Online Recalibration of the State Estimators for a System With Moving Boundaries Using Sparse Discrete-in-Time Temperature Measurements
Online Recalibration of the State Estimators for a System With Moving Boundaries Using Sparse Discrete-in-Time Temperature Measurements
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DOI：
10.1109/tac.2017.2736950
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发表时间：
2018-04-01
影响因子：
6.8
通讯作者：
Thomas, Brian G.
中科院分区：
文献类型：
--
作者：
Petrus, Bryan;Chen, Zhelin;Thomas, Brian G.
本文考虑了一类含固化材料的过程的估计问题。这些过程具有自然的非线性无限维表示，并且测量仅在铸造机中的特定点处可用，每个点对应于Stefan问题偏微分方程（PDE）数学模型中的单个离散时间边界测量。两个以前的估计的结果进行了总结。第一个估计是基于Stefan问题，使用连续而不是离散的时间边界测量。第二个估计器采用了一个过程模型，比Stefan问题更详细，但没有输出注入，以减少估计误差，除了模型校准。这两个估计框架在当前的文件中扩展到一个更现实的传感设置。首先，估计被认为是使用Stefan问题下的一些简化，但实际上合理的假设在这个过程中的未知数。抛物型偏微分方程的最大值原理证明，在线校准使用一个单一的离散时间温度测量可以提供消除由于模型中的一个未知参数的失配所产生的估计误差。尽管未经证实，但随后在模拟中显示该结果以应用于更详细的过程模型。
In this paper, the problem of estimation is considered for a class of processes involving solidifying materials. These processes have natural nonlinear infinite-dimensional representations, and measurements are only available at particular points in the caster, each corresponding to a single discrete-in-time boundary measurement in the Stefan problem partial differential equation (PDE) mathematical model. The results for two previous estimators are summarized. The first estimator is based on the Stefan problem, using continuous instead of discrete-in-time boundary measurements. The second estimator employs a process model that is more detailed than the Stefan problem, but with no output injection to reduce estimation error, other than model calibration. Both of these estimation frameworks are extended in the current paper to a more realistic sensing setting. First, an estimator is considered that uses the Stefan problem under some simplifying but practically justified assumptions on the unknowns in the process. The maximum principle for parabolic PDEs is employed to prove that online calibration using a single discrete-in-time temperature measurement can provide removal of the estimation error arising due to mismatch of a single unknown parameter in the model. Although unproven, this result is then shown in simulation to apply to the more detailed process model.