, and the ARX model is black-box but adaptable. This paper aims to introduce interpretability into ARX models, thereby proposing a first-principle-based modeling paradigm for acquiring control-oriented ARX models, as an alternative to the existing data-driven ARX identification paradigm. That is, first to obtain interpretative SS models via linearizing the first-principle-based models at interesting points and then to transform interpretative SS models into their equivalent ARX models via the SS-to-ARX transformations. This paper presents the Cayley-Hamilton, Observer-Theory, and Kalman Filter based SS-to-ARX transformations, further showing that choosing the ARX model order should depend on the process noise to achieve a good closed-loop performance rather than the fitting criteria in data-driven ARX identification paradigm. An AFTI-16 MPC example is used to illustrate the equivalence of SS-based MPC and ARX-based MPC problems and to investigate the robustness of different SS-to-ARX transformations to noise.
