Online recalibration of the state estimators for a system with moving boundaries using sparse discrete-in-time temperature measurements

Petrus, Bryan; Chen, Zhelin; Bentsman, Joseph; Thomas, Brian G.

doi:10.1109/acc.2016.7525301

Cited by 1 publication

(3 citation statements)

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“…Boundary geomertic control has been proposed in Maidi and Corriou (2014), and trajectory tracking control for the Vertical Gradient Freeze crystal growth process has been developed in Ecklebe et al (2019Ecklebe et al ( , 2020. Numerous contributions on the feedback control of the Stefan problem with applications to continuous casting of steels have been achieved by Bentsman and coauthors, see Petrus et al (2010Petrus et al ( , 2012Petrus et al ( , 2014Petrus et al ( , 2017; Chen et al (2018Chen et al ( , 2019Chen et al ( , 2020.…”

Section: Control Of Stefan Systemmentioning

confidence: 99%

“…While the control problem for the Stefan system has been developed as mentioned above, a state estimation for the Stefan system has been focused relatively few. In Petrus et al (2017), an online recalibration method has been proposed for the state estimation of the Stefan problem, where the unknown parameters in the model are calibrated with the discrete-time measurements. In Pernsteiner et al (2021), an state estimation for the latent heat storage system modeled by the Stefan system is developed by the Extended Kalman Filter (EKF) for the reduced-order model of the Stefan system through truncation.…”

Section: State Estimators For Stefan Modelmentioning

confidence: 99%

“…To handle the discrete-time measurements in practice as in Petrus et al (2017), the designed observer should be discretized in time such as Euler or Runge-Kutta methods so that the estimation can be computed at every sampling of the discrete-time measurements. The free parameters λ, c, and ε have their physical units [1/s], [1/s], and [ • C/m], respectively.…”

Section: Observer Structurementioning

confidence: 99%

See 2 more Smart Citations

State Estimation of the Stefan PDE: A Tutorial on Design and Applications to Polar Ice and Batteries

Koga¹,

Krstić²

2021

Preprint

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The Stefan PDE system is a representative model for thermal phase change phenomena, such as melting and solidification, arising in numerous science and engineering processes. The mathematical description is given by a Partial Differential Equation (PDE) of the temperature distribution defined on a spatial interval with a moving boundary, where the boundary represents the liquid-solid interface and its dynamics are governed by an Ordinary Differential Equation (ODE). The PDE-ODE coupling at the boundary is nonlinear and creates a significant challenge for state estimation with provable convergence and robustness.This tutorial article presents a state estimation method based on PDE backstepping for the Stefan system, using measurements only at the moving boundary. PDE backstepping observer design generates an observer gain by employing a Volterra transformation of the observer error state into a desirable target system, solving a Goursat-form PDE for the transformation's kernel, and performing a Lyapunov analysis of the target observer error system.The observer is applied to models of problems motivated by climate change and the need for renewable energy storage: a model of polar ice dynamics and a model of charging and discharging in lithium-ion batteries. The numerical results for polar ice demonstrate a robust performance of the designed estimator with respect to the unmodeled salinity effect in sea ice. The results for an electrochemical PDE model of a lithium-ion battery with a phase transition material show the elimination of more than 15 % error in State-of-Charge estimate within 5 minutes even in the presence of sensor noise.

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