Boundary Geometric Control of a Nonlinear Diffusion System with Time‐Dependent Spatial Domain
Boundary Geometric Control of a Nonlinear Diffusion System with Time‐Dependent Spatial Domain
复制标题
时变空间域非线性扩散系统的边界几何控制
DOI：
10.1002/asjc.1248
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发表时间：
2016
影响因子：
2.4
通讯作者：
J. Corriou
中科院分区：
文献类型：
--
作者：
A. Maidi;J. Corriou
Stefan问题表示具有时间依赖空间域的分布参数系统。本文研究了具有Neumann激励的非线性Stefan问题中运动液固界面位置的边界控制问题。其主要思想是通过科尔-霍普夫正切变换导出一个等价的线性模型，即在一定的物理假设下，将原非线性Stefan问题转化为线性问题。然后，几何控制律推导直接从开发，由本文的作者，线性Stefan问题。基于科尔-霍普夫变换是双射的这一事实，证明了所提出的控制律能产生稳定的闭环系统.控制器的性能进行评估，通过数值模拟的不锈钢熔化的情况下，其特征在于温度依赖的导热系数，这是非线性的。其目的是通过控制边界处的热通量来控制液-固界面的位置。
A Stefan problem represents a distributed parameter system with a time‐dependent spatial domain. This paper addresses the boundary control of the position of the moving liquid–solid interface in the case of nonlinear Stefan problem with Neumann actuation. The main idea consists in deriving an equivalent linear model by means of Cole‐Hopf tangent transformation, i.e. under a certain physical assumption, the original nonlinear Stefan problem is converted to a linear one. Then, the geometric control law is deduced directly from that developed, by the authors of the present paper, for the linear Stefan problem. Based on the fact that the Cole‐Hopf transformation is bijective, it is shown that the developed control law yields a stable closed‐loop system. The performance of the controller is evaluated through numerical simulation in the case of stainless steel melting characterized by a temperature‐dependent thermal conductivity, which is nonlinear. The objective is to control the position of the liquid–solid interface by manipulating a heat flux at the boundary.