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A heat equation for freezing processes with phase change: stability analysis and applications

为与阶段变化冻结过程的一个热方程: 稳定性分析和应用

作     者:Backi, C. J. Bendtsen, J. D. Leth, J. Gravdahl, J. T. 

作者机构:Norwegian Univ Sci & Technol Dept Engn Cybernet N-7034 Trondheim Norway Aalborg Univ Dept Elect Syst Aalborg Denmark 

出 版 物:《INTERNATIONAL JOURNAL OF CONTROL》 (国际控制杂志)

年 卷 期:2016年第89卷第4期

页      面:833-849页

核心收录:

学科分类:0711[理学-系统科学] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 0701[理学-数学] 071101[理学-系统理论] 

基  金:Southern Danish Growth Forum European Regional Development Fund Norwegian Research Council as part of the project DANTEQ (Development and assessment of novel technologies improving the fishing operation and on board processing with respect to environmental impact and fish quality) [199447/I10] 

主  题:freezing process observer design Distributed parameter systems stability analysis 

摘      要:In this work, the stability properties as well as possible applications of a partial differential equation (PDE) with state-dependent parameters are investigated. Among other things, the PDE describes freezing of foodstuff, and is closely related to the (potential) Burgers equation. We show that for certain forms of coefficient functions, the PDE converges to a stationary solution given by (fixed) boundary conditions that make physical sense. These boundary conditions are either symmetric or asymmetric of Dirichlet type. Furthermore, we present an observer design based on the PDE model for estimation of inner-domain temperatures in block-frozen fish and for monitoring freezing time. We illustrate the results with numerical simulations.

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